In safety-critical robot planning or control, manually specifying safety constraints or learning them from demonstrations can be challenging. In this article, we propose a certifiable alignment method for a robot to learn a safety constraint in its model predictive control (MPC) policy with human online directional feedback. To our knowledge, it is the first method to learn safety constraints from human feedback. The proposed method is based on an empirical observation: human directional feedback, when available, tends to guide the robot toward safer regions. The method only requires the direction of human feedback to update the learning hypothesis space. It is certifiable, providing an upper bound on the total number of human feedback in the case of successful learning, or declaring the hypothesis misspecification, i.e., the true implicit safety constraint cannot be found within the specified hypothesis space. We evaluated the proposed method using numerical examples and user studies in two simulation games. Additionally, we implemented and tested the proposed method on a real-world Franka robot arm performing mobile water-pouring tasks. The results demonstrate the efficacy and efficiency of our method, showing that it enables a robot to successfully learn safety constraints with a small handful (tens) of human directional corrections.

Operator learning, which aims to approximate maps between infinite-dimensional function spaces, is an important area in scientific machine learning with applications across various physical domains. Here we introduce the Continuous Vision Transformer (CViT), a novel neural operator architecture that leverages advances in computer vision to address challenges in learning complex physical systems. CViT combines a vision transformer encoder, a novel grid-based coordinate embedding, and a query-wise cross-attention mechanism to effectively capture multi-scale dependencies. This design allows for flexible output representations and consistent evaluation at arbitrary resolutions. We demonstrate CViT's effectiveness across a diverse range of partial differential equation (PDE) systems, including fluid dynamics, climate modeling, and reaction-diffusion processes. Our comprehensive experiments show that CViT achieves state-of-the-art performance on multiple benchmarks, often surpassing larger foundation models, even without extensive pretraining and roll-out fine-tuning. Taken together, CViT exhibits robust handling of discontinuous solutions, multi-scale features, and intricate spatio-temporal dynamics. Our contributions can be viewed as a significant step towards adapting advanced computer vision architectures for building more flexible and accurate machine learning models in the physical sciences.

A fundamental question in data-driven decision making is how to quantify the uncertainty of predictions to inform risk-sensitive downstream actions, as often required in domains such as medicine. We develop a decision-theoretic foundation linking prediction sets to risk-averse decision-making, addressing three questions: (1) What is the correct notion of uncertainty quantification for risk-averse decision makers? We prove that prediction sets are optimal for decision makers who wish to optimize their value at risk. (2) What is the optimal policy that a risk averse decision maker should use to map prediction sets to actions? We show that a simple max-min decision policy is optimal for risk-averse decision makers. Finally, (3) How can we derive prediction sets that are optimal for such decision makers? We provide an exact characterization in the population regime and a distribution free finite-sample construction. These insights leads to *Risk-Averse Calibration (RAC)*, a principled algorithm that is both *practical*—exploiting black-box predictions to enhance downstream utility—and *safe*—adhering to user-defined risk thresholds. We experimentally demonstrate RAC's advantages in medical diagnosis and recommendation systems, showing that it substantially improves the trade-off between safety and utility, delivering higher utility than existing methods while avoiding critical errors.

As large language models (LLMs) are becoming more capable and widespread, the study of their failure cases is becoming increasingly important. Recent advances in standardizing, measuring, and scaling test-time compute suggest new methodologies for optimizing models to achieve high performance on hard tasks. In this paper, we apply these advances to the task of model jailbreaking: eliciting harmful responses from aligned LLMs. We develop an adversarial reasoning approach to automatic jailbreaking that leverages a loss signal to guide the test-time compute, achieving SOTA attack success rates against many aligned LLMs, even those that aim to trade inference-time compute for adversarial robustness. Our approach introduces a new paradigm in understanding LLM vulnerabilities, laying the foundation for the development of more robust and trustworthy AI systems.

Flying quadrotors in tight formations is a challenging problem. It is known that in the near-field airflow of a quadrotor, the aerodynamic effects induced by the propellers are complex and difficult to characterize. Although machine learning tools can potentially be used to derive models that capture these effects, these data-driven approaches can be sample inefficient and the resulting models often do not generalize as well as their first-principles counterparts. In this work, we propose a framework that combines the benefits of first-principles modeling and data-driven approaches to construct an accurate and sample efficient representation of the complex aerodynamic effects resulting from quadrotors flying in formation. The data-driven component within our model is lightweight, making it amenable for optimization-based control design. Through simulations and physical experiments, we show that incorporating the model into a novel learning-based nonlinear model predictive control (MPC) framework results in substantial performance improvements in terms of trajectory tracking and disturbance rejection. In particular, our framework significantly outperforms nominal MPC in physical experiments, achieving a 40.1% improvement in the average trajectory tracking errors and a 57.5% reduction in the maximum vertical separation errors. Our framework also achieves exceptional sample efficiency, using only a total of 46 seconds of flight data for training across both simulations and physical experiments. Furthermore, with our proposed framework, the quadrotors achieve an exceptionally tight formation, flying with an average separation of less than 1.5 body lengths throughout the flight.

As robots become increasingly capable, users will want to describe high-level missions and have robots infer the relevant details. Because pre-built maps are difficult to obtain in many realistic settings, accomplishing such missions will require the robot to map and plan online. While many semantic planning methods operate online, they are typically designed for well specified missions such as object search or exploration. Recently, Large Language Models (LLMs) have demonstrated powerful contextual reasoning abilities over a range of robotic tasks described in natural language. However, existing LLM-enabled planners typically do not consider online planning or complex missions; rather, relevant subtasks and semantics are provided by a pre-built map or a user. We address these limitations via SPINE, an online planner for missions with incomplete mission specifications provided in natural language. The planner uses an LLM to reason about subtasks implied by the mission specification and then realizes these subtasks in a receding horizon framework. Tasks are automatically validated for safety and refined online with new map observations. We evaluate SPINE in simulation and real-world settings with missions that require multiple steps of semantic reasoning and exploration in cluttered outdoor environments of over 20,000m2. Compared to baselines that use existing LLM-enabled planning approaches, our method is over twice as efficient in terms of time and distance, requires less user interactions, and does not require a full map. Additional resources are provided at https://zacravichandran.github.io/SPINE.

The recent introduction of large language models (LLMs) has revolutionized the field of robotics by enabling contextual reasoning and intuitive human-robot interaction in domains as varied as manipulation, locomotion, and self-driving vehicles. When viewed as a stand-alone technology, LLMs are known to be vulnerable to jailbreaking attacks, wherein mali-cious prompters elicit harmful text by bypassing LLM safety guardrails. To assess the risks of deploying LLMs in robotics, in this paper, we introduce ROBOPAIR, the first algorithm designed to jailbreak LLM-controlled robots. Unlike existing, textual attacks on LLM chatbots, Robopairelicits harmful physical actions from LLM-controlled robots, a phenomenon we experimentally demonstrate in three scenarios: (i) a white-box setting, wherein the attacker has full access to the NVID IA Dolphins self-driving LLM, (ii) a gray-box setting, wherein the attacker has partial access to a Clearpath Robotics Jackal UGV robot equipped with a GPT-40 planner, and (iii) a black-box setting, wherein the attacker has only query access to the GPT-3.5-integrated Unitree Robotics Go2robot dog. In each scenario and across three new datasets of harmful robotic actions, we demonstrate that ROBOPAIR, as well as several static baselines, finds jailbreaks quickly and effectively, often achieving 100 % attack success rates. Our results reveal, for the first time, that the risks of jailbroken LLMs extend far beyond text generation, given the distinct possibility that jailbroken robots could cause physical damage in the real world. Indeed, our results on the U nitree G02represent the first successful jailbreak of a deployed commercial robotic system. Addressing this emerging vulnerability is critical for ensuring the safe deployment of LLMs in robotics. Additional media is available at: https://robopair.org.

With multi-agent systems increasingly deployed autonomously at scale in complex environments, ensuring safety of the data-driven policies is critical. Control Barrier Functions have emerged as an effective tool for enforcing safety constraints, yet existing learning-based methods often lack in scalability, generalization and sampling efficiency as they overlook inherent geometric structures of the system. To address this gap, we introduce symmetries-infused distributed CBFs, enforcing the satisfaction of intrinsic symmetries on learnable graph-based safety certificates. We theoretically motivate the need for equivariant parametrization of CBFs and policies, and propose a simple, yet efficient and adaptable methodology for constructing such equivariant group-modular networks via the compatible group actions. This approach encodes safety constraints in a distributed data-efficient manner, enabling zero-shot generalization to larger and denser swarms. Through extensive simulations on multi-robot navigation tasks, we demonstrate that our method outperforms state-of-the-art baselines in terms of safety, scalability, and task success rates, highlighting the importance of embedding symmetries in safe distributed neural policies.

We consider the problem of conformal prediction under covariate shift. Given labeled data from a source domain and unlabeled data from a covariate shifted target domain, we seek to construct prediction sets with valid marginal coverage in the target domain. Most existing methods require estimating the unknown likelihood ratio function, which can be prohibitive for high-dimensional data such as images. To address this challenge, we introduce the likelihood ratio regularized quantile regression (LR-QR) algorithm, which combines the pinball loss with a novel choice of regularization in order to construct a threshold function without directly estimating the unknown likelihood ratio. We show that the LR-QR method has coverage at the desired level in the target domain, up to a small error term that we can control. Our proofs draw on a novel analysis of coverage via stability bounds from learning theory. Our experiments demonstrate that the LR-QR algorithm outperforms existing methods on high-dimensional prediction tasks, including a regression task for the Communities and Crime dataset, an image classification task from the WILDS repository, and an LLM question-answering task on the MMLU benchmark.

Uncertainty quantification (UQ) is essential for safe deployment of generative AI models such as large language models (LLMs), especially in high-stakes applications. Conformal prediction (CP) offers a principled uncertainty quantification framework, but classical methods focus on regression and classification, relying on geometric distances or softmax scores--tools that presuppose structured outputs. We depart from this paradigm by studying CP in a query-only setting, where prediction sets must be constructed solely from finite queries to a black-box generative model, introducing a new trade-off between coverage, test-time query budget, and informativeness. We introduce **Conformal Prediction with Query Oracle** (CPQ), a framework characterizing the optimal interplay between these objectives. Our finite-sample algorithm is built on two core principles: one governs the optimal query policy, and the other defines the optimal mapping from queried samples to prediction sets. Remarkably, both are rooted in the classical **missing mass problem** in statistics. Specifically, the optimal query policy depends on the rate of decay--or the derivative--of the missing mass, for which we develop a novel estimator. Meanwhile, the optimal mapping hinges on the missing mass itself, which we estimate using Good-Turing estimators. We then turn our focus to implementing our method for language models, particularly in open-ended LLM tasks involving question answering, multi-step reasoning, and structured information extraction, where outputs are vast, variable, and often under-specified. Fine-grained experiments on three real-world open-ended tasks and two LLMs, show CPQ's applicability to **any black-box LLM** and highlight: (1) individual contribution of each principle to CPQ’s performance, and (2) CPQ's ability to yield significantly more informative prediction sets than existing conformal methods for language uncertainty quantification.

We introduce a novel conformal prediction framework for constructing conformal prediction bands with high probability around biomarker trajectories observed at subject-specific, randomly-timed follow-up visits. Existing conformal methods typically assume fixed time grids, limiting their applicability in longitudinal clinical studies. Our approach addresses this limitation by defining a time-varying nonconformity score that normalizes prediction errors using model-derived uncertainty estimates, enabling conformal inference at arbitrary time points. We evaluate our method on two well-established brain biomarkers—hippocampal and ventricular volume—using a range of standard and state-of-the-art predictors. Across models, our conformalized predictors consistently achieve nominal coverage with tighter prediction intervals compared to baseline uncertainty estimates. To further account for population heterogeneity, we develop group-conditional conformal bands with formal coverage guarantees across clinically relevant and high-risk subgroups. Finally, we demonstrate the clinical utility of our approach in identifying subjects at risk of progression to Alzheimer’s disease. We introduce an uncertainty-aware progression metric based on the lower conformal bound and show that it enables the identification of 17.5\% more high-risk subjects compared to standard slope-based methods, highlighting the value of uncertainty calibration in real-world clinical decision making. We make the code available at \href{https://github.com/vatass/ConformalBiomarkerTrajectories}{\texttt{github.com/vatass/ConformalBiomarkerTrajectories}}.

Conformal prediction is a statistical tool for producing prediction regions of machine learning models that are valid with high probability. However, applying conformal prediction to time series data leads to conservative prediction regions. In fact, to obtain prediction regions over T time steps with confidence 1--delta, previous works require that each individual prediction region is valid with confidence 1--delta/T. We propose an optimization-based method for reducing this conservatism to enable long horizon planning and verification when using learning-enabled time series predictors. Instead of considering prediction errors individually at each time step, we consider a parameterized prediction error over multiple time steps. By optimizing the parameters over an additional dataset, we find prediction regions that are not conservative. We show that this problem can be cast as a mixed integer linear complementarity program (MILCP), which we then relax into a linear complementarity program (LCP). Additionally, we prove that the relaxed LP has the same optimal cost as the original MILCP. Finally, we demonstrate the efficacy of our method on case studies using pedestrian trajectory predictors and F16 fighter jet altitude predictors.

Motivated by applications in large-scale and multi-agent reinforcement learning, we study the non-asymptotic performance of stochastic approximation (SA) schemes with delayed updates under Markovian sampling. While the effect of delays has been extensively studied for optimization, the manner in which they interact with the underlying Markov process to shape the finite-time performance of SA remains poorly understood. In this context, our first main contribution is to show that under time-varying bounded delays, the delayed SA update rule guarantees exponentially fast convergence of the \emph{last iterate} to a ball around the SA operator’s fixed point. Notably, our bound is \emph{tight} in its dependence on both the maximum delay $\tau_{max}$, and the mixing time $\tau_{mix}$. To achieve this tight bound, we develop a novel inductive proof technique that, unlike various existing delayed-optimization analyses, relies on establishing uniform boundedness of the iterates. As such, our proof may be of independent interest. Next, to mitigate the impact of the maximum delay on the convergence rate, we provide the first finite-time analysis of a delay-adaptive SA scheme under Markovian sampling. In particular, we show that the exponent of convergence of this scheme gets scaled down by $\tau_{avg}$, as opposed to $\tau_{max}$ for the vanilla delayed SA rule; here, $\tau_{avg}$ denotes the average delay across all iterations. Moreover, the adaptive scheme requires no prior knowledge of the delay sequence for step-size tuning. Our theoretical findings shed light on the finite-time effects of delays for a broad class of algorithms, including TD learning, Q-learning, and stochastic gradient descent under Markovian sampling.

One prominent approach toward resolving the adversarial vulnerability of deep neural networks is the two-player zero-sum paradigm of adversarial training, in which predictors are trained against adversarially chosen perturbations of data. Despite the promise of this approach, algorithms based on this paradigm have not engendered sufficient levels of robustness and suffer from pathological behavior like robust overfitting. To understand this shortcoming, we first show that the commonly used surrogate-based relaxation used in adversarial training algorithms voids all guarantees on the robustness of trained classifiers. The identification of this pitfall informs a novel non-zero-sum bilevel formulation of adversarial training, wherein each player optimizes a different objective function. Our formulation yields a simple algorithmic framework that matches and in some cases outperforms state-of-the-art attacks, attains comparable levels of robustness to standard adversarial training algorithms, and does not suffer from robust overfitting.

In this paper, we focus on the problem of conformal prediction with conditional guarantees. Prior work has shown that it is impossible to construct nontrivial prediction sets with full conditional coverage guarantees. A wealth of research has considered relaxations of full conditional guarantees, relying on some *predefined* uncertainty structures. Departing from this line of thinking, we propose Partition Learning Conformal Prediction (PLCP), a framework to improve conditional validity of prediction sets through *learning* uncertainty-guided features from the calibration data. We implement PLCP efficiently with alternating gradient descent, utilizing off-the-shelf machine learning models. We further analyze PLCP theoretically and provide conditional guarantees for infinite and finite sample sizes. Finally, our experimental results over four real-world and synthetic datasets show the superior performance of PLCP compared to state-of-the-art methods in terms of coverage and length in both classification and regression scenarios.

A driving force behind the diverse applicability of modern machine learning is the ability to extract meaningful features across many sources. However, many practical domains involve data that are non-identically distributed across sources, and possibly statistically dependent within its source, violating vital assumptions in existing theoretical studies of representation learning. Toward addressing these issues, we establish statistical guarantees for learning general *nonlinear* representations from multiple data sources that admit different input distributions and possibly dependent data. Specifically, we study the sample-complexity of learning $T+1$ functions $f_\star^{(t)} \circ g_\star$ from a function class $\mathcal{F} \times \mathcal{G}$, where $f_\star^{(t)}$ are task specific linear functions and $g_\star$ is a shared non-linear representation. An approximate representation $\hat g$ is estimated using $N$ samples from each of $T$ source tasks, and a fine-tuning function $\hat f^{(0)}$ is fit using $N'$ samples from a target task passed through $\hat g$. Our results show that the excess risk of the estimate $\hat f^{(0)} \circ \hat g$ on the target task decays as $\tilde{\mathcal{O}}\Big(\frac{\mathrm{C}(\mathcal{G})}{N T} + \frac{\text{dim}(\mathcal{F})}{N'}\Big)$, where $\mathrm{C}(\mathcal{G})$ denotes the complexity of $\mathcal{G}$. Notably, our rates match that of the iid setting, while requiring fewer samples per task than prior analysis and admitting *no dependence on the mixing time*. We support our analysis with numerical experiments performing imitation learning over non-linear dynamical systems.

In this work, we study statistical learning with dependent data and square loss in a hypothesis class with tail decay in Orlicz space: $\mathscr{F}\subset L_{\Psi_p}$. Our inquiry is motivated by the search for a sharp noise interaction term, or variance proxy, in learning with dependent (e.g. $\beta$-mixing) data. Typical non-asymptotic results exhibit variance proxies that are deflated multiplicatively in the mixing time of the underlying covariates process. We show that whenever the topologies of $L^2$ and $\Psi_p$ are comparable on our hypothesis class $\mathscr{F}$, the empirical risk minimizer achieves a rate that only depends on the complexity of the class and second order statistics in its leading term. We refer to this as a near mixing-free rate, since direct dependence on mixing is relegated to an additive higher order term. Our approach, reliant on mixed tail generic chaining, allows us to obtain sharp, instance-optimal rates. Examples that satisfy our framework include for instance sub-Gaussian linear regression and bounded smoothness classes.

Recent advances in metric, semantic, and topological mapping have equipped autonomous robots with concept grounding capabilities to interpret natural language tasks. Leveraging these capabilities, this work develops an efficient task planning algorithm for hierarchical metric-semantic models. We consider a scene graph model of the environment and utilize a large language model (LLM) to convert a natural language task into a linear temporal logic (LTL) automaton. Our main contribution is to enable optimal hierarchical LTL planning with LLM guidance over scene graphs. To achieve efficiency, we construct a hierarchical planning domain that captures the attributes and connectivity of the scene graph and the task automaton, and provide semantic guidance via an LLM heuristic function. To guarantee optimality, we design an LTL heuristic function that is provably consistent and supplements the potentially inadmissible LLM guidance in multi-heuristic planning. We demonstrate efficient planning of complex natural language tasks in scene graphs of virtualized real environments.

Jailbreak attacks cause large language models (LLMs) to generate harmful, unethical, or otherwise objectionable content. Evaluating these attacks presents a number of challenges, which the current collection of benchmarks and evaluation techniques do not adequately address. First, there is no clear standard of practice regarding jailbreaking evaluation. Second, existing works compute costs and success rates in incomparable ways. And third, numerous works are not reproducible, as they withhold adversarial prompts, involve closed-source code, or rely on evolving proprietary APIs. To address these challenges, we introduce JailbreakBench, an open-sourced benchmark with the following components: (1) an evolving repository of state-of-the-art adversarial prompts, which we refer to as jailbreak artifacts; (2) a jailbreaking dataset comprising 100 behaviors---both original and sourced from prior work---which align with OpenAI's usage policies; (3) a standardized evaluation framework at https://github.com/JailbreakBench/jailbreakbench that includes a clearly defined threat model, system prompts, chat templates, and scoring functions; and (4) a leaderboard at https://jailbreakbench.github.io/ that tracks the performance of attacks and defenses for various LLMs. We have carefully considered the potential ethical implications of releasing this benchmark, and believe that it will be a net positive for the community.

Conditional validity and length efficiency are two crucial aspects of conformal prediction (CP). Conditional validity ensures accurate uncertainty quantification for data subpopulations, while proper length efficiency ensures that the prediction sets remain informative. Despite significant efforts to address each of these issues individually, a principled framework that reconciles these two objectives has been missing in the CP literature. In this paper, we develop Conformal Prediction with Length-Optimization (CPL) - a novel and practical framework that constructs prediction sets with (near-) optimal length while ensuring conditional validity under various classes of covariate shifts, including the key cases of marginal and group-conditional coverage. In the infinite sample regime, we provide strong duality results which indicate that CPL achieves conditional validity and length optimality. In the finite sample regime, we show that CPL constructs conditionally valid prediction sets. Our extensive empirical evaluations demonstrate the superior prediction set size performance of CPL compared to state-of-the-art methods across diverse real-world and synthetic datasets in classification, regression, and large language model-based multiple choice question answering. An Implementation of our algorithm can be accessed at the following link: https://github.com/shayankiyani98/CP.

Unsupervised learning with functional data is an emerging paradigm of machine learning research with applications to computer vision, climate modeling and physical systems. A natural way of modeling functional data is by learning operators between infinite dimensional spaces, leading to discretization invariant representations that scale independently of the sample grid resolution. Here we present Variational Autoencoding Neural Operators (VANO), a general strategy for making a large class of operator learning architectures act as variational autoencoders. For this purpose, we provide a novel rigorous mathematical formulation of the variational objective in function spaces for training. VANO first maps an input function to a distribution over a latent space using a parametric encoder and then decodes a sample from the latent distribution to reconstruct the input, as in classic variational autoencoders. We test VANO with different model set-ups and architecture choices for a variety of benchmarks. We start from a simple Gaussian random field where we can analytically track what the model learns and progressively transition to more challenging benchmarks including modeling phase separation in Cahn-Hilliard systems and real world satellite data for measuring Earth surface deformation.

This paper addresses a new semantic multi-robot planning problem in uncertain and dynamic environments. Particularly, the environment is occupied with mobile and uncertain semantic targets. These targets are governed by stochastic dynamics while their current and future positions as well as their semantic labels are uncertain. Our goal is to control mobile sensing robots so that they can accomplish collaborative semantic tasks defined over the uncertain current/future positions and semantic labels of these targets. We express these tasks using Linear Temporal Logic (LTL). We propose a sampling-based approach that explores the robot motion space, the mission specification space, as well as the future configurations of the semantic targets to design optimal paths. These paths are revised online to adapt to uncertain perceptual feedback. To the best of our knowledge, this is the first work that addresses semantic mission planning problems in uncertain and dynamic semantic environments. We provide extensive experiments that demonstrate the efficiency of the proposed method.

We investigate and develop algorithms for social fairness in coverage control problems. Existing coverage control methods are efficient, optimizing the average expected distance from any event to the nearest robot. However, in societal applications like disaster response or transportation, these conventional objectives lead to disparate coverage costs with respect to different groups within a population. We formulate social fairness for coverage control as the minimization of the maximum coverage cost among a set of groups within a population. Our approach uses Voronoi iteration to solve this novel problem by approximating the non-differentiable objective with the log-sum-exp and defining a gradient based controller that prioritizes fairness while also optimizing average performance when disparities between groups are low. We show convergence properties of this proposed control law and demonstrate the approach in simulations of randomly generated population densities as well as environments generated from U.S. census data on population rates and demographics. Our approach provides greater fairness than existing methods while maintaining similar computational time and convergence properties.

This paper addresses the Multi-Robot Active In-formation Acquisition (AIA) problem, where a team of mobile robots, communicating through an underlying graph, estimates a hidden state expressing a phenomenon of interest. Applications like target tracking, coverage and SLAM can be expressed in this framework. Existing approaches, though, are either not scalable, unable to handle dynamic phenomena or not robust to changes in the communication graph. To counter these shortcomings, we propose an Information-aware Graph Block Network (I-GBNet), an AIA adaptation of Graph Neural Networks, that aggregates information over the graph represen-tation and provides sequential-decision making in a distributed manner. The I-GBNet, trained via imitation learning with a centralized sampling-based expert solver, exhibits permutation equivariance and time invariance, while harnessing the superior scalability, robustness and generalizability to previously unseen environments and robot configurations. Numerical simulations on significantly larger graphs and dimensionality of the hidden state and more complex environments than those seen in training validate the properties of the proposed architecture and its efficacy in the application of localization and tracking of dynamic targets.

The recent increase in data availability and reliability has led to a surge in the development of learning-based model predictive control (MPC) frameworks for robot systems. Despite attaining substantial performance improvements over their non-learning counterparts, many of these frameworks rely on an offline learning procedure to synthesize a dynamics model. This implies that uncertainties encountered by the robot during deployment are not accounted for in the learning process. On the other hand, learning-based MPC methods that learn dynamics models online are computationally expensive and often require a significant amount of data. To alleviate these shortcomings, we propose a novel learning-enhanced MPC framework that incorporates components from C1adaptive control into learning-based MPC. This integration enables the accurate compensation of both matched and unmatched uncertainties in a sample-efficient way, enhancing the control performance during deployment. In our proposed framework, we present two variants and apply them to the control of a quadrotor system. Through simulations and physical experiments, we demonstrate that the proposed framework not only allows the synthesis of an accurate dynamics model on-the-fly, but also significantly improves the closed-loop control performance under a wide range of spatio-temporal uncertainties.

This paper addresses the problem of active collaborative localization in heterogeneous robot teams with unknown data association. It involves positioning a small number of identical unmanned ground vehicles (UGVs) at desired positions so that an unmanned aerial vehicle (UAV) can, through unlabelled measurements of UGVs, uniquely determine its global pose. We model the problem as a sequential two player game, in which the first player positions the UGVs and the second identifies the two distinct hypothetical poses of the UAV at which the sets of measurements to the UGVs differ by as little as possible. We solve the underlying problem from the vantage point of the first player for a subclass of measurement models using a mixture of local optimization and exhaustive search procedures. Real-world experiments with a team of UAV and UGVs show that our method can achieve centimeter-level global localization accuracy. We also show that our method consistently outperforms random positioning of UGVs by a large margin, with as much as a 90% reduction in position and angular estimation error. Our method can tolerate a significant amount of random as well as non-stochastic measurement noise. This indicates its potential for reliable state estimation on board size, weight, and power (SWaP) constrained UAVs. This work enables robust localization in perceptually-challenged GPS-denied environments, thus paving the road for large-scale multi-robot navigation and mapping.

We derive upper bounds for random design linear regression with dependent ($\beta$-mixing) data absent any realizability assumptions. In contrast to the strictly realizable martingale noise regime, no sharp \emph{instance-optimal} non-asymptotics are available in the literature. Up to constant factors, our analysis correctly recovers the variance term predicted by the Central Limit Theorem---the noise level of the problem---and thus exhibits graceful degradation as we introduce misspecification. Past a burn-in, our result is sharp in the moderate deviations regime, and in particular does not inflate the leading order term by mixing time factors.

The wide availability of data coupled with the computational advances in artificial intelligence and machine learning promise to enable many future technologies such as autonomous driving. While there has been a variety of successful demonstrations of these technologies, critical system failures have repeatedly been reported. Even if rare, such system failures pose a serious barrier to adoption without a rigorous risk assessment. This article presents a framework for the systematic and rigorous risk verification of systems. We consider a wide range of system specifications formulated in signal temporal logic (STL) and model the system as a stochastic process, permitting discrete-time and continuous-time stochastic processes. We then define the STL robustness risk as the risk of lacking robustness against failure . This definition is motivated as system failures are often caused by missing robustness to modeling errors, system disturbances, and distribution shifts in the underlying data generating process. Within the definition, we permit general classes of risk measures and focus on tail risk measures such as the value-at-risk and the conditional value-at-risk. While the STL robustness risk is in general hard to compute, we propose the approximate STL robustness risk as a more tractable notion that upper bounds the STL robustness risk. We show how the approximate STL robustness risk can accurately be estimated from system trajectory data. For discrete-time stochastic processes, we show under which conditions the approximate STL robustness risk can even be computed exactly. We illustrate our verification algorithm in the autonomous driving simulator CARLA and show how a least risky controller can be selected among four neural network lane-keeping controllers for five meaningful system specifications.

We study the temporal robustness of temporal logic specifications and show how to design temporally robust control laws for time-critical control systems. This topic is of particular interest in connected systems and interleaving processes such as multi-robot and human-robot systems where uncertainty in the behavior of individual agents and humans can induce timing uncertainty. Despite the importance of time-critical systems, temporal robustness of temporal logic specifications has not been studied, especially from a control design point of view. We define synchronous and asynchronous temporal robustness and show that these notions quantify the robustness with respect to synchronous and asynchronous time shifts in the predicates of the temporal logic specification. It is further shown that the synchronous temporal robustness upper bounds the asynchronous temporal robustness. We then study the control design problem in which we aim to design a control law that maximizes the temporal robustness of a dynamical system. Our solution consists of a Mixed-Integer Linear Programming (MILP) encoding that can be used to obtain a sequence of optimal control inputs. While asynchronous temporal robustness is arguably more nuanced than synchronous temporal robustness, we show that control design using synchronous temporal robustness is computationally more efficient. This tradeoff can be exploited by the designer depending on the particular application at hand. We conclude the article with a variety of case studies.

With the rapid development of cities, heterogeneous urban cyber-physical systems are designed to improve citizens’ experience, e.g., navigation and delivery service. However, the integration of services is not designed for disruptive events, an oversight that has rippling effects on service quality. For example, urban transportation systems consist of multiple transport modes that have complementary characteristics of capacities, speeds, and costs, facilitating smooth passenger transfers by planned schedules. Such integration may experience significantly increased delays during disruptions. Current solutions rely on a substitute service to transport passengers from and to affected areas using ad-hoc schedules and static routes, which are inefficient and do not utilize mobility patterns of mobile systems, e.g., dynamic passenger demand. To coordinate heterogeneous transportation systems under disruptions, we design a service to automatically select and integrate part of three systems (subway, bus, and taxi) using systems’ mobility patterns, e.g., predicted supply and demand. The service is presented in a normal version, eRoute, considering both subway and bus, and in a version taking taxis into account, called enhanced eRoute. We implement and evaluate eRoute with datasets including subway, bus and taxi, and a fare collection system. The data-driven evaluation results show that eRoute improves the ratio of served passengers per time interval by up to 11.5 times and reduces the average traveling time by up to 82.1 percent compared with existing solutions.

This article considers the problem of safely coordinating a team of sensor-equipped robots to reduce uncertainty about a dynamical process, where the objective tradeoffs information gain and energy cost. Optimizing this tradeoff is desirable, but leads to a nonmonotone objective function in the set of robot trajectories. Therefore, common multirobot planners based on coordinate descent lose their performance guarantees. Furthermore, methods that handle nonmonotonicity lose their performance guarantees when subject to interrobot collision avoidance constraints. As it is desirable to retain both theperformance guaranteeandsafety guarantee, this work proposes a hierarchical approach with a distributed planner that uses local search with a worst-case performance guarantees and a decentralized controller based on control barrier functions that ensures safety and encourages timely arrival at sensing locations. Via extensive simulations, hardware-in-the-loop tests, and hardware experiments, we demonstrate that the proposed approach achieves a better tradeoff between sensing and energy cost than coordinate-descent-based algorithms.

In this paper, we study the statistical difficulty of learning to control linear systems. We focus on two standard benchmarks, the sample complexity of stabilization, and the regret of the online learning of the Linear Quadratic Regulator (LQR). Prior results state that the statistical difficulty for both benchmarks scales polynomially with the system state dimension up to system-theoretic quantities. However, this does not reveal the whole picture. By utilizing minimax lower bounds for both benchmarks, we prove that there exist non-trivial classes of systems for which learning complexity scales dramatically, i.e. exponentially, with the system dimension. This situation arises in the case of underactuated systems, i.e. systems with fewer inputs than states. Such systems are structurally difficult to control and their system theoretic quantities can scale exponentially with the system dimension dominating learning complexity. Under some additional structural assumptions (bounding systems away from uncontrollability), we provide qualitatively matching upper bounds. We prove that learning complexity can be at most exponential with the controllability index of the system, that is the degree of underactuation.

We study the temporal robustness of stochastic signals. This topic is of particular interest in interleaving processes such as multi-agent systems where communication and individual agents induce timing uncertainty. For a deterministic signal and a given specification, we first introduce the synchronous and the asynchronous temporal robustness to quantify the signal’s robustness with respect to synchronous and asynchronous time shifts in its sub-signals. We then define the temporal robustness risk by investigating the temporal robustness of the realizations of a stochastic signal. This definition can be interpreted as the risk associated with a stochastic signal to not satisfy a specification robustly in time. In this definition, general forms of specifications such as signal temporal logic specifications are permitted. We show how the temporal robustness risk is estimated from data for the value-at-risk. The usefulness of the temporal robustness risk is underlined by both theoretical and empirical evidence. In particular, we provide various numerical case studies including a T-intersection scenario in autonomous driving.

Many of the successes of machine learning are based on minimizing an averaged loss function. However, it is well-known that this paradigm suffers from robustness issues that hinder its applicability in safety-critical domains. These issues are often addressed by training against worst-case perturbations of data, a technique known as adversarial training. Although empirically effective, adversarial training can be overly conservative, leading to unfavorable trade-offs between nominal performance and robustness. To this end, in this paper we propose a framework called probabilistic robustness that bridges the gap between the accurate, yet brittle average case and the robust, yet conservative worst case by enforcing robustness to most rather than to all perturbations. From a theoretical point of view, this framework overcomes the trade-offs between the performance and the sample-complexity of worst-case and average-case learning. From a practical point of view, we propose a novel algorithm based on risk-aware optimization that effectively balances average- and worst-case performance at a considerably lower computational cost relative to adversarial training. Our results on MNIST, CIFAR-10, and SVHN illustrate the advantages of this framework on the spectrum from average- to worst-case robustness. Our code is available at: https://github.com/arobey1/advbench.

In this paper we address mobile manipulation planning problems in the presence of sensing and environmental uncertainty. In particular, we consider mobile sensing manipulators operating in environments with unknown geometry and uncertain movable objects, while being responsible for accomplishing tasks requiring grasping and releasing objects in a logical fashion. Existing algorithms either do not scale well or neglect sensing and/or environmental uncertainty. To face these challenges, we propose a hybrid control architecture, where a symbolic controller generates high-level manipulation commands (e.g., grasp an object) based on environmental feedback, an informative planner designs paths to actively decrease the uncertainty of objects of interest, and a continuous reactive controller tracks the sparse waypoints comprising the informative paths while avoiding a priori unknown obstacles. The overall architecture can handle environmental and sensing uncertainty online, as the robot explores its workspace. Using numerical simulations, we show that the proposed architecture can handle tasks of increased complexity while responding to unanticipated adverse configurations.

In this paper, we present an online adaptive planning strategy for a team of robots with heterogeneous sensors to sample from a latent spatial field using a learned model for decision making. Current robotic sampling methods seek to gather information about an observable spatial field. However, many applications, such as environmental monitoring and precision agriculture, involve phenomena that are not directly observable or are costly to measure, called latent phenomena. In our approach, we seek to reason about the latent phenomenon in real-time by effectively sampling the observable spatial fields using a team of robots with heterogeneous sensors, where each robot has a distinct sensor to measure a different observable field. The information gain is estimated using a learned model that maps from the observable spatial fields to the latent phenomenon. This model captures aleatoric uncertainty in the relationship to allow for information theoretic measures. Additionally, we explicitly consider the correlations among the observable spatial fields, capturing the relationship between sensor types whose observations are not independent. We show it is possible to learn these correlations, and investigate the impact of the learned correlation models on the performance of our sampling approach. Through our qualitative and quantitative results, we illustrate that empirically learned correlations improve the overall sampling efficiency of the team. We simulate our approach using a data set of sensor measurements collected on Lac Hertel, in Quebec, which we make publicly available.

Domain generalization (DG) seeks predictors which perform well on unseen test distributions by leveraging data drawn from multiple related training distributions or domains. To achieve this, DG is commonly formulated as an average- or worst-case problem over the set of possible domains. However, predictors that perform well on average lack robustness while predictors that perform well in the worst case tend to be overly-conservative. To address this, we propose a new probabilistic framework for DG where the goal is to learn predictors that perform well with high probability. Our key idea is that distribution shifts seen during training should inform us of probable shifts at test time, which we realize by explicitly relating training and test domains as draws from the same underlying meta-distribution. To achieve probable DG, we propose a new optimization problem called Quantile Risk Minimization (QRM). By minimizing the $\alpha$-quantile of predictor's risk distribution over domains, QRM seeks predictors that perform well with probability $\alpha$. To solve QRM in practice, we propose the Empirical QRM (EQRM) algorithm and provide: (i) a generalization bound for EQRM; and (ii) the conditions under which EQRM recovers the causal predictor as $\alpha \to 1$. In our experiments, we introduce a more holistic quantile-focused evaluation protocol for DG, and demonstrate that EQRM outperforms state-of-the-art baselines on datasets from WILDS and DomainBed.

We consider a linear stochastic bandit problem involving $M$ agents that can collaborate via a central server to minimize regret. A fraction $\alpha$ of these agents are adversarial and can act arbitrarily, leading to the following tension: while collaboration can potentially reduce regret, it can also disrupt the process of learning due to adversaries. In this work, we provide a fundamental understanding of this tension by designing new algorithms that balance the exploration-exploitation trade-off via carefully constructed robust confidence intervals. We also complement our algorithms with tight analyses. First, we develop a robust collaborative phased elimination algorithm that achieves $\tilde{O}\left(\alpha+ 1/\sqrt{M}\right) \sqrt{dT}$ regret for each good agent; here, $d$ is the model-dimension and $T$ is the horizon. For small $\alpha$, our result thus reveals a clear benefit of collaboration despite adversaries. Using an information-theoretic argument, we then prove a matching lower bound, thereby providing the first set of tight, near-optimal regret bounds for collaborative linear bandits with adversaries. Furthermore, by leveraging recent advances in high-dimensional robust statistics, we significantly extend our algorithmic ideas and results to (i) the generalized linear bandit model that allows for non-linear observation maps; and (ii) the contextual bandit setting that allows for time-varying feature vectors.

Supervised learning in function spaces is an emerging area of machine learning research with applications to the prediction of complex physical systems such as fluid flows, solid mechanics, and climate modeling. By directly learning maps (operators) between infinite dimensional function spaces, these models are able to learn discretization invariant representations of target functions. A common approach is to represent such target functions as linear combinations of basis elements learned from data. However, there are simple scenarios where, even though the target functions form a low dimensional submanifold, a very large number of basis elements is needed for an accurate linear representation. Here we present NOMAD, a novel operator learning framework with a nonlinear decoder map capable of learning finite dimensional representations of nonlinear submanifolds in function spaces. We show this method is able to accurately learn low dimensional representations of solution manifolds to partial differential equations while outperforming linear models of larger size. Additionally, we compare to state-of-the-art operator learning methods on a complex fluid dynamics benchmark and achieve competitive performance with a significantly smaller model size and training cost.

Supervised operator learning is an emerging machine learning paradigm with applications to modeling the evolution of spatio-temporal dynamical systems and approximating general black-box relationships between functional data. We propose a novel operator learning method, LOCA (Learning Operators with Coupled Attention), motivated from the recent success of the attention mechanism. In our architecture, the input functions are mapped to a finite set of features which are then averaged with attention weights that depend on the output query locations. By coupling these attention weights together with an integral transform, LOCA is able to explicitly learn correlations in the target output functions, enabling us to approximate nonlinear operators even when the number of output function measurements in the training set is very small. Our formulation is accompanied by rigorous approximation theoretic guarantees on the universal expressiveness of the proposed model. Empirically, we evaluate the performance of LOCA on several operator learning scenarios involving systems governed by ordinary and partial differential equations, as well as a black-box climate prediction problem. Through these scenarios we demonstrate state of the art accuracy, robustness with respect to noisy input data, and a consistently small spread of errors over testing data sets, even for out-of-distribution prediction tasks.

In this article, we address a multi-robot planning problem in environments with partially unknown semantics. The environment is assumed to have a known geometric structure (e.g., walls) and to be occupied by static labeled landmarks with uncertain positions and classes. This modeling approach gives rise to an uncertain semantic map generated by semantic simultaneous localization and mapping algorithms. Our goal is to design control policies for robots equipped with noisy perception systems so that they can accomplish collaborative tasks captured by global temporal logic specifications. To specify missions that account for environmental and perceptual uncertainty, we employ a fragment of linear temporal logic (LTL), called co-safe LTL, defined over perception-based atomic predicates modeling probabilistic satisfaction requirements. The perception-based LTL planning problem gives rise to an optimal control problem, solved by a novel sampling-based algorithm, that generates open-loop control policies that are updated online to adapt to a continuously learned semantic map. We provide extensive experiments to demonstrate the efficiency of the proposed planning architecture.

Emerging applications of collaborative autonomy, such asmultitarget tracking,unknown map exploration, andpersistent surveillance, require robots plan paths to navigate an environment while maximizing the information collected via on-board sensors. In this article, we consider such information acquisition tasks but in adversarial environments, where attacks may temporarily disable the robots’ sensors. We propose the first receding horizon algorithm, aiming for robust and adaptive multirobot planning against any number of attacks, which we callResilient Active Information acquisitioN(RAIN).RAINcalls, in an online fashion, arobust trajectory planning(RTP) subroutine that plans attack-robust control inputs over a look-ahead planning horizon. We quantifyRTP’s performance by bounding its suboptimality. We base our theoretical analysis on notions of curvature introduced in combinatorial optimization. We evaluateRAINin three information acquisition scenarios:multitarget tracking,occupancy grid mapping, andpersistent surveillance. The scenarios are simulated in C++ and a unity-based simulator. In all simulations,RAINruns in real time, and exhibits superior performance against a state-of-the-art baseline information acquisition algorithm, even in the presence of a high number of attacks. We also demonstrateRAIN’s robustness and effectiveness against varying models of attacks (worst case and random), as well as varying replanning rates.

In this article, we design algorithms to protect swarm-robotics applications against sensor denial-of-service attacks on robots. We focus on applications requiring the robots to jointly select actions, e.g., which trajectory to follow, among a set of available actions. Such applications are central in large-scale robotic applications, such as multirobot motion planning for target tracking. But the current attack-robust algorithms are centralized. In this article, we propose a general-purpose distributed algorithm toward robust optimization at scale, with local communications only. We name itdistributed robust maximization(DRM).DRMproposes a divide-and-conquer approach that distributively partitions the problem among cliques of robots. Then, the cliques optimize in parallel, independently of each other. We proveDRMachieves a close-to-optimal performance. We demonstrateDRM’s performance in Gazebo and MATLAB simulations, in scenarios ofactive target tracking with swarms of robots. In the simulations,DRMachieves computational speed-ups, being 1 to 2 orders faster than the centralized algorithms.Yet, it nearly matches the tracking performance of the centralized counterparts. Since,DRMoverestimates the number of attacks in each clique, in this article, we also introduce animproved distributed robust maximization(IDRM) algorithm.IDRMinfers the number of attacks in each clique less conservatively thanDRMby leveraging three-hop neighboring communications. We verifyIDRMimprovesDRM’s performance in simulations.

Abstract This paper presents Verisig 2.0, a verification tool for closed-loop systems with neural network (NN) controllers. We focus on NNs with tanh/sigmoid activations and develop a Taylor-model-based reachability algorithm through Taylor model preconditioning and shrink wrapping. Furthermore, we provide a parallelized implementation that allows Verisig 2.0 to efficiently handle larger NNs than existing tools can. We provide an extensive evaluation over 10 benchmarks and compare Verisig 2.0 against three state-of-the-art verification tools. We show that Verisig 2.0 is both more accurate and faster, achieving speed-ups of up to 21x and 268x against different tools, respectively.

We propose a sampling-based approach to learn Lyapunov functions for a class of discrete-time autonomous hybrid systems that admit a mixed-integer representation. Such systems include autonomous piecewise affine systems, closed-loop dynamics of linear systems with model predictive controllers, piecewise affine/linear complementarity/mixed-logical dynamical systems in feedback with a ReLU neural network controller, etc. The proposed method comprises an alternation between a learner and a verifier to search for a Lyapunov function from a family of parameterized Lyapunov function candidates. In each iteration, the learner uses a collection of state samples to select a Lyapunov function candidate through a convex program in the parameter space. The verifier then solves a nonconvex mixed-integer quadratic program in the state space to either validate the proposed Lyapunov function candidate or reject it with a counterexample, i.e., a state where the Lyapunov condition fails. This counterexample is then added to the sample set of the learner to refine the set of Lyapunov function candidates in the next iteration. By designing the learner and the verifier according to the analytic center cutting-plane method from convex optimization, we show that when the set of Lyapunov functions is full-dimensional in the parameter space, our method finds a Lyapunov function in a finite number of steps. We demonstrate our stability analysis method on closed-loop MPC dynamical systems and a ReLU neural network controlled PWA system.

This paper considers the problem of planning trajectories for a team of sensor-equipped robots to reduce uncertainty about a dynamical process. Optimizing the trade-off between information gain and energy cost (e.g., control effort, distance travelled) is desirable but leads to a non-monotone objective function in the set of robot trajectories. Therefore, common multi-robot planning algorithms based on techniques such as coordinate descent lose their performance guarantees. Methods based on local search provide performance guarantees for optimizing a non-monotone submodular function, but require access to all robots’ trajectories, making it not suitable for distributed execution. This work proposes a distributed planning approach based on local search and shows how lazy/greedy methods can be adopted to reduce the computation and communication of the approach. We demonstrate the efficacy of the proposed method by coordinating robot teams composed of both ground and aerial vehicles with different sensing/control profiles and evaluate the algorithm’s performance in two target tracking scenarios. Compared to the naive distributed execution of local search, our approach saves up to 60% communication and 80–92% computation on average when coordinating up to 10 robots, while outperforming the coordinate descent based algorithm in achieving a desirable trade-off between sensing and energy cost.

We solve active target tracking, one of the essential tasks in autonomous systems, using a deep reinforcement learning (RL) approach. In this problem, an autonomous agent is tasked with acquiring information about targets of interests using its on-board sensors. The classical challenges in this problem are system model dependence and the difficulty of computing information-theoretic cost functions for a long planning horizon. RL provides solutions for these challenges as the length of its effective planning horizon does not affect the computational complexity, and it drops the strong dependency of an algorithm on system models. In particular, we introduce Active Tracking Target Network (ATTN), a unified deep RL policy that is capable of solving major sub-tasks of active target tracking – in-sight tracking, navigation, and exploration. The policy shows robust behavior for tracking agile and anomalous targets with a partially known target model. Additionally, the same policy is able to navigate in obstacle environments to reach distant targets as well as explore the environment when targets are positioned in unexpected locations.

This paper proposes a novel highly scalable nonmyopic planning algorithm for multi-robot Active Information Acquisition (AIA) tasks. AIA scenarios include target localization and tracking, active SLAM, surveillance, environmental monitoring and others. The objective is to compute control policies for multiple robots which minimize the accumulated uncertainty of a static hidden state over an a priori unknown horizon. The majority of existing AIA approaches are centralized and, therefore, face scaling challenges. To mitigate this issue, we propose an online algorithm that relies on decomposing the AIA task into local tasks via a dynamic space-partitioning method. The local subtasks are formulated online and require the robots to switch between exploration and active information gathering roles depending on their functionality in the environment. The switching process is tightly integrated with optimizing information gathering giving rise to a hybrid control approach. We show that the proposed decomposition-based algorithm is probabilistically complete for homogeneous sensor teams and under linearity and Gaussian assumptions. We provide extensive simulation results showing that the proposed algorithm can address large-scale estimation tasks that are computationally challenging to solve using existing centralized approaches.

Complex manipulation tasks, such as rearrangement planning of numerous objects, are combinatorially hard problems. Existing algorithms either do not scale well or assume a great deal of prior knowledge about the environment, and few offer any rigorous guarantees. In this paper, we propose a novel hybrid control architecture for achieving such tasks with mobile manipulators. On the discrete side, we enrich a temporal logic specification with mobile manipulation primitives such as moving to a point, and grasping or moving an object. Such specifications are translated to an automaton representation, which orchestrates the physical grounding of the task to mobility or manipulation controllers. The grounding from the discrete to the continuous reactive controller is online and can respond to the discovery of unknown obstacles or decide to push out of the way movable objects that prohibit task accomplishment. Despite the problem complexity, we prove that, under specific conditions, our architecture enjoys provable completeness on the discrete side, provable termination on the continuous side, and avoids all obstacles in the environment. Simulations illustrate the efficiency of our architecture that can handle tasks of increased complexity while also responding to unknown obstacles or unanticipated adverse configurations.

We develop a Multi-Agent Reinforcement Learning (MARL) method to learn scalable control policies for target tracking. Our method can handle an arbitrary number of pursuers and targets; we show results for tasks consisting up to 1000 pursuers tracking 1000 targets. We use a decentralized, partially-observable Markov Decision Process framework to model pursuers as agents receiving partial observations (range and bearing) about targets which move using fixed, unknown policies. An attention mechanism is used to parameterize the value function of the agents; this mechanism allows us to handle an arbitrary number of targets. Entropy-regularized off-policy RL methods are used to train a stochastic policy, and we discuss how it enables a hedging behavior between pursuers that leads to a weak form of cooperation in spite of completely decentralized control execution. We further develop a masking heuristic that allows training on smaller problems with few pursuers-targets and execution on much larger problems. Thorough simulation experiments and comparisons to state of the art algorithms are performed to study the scalability of the approach and robustness of performance to varying numbers of agents and targets.

This paper addresses the problem of active information gathering for multi-robot systems. Specifically, we consider scenarios where robots are tasked with reducing uncertainty of dynamical hidden states evolving in complex environments. The majority of existing information gathering approaches are centralized and, therefore, they cannot be applied to distributed robot teams where communication to a central user is not available. To address this challenge, we propose a novel distributed sampling-based planning algorithm that can significantly increase robot and target scalability while decreasing computational cost. In our non-myopic approach, all robots build in parallel local trees exploring the information space and their corresponding motion space. As the robots construct their respective local trees, they communicate with their neighbors to exchange and aggregate their local beliefs about the hidden state through a distributed Kalman filter. We show that the proposed algorithm is probabilistically complete and asymptotically optimal. We provide extensive simulation results that demonstrate the scalability of the proposed algorithm and that it can address large-scale, multi-robot information gathering tasks, that are computationally challenging for centralized methods.

Deterministic policies demonstrate substantial empirical success over their stochastic counterparts as they remove a level of randomness in Policy Gradient (PG) methods when applied to stochastic search problems involving Markov decision processes. However, current implementations require the use of state-action value ($Q$-function) approximators, also known as critics, to obtain estimates of the associated policy-reward gradient. In this work, we propose the use of two-point stochastic evaluations to obtain gradient estimates of a smoothed$Q$-function surrogate, constructed by evaluating pairs of the$Q$-function at low-dimensional, randomized initial action perturbations. This procedure lifts the dependence on a critic and restores true model-free policy learning, and with provable algorithmic stability. In fact, our finite complexity bounds improve upon existing results by up to 2 orders of magnitude in terms of iteration complexity, and by up to 3/2 orders of magnitude in terms of sample complexity. Simulation results on an agent navigation problem showcase the effectiveness of our proposed algorithm in a practical setting, as well.

We propose a Safe Pontryagin Differentiable Programming (Safe PDP) methodology, which establishes a theoretical and algorithmic framework to solve a broad class of safety-critical learning and control tasks---problems that require the guarantee of safety constraint satisfaction at any stage of the learning and control progress. In the spirit of interior-point methods, Safe PDP handles different types of system constraints on states and inputs by incorporating them into the cost or loss through barrier functions. We prove three fundamentals of the proposed Safe PDP: first, both the solution and its gradient in the backward pass can be approximated by solving their more efficient unconstrained counterparts; second, the approximation for both the solution and its gradient can be controlled for arbitrary accuracy by a barrier parameter; and third, importantly, all intermediate results throughout the approximation and optimization strictly respect the constraints, thus guaranteeing safety throughout the entire learning and control process. We demonstrate the capabilities of Safe PDP in solving various safety-critical tasks, including safe policy optimization, safe motion planning, and learning MPCs from demonstrations, on different challenging systems such as 6-DoF maneuvering quadrotor and 6-DoF rocket powered landing.

We consider a standard federated learning (FL) setup where a group of clients periodically coordinate with a central server to train a statistical model. We develop a general algorithmic framework called FedLin to tackle some of the key challenges intrinsic to FL, namely objective heterogeneity, systems heterogeneity, and infrequent and imprecise communication. Our framework is motivated by the observation that under these challenges, various existing FL algorithms suffer from a fundamental speed-accuracy conflict: they either guarantee linear convergence but to an incorrect point, or convergence to the global minimum but at a sub-linear rate, i.e., fast convergence comes at the expense of accuracy. In contrast, when the clients' local loss functions are smooth and strongly convex, we show that FedLin guarantees linear convergence to the global minimum, despite arbitrary objective and systems heterogeneity. We then establish matching upper and lower bounds on the convergence rate of FedLin that highlight the effects of infrequent, periodic communication. Finally, we show that FedLin preserves linear convergence rates under aggressive gradient sparsification, and quantify the effect of the compression level on the convergence rate. Notably, our work is the first to provide tight linear convergence rate guarantees, and constitutes the first comprehensive analysis of gradient sparsification in FL.

Despite strong performance in numerous applications, the fragility of deep learning to input perturbations has raised serious questions about its use in safety-critical domains. While adversarial training can mitigate this issue in practice, state-of-the-art methods are increasingly application-dependent, heuristic in nature, and suffer from fundamental trade-offs between nominal performance and robustness. Moreover, the problem of finding worst-case perturbations is non-convex and underparameterized, both of which engender a non-favorable optimization landscape. Thus, there is a gap between the theory and practice of robust learning, particularly with respect to when and why adversarial training works. In this paper, we take a constrained learning approach to address these questions and to provide a theoretical foundation for robust learning. In particular, we leverage semi-infinite optimization and non-convex duality theory to show that adversarial training is equivalent to a statistical problem over perturbation distributions. Notably, we show that a myriad of previous robust training techniques can be recovered for particular, sub-optimal choices of these distributions. Using these insights, we then propose a hybrid Langevin Markov Chain Monte Carlo approach for which several common algorithms (e.g., PGD) are special cases. Finally, we show that our approach can mitigate the trade-off between nominal and robust performance, yielding state-of-the-art results on MNIST and CIFAR-10. Our code is available at: https://github.com/arobey1/advbench.

Despite remarkable success in a variety of applications, it is well-known that deep learning can fail catastrophically when presented with out-of-distribution data. Toward addressing this challenge, we consider the \emph{domain generalization} problem, wherein predictors are trained using data drawn from a family of related training domains and then evaluated on a distinct and unseen test domain. We show that under a natural model of data generation and a concomitant invariance condition, the domain generalization problem is equivalent to an infinite-dimensional constrained statistical learning problem; this problem forms the basis of our approach, which we call Model-Based Domain Generalization. Due to the inherent challenges in solving constrained optimization problems in deep learning, we exploit nonconvex duality theory to develop unconstrained relaxations of this statistical problem with tight bounds on the duality gap. Based on this theoretical motivation, we propose a novel domain generalization algorithm with convergence guarantees. In our experiments, we report improvements of up to 30% over state-of-the-art domain generalization baselines on several benchmarks including ColoredMNIST, Camelyon17-WILDS, FMoW-WILDS, and PACS.

With the transformation to smarter cities and the development of technologies, a large amount of data is collected from sensors in real time. Services provided by ride-sharing systems such as taxis, mobility-on-demand autonomous vehicles, and bike sharing systems are popular. This paradigm provides opportunities for improving transportation systems’ performance by allocating ride-sharing vehicles toward predicted demand proactively. However, how to deal with uncertainties in the predicted demand probability distribution for improving the average system performance is still a challenging and unsolved task. Considering this problem, in this work, we develop a data-driven distributionally robust vehicle balancing method to minimize the worst-case expected cost. We design efficient algorithms for constructing uncertainty sets of demand probability distributions for different prediction methods and leverage a quad-tree dynamic region partition method for better capturing the dynamic spatial-temporal properties of the uncertain demand. We then derive an equivalent computationally tractable form for numerically solving the distributionally robust problem. We evaluate the performance of the data-driven vehicle balancing algorithm under different demand prediction and region partition methods based on four years of taxi trip data for New York City (NYC). We show that the average total idle driving distance is reduced by 30% with the distributionally robust vehicle balancing method using quad-tree dynamic region partitions, compared with vehicle balancing methods based on static region partitions without considering demand uncertainties. This is about a 60-million-mile or a 8-million-dollar cost reduction annually in NYC.

This article addresses the problem of verifying the safety of autonomous systems with neural network (NN) controllers. We focus on NNs with sigmoid/tanh activations and use the fact that the sigmoid/tanh is the solution to a quadratic differential equation. This allows us to convert the NN into an equivalent hybrid system and cast the problem as a hybrid system verification problem, which can be solved by existing tools. Furthermore, we improve the scalability of the proposed method by approximating the sigmoid with a Taylor series with worst-case error bounds. Finally, we provide an evaluation over four benchmarks, including comparisons with alternative approaches based on mixed integer linear programming as well as on star sets.

In this article, we address the problem of stochastic motion planning under partial observability, more specifically, how to navigate a mobile robot equipped with continuous range sensors, such as LIDAR. In contrast to many existing robotic motion planning methods, we explicitly consider the uncertainty of the robot state by modeling the system as a partially observable Markov decision process (POMDP). Recent work on general purpose POMDP solvers is typically limited to discrete observation spaces, and does not readily apply to the proposed problem due to the continuous measurements from LIDAR. In this article, we build upon an existing Monte Carlo tree search method, partially observable Monte Carlo planning (POMCP), and propose a new algorithm POMCP++. Our algorithm can handle continuous observation spaces with a novel measurement selection strategy. The POMCP++ algorithm overcomes overoptimism in the value estimation of a rollout policy by removing the implicit perfect state assumption at the rollout phase. We validate POMCP++ in theory by proving it is a Monte Carlo tree search algorithm. Through comparisons with other methods that can also be applied to the proposed problem, we show that POMCP++ yields significantly higher success rate and total reward.

This paper describes a verification case study on an autonomous racing car with a neural network (NN) controller. Although several verification approaches have been recently proposed, they have only been evaluated on low-dimensional systems or systems with constrained environments. To explore the limits of existing approaches, we present a challenging benchmark in which the NN takes raw LiDAR measurements as input and outputs steering for the car. We train a dozen NNs using reinforcement learning (RL) and show that the state of the art in verification can handle systems with around 40 LiDAR rays. Furthermore, we perform real experiments to investigate the benefits and limitations of verification with respect to the sim2real gap, i.e., the difference between a system's modeled and real performance. We identify cases, similar to the modeled environment, in which verification is strongly correlated with safe behavior. Finally, we illustrate LiDAR fault patterns that can be used to develop robust and safe RL algorithms.

Despite the simplicity and intuitive interpretation of minimum mean squared error (MMSE) estimators, their effectiveness in certain scenarios is questionable. Indeed, minimizing squared errors on average does not provide any form of stability, as the volatility of the estimation error is left unconstrained. When this volatility is statistically significant, the difference between the average and realized performance of the MMSE estimator can be drastically different. To address this issue, we introduce a new risk-aware MMSE formulation which trades between mean performance and risk by explicitly constraining the expected predictive variance of the involved squared error. We show that, under mild moment boundedness conditions, the corresponding risk-aware optimal solution can be evaluated explicitly, and has the form of an appropriately biased nonlinear MMSE estimator. We further illustrate the effectiveness of our approach via several numerical examples, which also showcase the advantages of risk-aware against risk-neutral MMSE estimation, especially in models involving skewed, heavy-tailed distributions.

Optimal resource allocation in real-world wireless systems is rather challenging, not only due to the unavailability of accurate statistical channel models, but also because expressions of maximal or achievable information rates are most often unknown, or not adequately precise. Under a modular stochastic functional optimization framework, we propose a new zeroth-order stochastic primal-dual algorithm for completely data-driven, model-free and gradient-free learning of optimal resource allocation policies for ergodic network optimization. Our contribution relies on Gaussian smoothing of the corresponding constrained policy search problem, and on the representation power of universal policy parameterizations, such as Deep Neural Networks (DNNs). Indeed, our simulations demonstrate that DNN-based policies produced by the proposed primal-dual method attain near-ideal performance, based exclusively on limited channel probing, completely bypassing the need for gradient computations, and at the absence of channel or information rate models.

This paper proposes a new reactive mission planning algorithm for multiple robots that operate in unknown environments. The robots are equipped with individual sensors that allow them to collectively learn and continuously update a map of the unknown environment. The goal of the robots is to accomplish complex tasks, captured by global co-safe Linear Temporal Logic (LTL) formulas. The majority of existing temporal logic planning approaches rely on discrete abstractions of the robot dynamics operating in known environments and, as a result, they cannot be applied to the more realistic scenarios where the environment is initially unknown. In this paper, we address this novel challenge by proposing the first reactive, and abstraction-free LTL planning algorithm that can be applied for complex mission planning of multiple robots operating in unknown environments. Our algorithm is reactive in the sense that temporal logic planning is adapting to the updated map of the environment and abstraction-free as it does not rely on designing abstractions of robot dynamics. Our proposed algorithm is complete under mild assumptions on the structure of the environment and the sensor models. Our paper provides extensive numerical simulations and hardware experiments that illustrate the theoretical analysis and show that the proposed algorithm can address complex planning tasks in unknown environments.

This paper focuses on exploration and occupancy mapping of unknown environments using a mobile robot. While a truncated signed distance field (TSDF) is a popular, efficient, and highly accurate representation of occupancy, few works have considered optimizing robot sensing trajectories for autonomous TSDF mapping. We propose an efficient approach for maintaining TSDF uncertainty and predicting its evolution from potential future sensor measurements without actually receiving them. Efficient uncertainty prediction is critical for long-horizon optimization of potential sensing trajectories. We develop a deterministic tree-search algorithm that evaluates the information gain between the TSDF distribution and potential observations along sequences of robot motion primitives. Efficient planning is achieved by branch-and-bound pruning of uninformative sensing trajectories. The effectiveness of our active TSDF mapping approach is evaluated in several simulated environments with complex visibility constraints.

We aim to guard swarm-robotics applications against denial-of-service (DoS) attacks that result in withdrawals of robots. We focus on applications requiring the selection of actions for each robot, among a set of available ones, e.g., which trajectory to follow. Such applications are central in large-scale robotic applications, e.g., multi-robot motion planning for target tracking. But the current attack-robust algorithms are centralized, and scale quadratically with the problem size (e.g., number of robots). In this paper, we propose a general-purpose distributed algorithm towards robust optimization at scale, with local communications only. We name it distributed robust maximization (DRM). DRM proposes a divide-and-conquer approach that distributively partitions the problem among K cliques of robots. The cliques optimize in parallel, independently of each other. That way, DRM also offers computational speed-ups up to 1/K2the running time of its centralized counterparts. K depends on the robots' communication range, which is given as input to DRM. DRM also achieves a close-to-optimal performance. We demonstrate DRM's performance in Gazebo and MATLAB simulations, in scenarios of active target tracking with multiple robots. We observe DRM achieves significant computational speed-ups (it is 3 to 4 orders faster) and, yet, nearly matches the tracking performance of its centralized counterparts.

Multi-Robot Systems have been recently employed in different applications and have advantages over single-robot systems, such as increased robustness and task performance efficiency. We consider such assemblies specifically in the scenario of perimeter defense, where the task is to defend a circular perimeter by intercepting radially approaching targets. Possible intruders appear randomly at a fixed distance from the perimeter and with azimuthal location determined by some unknown probability density. Coordination among multiple defenders is a complex combinatorial optimization problem. In this work, we focus on the following two aspects: (i) estimating the probability density that describes the direction from which the next intruders are going to arrive, and (ii) partitioning of the space so that the defenders focus on capturing a disjoint subset of intruders. Results show that the proposed strategy increases the number of captures over a naive baseline strategy, especially in scenarios with non-uniform spatial distributions of intruder arrival. The proposed approach is also efficient and able to quickly adapt to time-varying intruder distributions.

This paper presents Verisig, a hybrid system approach to verifying safety properties of closed-loop systems using neural networks as controllers. We focus on sigmoid-based networks and exploit the fact that the sigmoid is the solution to a quadratic differential equation, which allows us to transform the neural network into an equivalent hybrid system. By composing the network's hybrid system with the plant's, we transform the problem into a hybrid system verification problem which can be solved using state-of-the-art reachability tools. We show that reachability is decidable for networks with one hidden layer and decidable for general networks if Schanuel's conjecture is true. We evaluate the applicability and scalability of Verisig in two case studies, one from reinforcement learning and one in which the neural network is used to approximate a model predictive controller.

While off-policy temporal difference (TD) methods have widely been used in reinforcement learning due to their efficiency and simple implementation, their Bayesian counterparts have not been utilized as frequently. One reason is that the non-linear max operation in the Bellman optimality equation makes it difficult to define conjugate distributions over the value functions. In this paper, we introduce a novel Bayesian approach to off-policy TD methods, called as ADFQ, which updates beliefs on state-action values, Q, through an online Bayesian inference method known as Assumed Density Filtering. We formulate an efficient closed-form solution for the value update by approximately estimating analytic parameters of the posterior of the Q-beliefs. Uncertainty measures in the beliefs not only are used in exploration but also provide a natural regularization for the value update considering all next available actions. ADFQ converges to Q-learning as the uncertainty measures of the Q-beliefs decrease and improves common drawbacks of other Bayesian RL algorithms such as computational complexity. We extend ADFQ with a neural network. Our empirical results demonstrate that ADFQ outperforms comparable algorithms on various Atari 2600 games, with drastic improvements in highly stochastic domains or domains with a large action space.

In this paper, we propose a novel Reinforcement Learning approach for solving the Active Information Acquisition problem, which requires an agent to choose a sequence of actions in order to acquire information about a process of interest using on-board sensors. The classic challenges in the information acquisition problem are the dependence of a planning algorithm on known models and the difficulty of computing information-theoretic cost functions over arbitrary distributions. In contrast, the proposed framework of reinforcement learning does not require any knowledge on models and alleviates the problems during an extended training stage. It results in policies that are efficient to execute online and applicable for real-time control of robotic systems. Furthermore, the state-of-the-art planning methods are typically restricted to short horizons, which may become problematic with local minima. Reinforcement learning naturally handles the issue of planning horizon in information problems as it maximizes a discounted sum of rewards over a long finite or infinite time horizon. We discuss the potential benefits of the proposed framework and compare the performance of the novel algorithm to an existing information acquisition method for multi-target tracking scenarios.

This paper addresses a multi-robot motion planning problem in probabilistic maps obtained by semantic simultaneous localization and mapping (SLAM). The goal of the robots is to accomplish complex collaborative high level tasks captured by global temporal logic specifications in the presence of uncertainty in the workspace. Specifically, the robots operate in an unknown environment modeled as a semantic map determined by Gaussian distributions over landmark positions and arbitrary discrete distributions over landmark classes. We extend Linear Temporal Logic by including information-based predicates allowing us to incorporate uncertainty and probabilistic satisfaction requirements directly into the task specification. We propose a new highly scalable sampling-based approach that synthesizes paths that satisfy the assigned task specification while minimizing a user-specified motion cost function. Finally, we show that the proposed algorithm is probabilistically complete, asymptotically optimal and supported by convergence rate bounds. We provide extensive simulation results that corroborate the theoretical analysis and show that the proposed algorithm can address large-scale planning tasks.

This paper considers the problem of planning trajectories for robots equipped with sensors whose task is to track an evolving target process in the world. We focus on processes which can be represented by a Gaussian random variable, which is known to reduce the general stochastic information acquisition problem to a deterministic problem, which is much simpler to solve. Previous work on solving the resulting deterministic problem focuses on computing a search tree by Forward Value Iteration and pruning uninformative nodes early on in the search via a domination criteria. In this work we formulate the Active Information Acquisition problem as a deterministic planning problem where algorithms like Dijkstra and A* can produce optimal solutions. To use A* effectively in long planning horizons we derive a consistent and admissible heuristic as a function of the sensor model which can be used in information acquisition tasks such as actively mapping static and moving targets in an environment with obstacles. We validate the results in several simulations indicating that the resulting heuristic informed algorithm can recover optimal solutions faster than existing search-based methods.

Tight estimation of the Lipschitz constant for deep neural networks (DNNs) is useful in many applications ranging from robustness certification of classifiers to stability analysis of closed-loop systems with reinforcement learning controllers. Existing methods in the literature for estimating the Lipschitz constant suffer from either lack of accuracy or poor scalability. In this paper, we present a convex optimization framework to compute guaranteed upper bounds on the Lipschitz constant of DNNs both accurately and efficiently. Our main idea is to interpret activation functions as gradients of convex potential functions. Hence, they satisfy certain properties that can be described by quadratic constraints. This particular description allows us to pose the Lipschitz constant estimation problem as a semidefinite program (SDP). The resulting SDP can be adapted to increase either the estimation accuracy (by capturing the interaction between activation functions of different layers) or scalability (by decomposition and parallel implementation). We illustrate the utility of our approach with a variety of experiments on randomly generated networks and on classifiers trained on the MNIST and Iris datasets. In particular, we experimentally demonstrate that our Lipschitz bounds are the most accurate compared to those in the literature. We also study the impact of adversarial training methods on the Lipschitz bounds of the resulting classifiers and show that our bounds can be used to efficiently provide robustness guarantees.

This paper considers the resource allocation problem in wireless systems over an unknown time-varying non-stationary channel. The goal is to maximize a utility function, such as a capacity function, over a set of wireless nodes while satisfying a set of resource constraints. To bypass the need for a model for channel distribution as it varies over time, samples of the channel are taken at every time epoch to estimate the channel. The resulting stochastic optimization problem is converted in its Lagrange dual problem, where the resulting stochastic optimization problem can viewed equivalently as minimizing a certain empirical risk measure, a well-studied problem in machine learning. The second order Newton's method is used to quickly learn statistically approximated optimal resource allocation policies over the sampled dual function as the channel evolves over time epochs. The quadratic convergence rate of Newton is used to establish, under certain conditions on the sampling size and rate of channel variation, an instantaneous learning and tracking of these policies. Numerical simulations demonstrate the effectiveness of the learning algorithm on a low-dimensional wireless capacity maximization problem.

Traditional approaches for simultaneous localization and mapping (SLAM) rely on geometric features such as points, lines, and planes to infer the environment structure. They make hard decisions about the (data) association between observed features and mapped landmarks to update the environment model. This paper makes two contributions to the state of the art in SLAM. First, it generalizes the purely geometric model by introducing semantically meaningful objects, represented as structured models of mid-level part features. Second, instead of making hard, potentially wrong associations between semantic features and objects, it shows that SLAM inference can be performed efficiently with probabilistic data association. The approach not only allows building meaningful maps (containing doors, chairs, cars, etc.) but also offers significant advantages in ambiguous environments.

Applications of safety, security, and rescue in robotics, such as multi-robot target tracking, involve the execution of information acquisition tasks by teams of mobile robots. However, in failure-prone or adversarial environments, robots get attacked, their communication channels get jammed, and their sensors may fail, resulting in the withdrawal of robots from the collective task, and consequently the inability of the remaining active robots to coordinate with each other. As a result, traditional design paradigms become insufficient and, in contrast, resilient designs against system-wide failures and attacks become important. In general, resilient design problems are hard, and even though they often involve objective functions that are monotone or submodular, scalable approximation algorithms for their solution have been hitherto unknown. In this paper, we provide the first algorithm, enabling the following capabilities: minimal communication, i.e., the algorithm is executed by the robots based only on minimal communication between them; system-wide resiliency, i.e., the algorithm is valid for any number of denial-of-service attacks and failures; and provable approximation performance, i.e., the algorithm ensures for all monotone (and not necessarily submodular) objective functions a solution that is finitely close to the optimal. We quantify our algorithms approximation performance using a notion of curvature for monotone set functions. We support our theoretical analyses with simulated and real-world experiments, by considering an active information gathering scenario, namely, multi-robot target tracking.

The design of cyber-physical systems (CPSs) requires methods and tools that can efficiently reason about the interaction between discrete models, e.g., representing the behaviors of “cyber” components, and continuous models of physical processes. Boolean methods such as satisfiability (SAT) solving are successful in tackling large combinatorial search problems for the design and verification of hardware and software components. On the other hand, problems in control, communications, signal processing, and machine learning often rely on convex programming as a powerful solution engine. However, despite their strengths, neither approach would work in isolation for CPSs. In this paper, we present a new satisfiability modulo convex programming (SMC) framework that integrates SAT solving and convex optimization to efficiently reason about Boolean and convex constraints at the same time. We exploit the properties of a class of logic formulas over Boolean and nonlinear real predicates, termed monotone satisfiability modulo convex formulas, whose satisfiability can be checked via a finite number of convex programs. Following the lazy satisfiability modulo theory (SMT) paradigm, we develop a new decision procedure for monotone SMC formulas, which coordinates SAT solving and convex programming to provide a satisfying assignment or determine that the formula is unsatisfiable. A key step in our coordination scheme is the efficient generation of succinct infeasibility proofs for inconsistent constraints that can support conflict-driven learning and accelerate the search. We demonstrate our approach on different CPS design problems, including spacecraft docking mission control, robotic motion planning, and secure state estimation. We show that SMC can handle more complex problem instances than state-of-the-art alternative techniques based on SMT solving and mixed integer convex programming.

We address the problem of determining the satisfiability of a Boolean combination of convex constraints over the real numbers, which is common in the context of hybrid system verification and control. We first show that a special type of logic formulas, termed monotone Satisfiability Modulo Convex (SMC) formulas, is the most general class of formulas over Boolean and nonlinear real predicates that reduce to convex programs for any satisfying assignment of the Boolean variables. For this class of formulas, we develop a new satisfiability modulo convex optimization procedure that uses a lazy combination of SAT solving and convex programming to provide a satisfying assignment or determine that the formula is unsatisfiable. Our approach can then leverage the efficiency and the formal guarantees of state-of-the-art algorithms in both the Boolean and convex analysis domains. A key step in lazy satisfiability solving is the generation of succinct infeasibility proofs that can support conflict-driven learning and decrease the number of iterations between the SAT and the theory solver. For this purpose, we propose a suite of algorithms that can trade complexity with the minimality of the generated infeasibility certificates. Remarkably, we show that a minimal infeasibility certificate can be generated by simply solving one convex program for a sub-class of SMC formulas, namely ordered positive unate SMC formulas, that have additional monotonicity properties. Perhaps surprisingly, ordered positive unate formulas appear themselves very frequently in a variety of practical applications. By exploiting the properties of monotone SMC formulas, we can then build and demonstrate effective and scalable decision procedures for problems in hybrid system verification and control, including secure state estimation and robotic motion planning.

Traditional approaches to simultaneous localization and mapping (SLAM) rely on low-level geometric features such as points, lines, and planes. They are unable to assign semantic labels to landmarks observed in the environment. Furthermore, loop closure recognition based on low-level features is often viewpoint-dependent and subject to failure in ambiguous or repetitive environments. On the other hand, object recognition methods can infer landmark classes and scales, resulting in a small set of easily recognizable landmarks, ideal for view-independent unambiguous loop closure. In a map with several objects of the same class, however, a crucial data association problem exists. While data association and recognition are discrete problems usually solved using discrete inference, classical SLAM is a continuous optimization over metric information. In this paper, we formulate an optimization problem over sensor states and semantic landmark positions that integrates metric information, semantic information, and data associations, and decompose it into two interconnected problems: an estimation of discrete data association and landmark class probabilities, and a continuous optimization over the metric states. The estimated landmark and robot poses affect the association and class distributions, which in turn affect the robot-landmark pose optimization. The performance of our algorithm is demonstrated on indoor and outdoor datasets.

We present a method for calibration-free, infrastructure-free localization in sensor networks. Our strategy is to estimate node positions and noise distributions of all links in the network simultaneously - a strategy that has not been attempted thus far. In particular, we account for biased, non-line-of-sight (NLOS) range measurements from ultra-wideband (UWB) devices that lead to multi-modal noise distributions, for which few solutions exist to date. Our approach circumvents cumbersome a-priori calibration, allows for rapid deployment in unknown environments, and facilitates adaptation to changing conditions. Our first contribution is a generalization of the classical multidimensional scaling algorithm to account for measurements that have multi-modal error distributions. Our second contribution is an online approach that iterates between node localization and noise parameter estimation. We validate our method in 3-dimensional networks, (i) through simulation to test the sensitivity of the algorithm on its design parameters, and (ii) through physical experimentation in a NLOS environment. Our setup uses UWB devices that provide time-of-flight measurements, which can lead to positively biased distance measurements in NLOS conditions. We show that our algorithm converges to accurate position estimates, even when initial position estimates are very uncertain, initial error models are unknown, and a significant proportion of the network links are in NLOS.

This paper considers robot motion planning under temporal logic constraints in probabilistic maps obtained by semantic simultaneous localization and mapping (SLAM). The uncertainty in a map distribution presents a great challenge for obtaining correctness guarantees with respect to the linear temporal logic (LTL) specification. We show that the problem can be formulated as an optimal control problem in which both the semantic map and the logic formula evaluation are stochastic. Our first contribution is to reduce the stochastic control problem for a subclass of LTL to a deterministic shortest path problem by introducing a confidence parameter δ. A robot trajectory obtained from the deterministic problem is guaranteed to have minimum cost and to satisfy the logic specification in the true environment with probability δ. Our second contribution is to design an admissible heuristic function that guides the planning in the deterministic problem towards satisfying the temporal logic specification. This allows us to obtain an optimal and very efficient solution using the A* algorithm. The performance and correctness of our approach are demonstrated in a simulated semantic environment using a differential-drive robot.

In this paper we consider an online planning problem for unmanned aerial vehicle (UAV) operations. Specifically, a UAV has the task of reaching a goal from a set of possible goals while minimizing the amount of energy required. Due to unforeseen disturbances, it is possible that initially attractive goals might end up being very expensive during the execution. Thus, two main problems are investigated here: i) how to predict and plan the motion of the UAV at run time to minimize its energy consumption and ii) when to schedule next replanning time to avoid unnecessary periodic re-evaluation executions. Our approach considers a nonlinear model of the system for which a model predictive controller is used to determine the desired control inputs for each possible goal. These control inputs are then used to estimate the energy required to reach the different goals. Finally, a self-triggered scheduling policy determines how long to wait before replanning the goal to aim for. The proposed framework is validated through simulations and experiments in which a quadrotor must choose and reach some goal while being subject to external disturbances.

Traditional taxi systems in metropolitan areas often suffer from inefficiencies due to uncoordinated actions as system capacity and customer demand change. With the pervasive deployment of networked sensors in modern vehicles, large amounts of information regarding customer demand and system status can be collected in real time. This information provides opportunities to perform various types of control and coordination for large-scale intelligent transportation systems. In this paper, we present a receding horizon control (RHC) framework to dispatch taxis, which incorporates highly spatiotemporally correlated demand/supply models and real-time Global Positioning System (GPS) location and occupancy information. The objectives include matching spatiotemporal ratio between demand and supply for service quality with minimum current and anticipated future taxi idle driving distance. Extensive trace-driven analysis with a data set containing taxi operational records in San Francisco, CA, USA, shows that our solution reduces the average total idle distance by 52%, and reduces the supply demand ratio error across the city during one experimental time slot by 45%. Moreover, our RHC framework is compatible with a wide variety of predictive models and optimization problem formulations. This compatibility property allows us to solve robust optimization problems with corresponding demand uncertainty models that provide disruptive event information.

Extensive empirical studies presented in this article confirm that the quality of radio communication between low-power sensor devices varies significantly with time and environment. This phenomenon indicates that the previous topology control solutions, which use static transmission power, transmission range, and link quality, might not be effective in the physical world. To address this issue, online transmission power control that adapts to external changes is necessary. This article presents ATPC, a lightweight algorithm for Adaptive Transmission Power Control in wireless sensor networks. In ATPC, each node builds a model for each of its neighbors, describing the correlation between transmission power and link quality. With this model, we employ a feedback-based transmission power control algorithm to dynamically maintain individual link quality over time. The intellectual contribution of this work lies in a novel pairwise transmission power control, which is significantly different from existing node-level or network-level power control methods. Also different from most existing simulation work, the ATPC design is guided by extensive field experiments of link quality dynamics at various locations over a long period of time. The results from the real-world experiments demonstrate that (1) with pairwise adjustment, ATPC achieves more energy savings with a finer tuning capability, and (2) with online control, ATPC is robust even with environmental changes over time.

We consider the problem of verification of software implementations of linear time-invariant controllers. Commonly, different implementations use different representations of the controller's state, for example due to optimizations in a third-party code generator. To accommodate this variation, we exploit input-output controller specification captured by the controller's transfer function and show how to automatically verify correctness of C code controller implementations using a Frama-C/Why3/Z3 toolchain. Scalability of the approach is evaluated using randomly generated controller specifications of realistic size.

This paper addresses the problem of controlling mobile sensing systems to improve the accuracy and efficiency of gathering information autonomously. It applies to scenarios such as environmental monitoring, search and rescue, surveillance and reconnaissance, and simultaneous localization and mapping (SLAM). A multi-sensor active information acquisition problem, capturing the common characteristics of these scenarios, is formulated. The goal is to design sensor control policies which minimize the entropy of the estimation task, conditioned on the future measurements. First, we provide a non-greedy centralized solution, which is computationally fast, since it exploits linearized sensing models, and memory efficient, since it exploits sparsity in the environment model. Next, we decentralize the control task to obtain linear complexity in the number of sensors and provide suboptimality guarantees. Finally, our algorithms are applied to the multi-robot active SLAM problem to enable a decentralized nonmyopic solution that exploits sparsity in the planning process.

Utilizing the capabilities of configurable sensing systems requires addressing difficult information gathering problems. Near-optimal approaches exist for sensing systems without internal states. However, when it comes to optimizing the trajectories of mobile sensors the solutions are often greedy and rarely provide performance guarantees. Notably, under linear Gaussian assumptions, the problem becomes deterministic and can be solved off-line. Approaches based on submodularity have been applied by ignoring the sensor dynamics and greedily selecting informative locations in the environment. This paper presents a non-greedy algorithm with suboptimality guarantees, which relies on concavity instead of submodularity and takes the sensor dynamics into account. Coupled with linearization and model predictive control, the algorithm can be used to generate adaptive policies for mobile sensors with non-linear sensing models. Applications in gas concentration mapping and target tracking are presented.

In this paper we present a methodology to control ground robots under malicious attack on sensors. Within the term attack we intend any malicious disturbance injection on sensors, actuators, and controller that would compromise the safety of a robot. In order to guarantee resilience against attacks, we use a control-level technique implemented within a recursive algorithm that takes advantage of redundancy in the information received by the controller. We use the case study of a vehicle cruise-control, however, the strategy we present in this work is general for several applications. Our methodology relays on redundancy in the sensor measurements: specifically we consider N velocity measurements and use a recursive filtering technique that estimates the state of the system while being resilient against sensor attacks by acting on the variance of the measurements noise. Finally, we move our focus on hardware validation demonstrating our algorithm through extensive outdoor experiments conducted on two unmanned ground robots.

We present a compositional motion planning framework for multi-robot systems based on an encoding to satisfiability modulo theories (SMT). In our framework, the desired behavior of a group of robots is specified using a set of safe linear temporal logic (LTL) properties. Our method relies on a library of motion primitives, each of which corresponds to a controller that ensures a particular trajectory in a given configuration. Using the closed-loop behavior of the robots under the action of different controllers, we formulate the motion planning problem as an SMT solving problem and use an off-the-shelf SMT solver to generate trajectories for the robots. Our approach can also be extended to synthesize optimal cost trajectories where optimality is defined with respect to the available motion primitives. Experimental results show that our framework can efficiently solve complex motion planning problems in the context of multi-robot systems.

One of the central problems in computer vision is the detection of semantically important objects and the estimation of their pose. Most of the work in object detection has been based on single image processing, and its performance is limited by occlusions and ambiguity in appearance and geometry. This paper proposes an active approach to object detection in which the point of view of a mobile depth camera is controlled. When an initial static detection phase identifies an object of interest, several hypotheses are made about its class and orientation. Then, a sequence of views, which balances the amount of energy used to move the sensor with the chance of identifying the correct hypothesis, is planned. We formulate an active hypothesis testing problem, which includes sensor mobility, and solve it using a point-based approximate partially observable Markov decision process algorithm. The validity of our approach is verified through simulation and realworld experiments with the PR2 robot. The results suggest that the approach outperforms the widely used greedy viewpoint selection and provides a significant improvement over static object detection.

One of the central problems in computer vision is the detection of semantically important objects and the estimation of their pose. Most of the work in object detection has been based on single image processing and its performance is limited by occlusions and ambiguity in appearance and geometry. This paper proposes an active approach to object detection by controlling the point of view of a mobile depth camera. When an initial static detection phase identifies an object of interest, several hypotheses are made about its class and orientation. The sensor then plans a sequence of viewpoints, which balances the amount of energy used to move with the chance of identifying the correct hypothesis. We formulate an active M-ary hypothesis testing problem, which includes sensor mobility, and solve it using a point-based approximate POMDP algorithm. The validity of our approach is verified through simulation and experiments with real scenes captured by a kinect sensor. The results suggest a significant improvement over static object detection.

We study the problem of stabilizing a linear system over a wireless network using a simple in-network computation method. Specifically, we study an architecture called the "Wireless Control Network" (WCN), where each wireless node maintains a state, and periodically updates it as a linear combination of neighboring plant outputs and node states. This architecture has previously been shown to have low computational overhead and beneficial scheduling and compositionality properties. In this paper we characterize fundamental topological conditions to allow stabilization using such a scheme. To achieve this, we exploit the fact that the WCN scheme causes the network to act as a linear dynamical system, and analyze the coupling between the plant's dynamics and the dynamics of the network. We show that stabilizing control inputs can be computed in-network if the vertex connectivity of the network is larger than the geometric multiplicity of any unstable eigenvalue of the plant. This condition is analogous to the typical min-cut condition required in classical information dissemination problems. Furthermore, we specify equivalent topological conditions for stabilization over a wired (or point-to-point) network that employs network coding in a traditional way - as a communication mechanism between the plant's sensors and decentralized controllers at the actuators.

This paper proposes a compositional method for verifying the safety of a dynamical system, given as an interconnection of subsystems. The safety verification is conducted by the use of the barrier certificate method; hence, the contribution of this paper is to show how to obtain compositional conditions for safety verification.

The objective of source seeking problems is to determine the minimum of an unknown signal field, which represents a physical quantity of interest, such as heat, chemical concentration, or sound. This paper proposes a strategy for source seeking in a noisy signal field using a mobile robot and based on a stochastic gradient descent algorithm. Our scheme does not require a prior map of the environment or a model of the signal field and is simple enough to be implemented on platforms with limited computational power. We discuss the asymptotic convergence guarantees of algorithm and give specific guidelines for its application to mobile robots in unknown indoor environments with obstacles. Both simulations and real-world experiments were carried out to evaluate the performance of our approach. The results suggest that the algorithm has good finite time performance in complex environments.

We present a general notion of robust controller specification and a mechanism for sequentially composing them. These specifications form tubular abstractions of the trajectories of a system in different control modes, and are motivated by the techniques available for certifying the performance of low-level controllers. The notion of controller specification provides a rigorous interface for connecting a planner and lower-level controllers that are designed independently. With this approach, the planning layer does not integrate the closed-loop system dynamics and does not require the knowledge of how the controllers operate, but relies only on the specifications of the output tracking performance achieved by these controllers. The control layer aims at satisfying specifications that account quantitatively for robustness to unmodeled dynamics and various sources of disturbance and sensor noise, so that this robustness does not need to be revalidated at the planning level. As an illustrative example, we describe a randomized planner that composes different controller specifications from a given database to guarantee that any corresponding sequence of control modes steers a robot to a given region while avoiding obstacles.

We present a distributed scheme used for control over a network of wireless nodes. As opposed to traditional networked control schemes where the nodes simply route information to and from a dedicated controller (perhaps performing some encoding along the way), our approach, Wireless Control Network (WCN), treats the network itself as the controller. In other words, the computation of the control law is done in a fully distributed way inside the network. We extend the basic WCN strategy, where at each time-step, each node updates its internal state to be a linear combination of the states of the nodes in its neighborhood. This causes the entire network to behave as a linear dynamical system, with sparsity constraints imposed by the network topology. We demonstrate that with observer style updates, the WCN's robustness to link failures is substantially improved. Furthermore, we show how to design a WCN that can maintain stability even in cases of node failures. We also address the problem of WCN synthesis with guaranteed optimal performance of the plant, with respect to standard cost functions. We extend the synthesis procedure to deal with continuous-time plants and demonstrate how the WCN can be used on a practical, industrial application, using a process-in-the-loop setup with real hardware.

Cooperation between multiple autonomous vehicles requires inter-vehicle communication, which in many scenarios must be established over an ad-hoc wireless network. This paper proposes an optimization-based approach to the deployment of such mobile robotic networks. A primal-dual gradient descent algorithm jointly optimizes the steady-state positions of the robots based on the specification of a high-level task in the form of a potential field, and routes packets through the network to support the communication rates desired for the application. The motion planning and communication objectives are tightly coupled since the link capacities depend heavily on the relative distances between vehicles. The algorithm decomposes naturally into two components, one for position optimization and one for communication optimization, coupled via a set of Lagrange multipliers. Crucially and in contrast to previous work, our method can rely on on-line evaluation of the channel capacities during deployment instead of a prespecified model. In this case, a randomized sampling scheme along the trajectories allows the robots to implement the algorithm with minimal coordination overhead.

Bridging the gap between model-based design and platform-based implementation is one of the critical challenges for embedded software systems. In the context of embedded control systems that interact with an environment, a variety of errors due to quantization, delays, and scheduling policies may generate executable code that does not faithfully implement the model-based design. In this article, we show that the performance gap between the model-level semantics of linear dynamic controllers, for example, the proportional-integral-derivative (PID) controllers and their implementation-level semantics, can be rigorously quantified if the controller implementation is executed on a predictable time-triggered architecture. Our technical approach uses lifting techniques for periodic time-varying linear systems in order to compute the exact error between the model semantics and the execution semantics. Explicitly computing the impact of the implementation on overall system performance allows us to compare and partially order different implementations with various scheduling or timing characteristics.

We investigate a state feedback Linear Quadratic Regulation problem with a constraint on the number of actuation signals that can be updated simultaneously. Such a constraint arises for example in networked and embedded control systems, due to limited communication and computation capabilities. Following recent results on the dual problem of scheduling Kalman filters, we first develop a bound on the achievable performance that can be computed efficiently by semidefinite programming. This bound can be approached arbitrarily closely by an analog periodic controller that can switch between control inputs arbitrarily fast. We then discuss implementation issues on digital platforms, i.e., the discretization of the analog controller in the presence of a relatively fast but finite sampling rate.

Control networks are based on time-triggered wireless substrates for industrial automation control, such as the WirelessHART and Honeywell's OneWireless. Control networks have fundamental differences over their sensor network counterparts as they also include actuation and the physical dynamics. A great challenge in such systems is understanding cross-cutting interfaces between computing systems, control systems, sensor networks, and time-triggered communications.

We examine the problem of reliable networked control when the communication channel between the controller and the actuator periodically drops packets and is faulty (i.e., corrupts/alters data). We first examine the use of a standard triple modular redundancy scheme (where the control input is sent via three independent channels) with majority voting to achieve mean square stability. While such a scheme is able to tolerate a single faulty channel when there are no packet drops, we show that the presence of lossy channels prevents a simple majority-voting approach from stabilizing the system. Moreover, the number of redundant channels that are required in order to maintain stability under majority voting increases with the probability of packet drops. We then propose the use of a reputation management scheme to overcome this problem, where each channel is assigned a reputation score that predicts its potential accuracy based on its past behavior. The reputation system builds on the majority voting scheme and improves the overall probability of applying correct (stabilizing) inputs to the system. Finally, we provide analytical conditions on the probabilities of packet drops and corrupted control inputs under which mean square stability can be maintained, generalizing existing results on stabilization under packet drops.

For such biomedical applications as single cell manipulation and targeted delivery of chemicals, it is important to fabricate microstructures that can be powered and controlled without a tether in fluidic environments. In this work, we describe the construction and operation of micronsized, biocompatible ferromagnetic microtransporters driven by external magnetic fields capable of exerting forces at the pico Newton scale. We develop microtransporters using a simple, single step micro fabrication technique that allows us to produce large numbers in the same step. We also fabricate microgels to deliver drugs. We demonstrate that the microtransporters can be navigated to separate individual targeted cells with micron-scale precision, and deliver microgels without disturbing the cells in the neighborhood and the local microenvironment.

Peak power consumption of buildings in large facilities like hospitals and universities becomes a big issue because peak prices are much higher than normal rates. During a power demand surge an automated power controller of a building may need to schedule ON and OFF different environment actuators such as heaters and air quality control while maintaining the state variables such as temperature or air quality of any room within comfortable ranges. The green scheduling problem asks whether a scheduling policy is possible for a system and what is the necessary and sufficient condition for systems to be feasible. In this paper we study the feasibility of the green scheduling problem for HVAC(Heating, Ventilating, and Air Conditioning) systems which are approximated by a discrete-time model with constant increasing and decreasing rates of the state variables. We first investigate the systems consisting of two tasks and find the analytical form of the necessary and sufficient conditions for such systems to be feasible under certain assumptions. Then we present our algorithmic solution for general systems of more than 2 tasks. Given the increasing and decreasing rates of the tasks, our algorithm returns a subset of the state space such that the system is feasible if and only if the initial state is in this subset. With the knowledge of that subset, a scheduling policy can be computed on the fly as the system runs, with the flexibility to add power-saving, priority-based or fair sub-policies.

We provide a theoretical framework for controlling graph connectivity in mobile robot networks. We discuss proximity-based communication models composed of disk-based or uniformly-fading-signal-strength communication links. A graph-theoretic definition of connectivity is provided, as well as an equivalent definition based on algebraic graph theory, which employs the adjacency and Laplacian matrices of the graph and their spectral properties. Based on these results, we discuss centralized and distributed algorithms to maintain, increase, and control connectivity in mobile robot networks. The various approaches discussed in this paper range from convex optimization and subgradient-descent algorithms, for the maximization of the algebraic connectivity of the network, to potential fields and hybrid systems that maintain communication links or control the network topology in a least restrictive manner. Common to these approaches is the use of mobility to control the topology of the underlying communication network. We discuss applications of connectivity control to multirobot rendezvous, flocking and formation control, where so far, network connectivity has been considered an assumption.

We present a Monte-Carlo optimization technique for finding inputs to a system that falsify a given Metric Temporal Logic (MTL) property. Our approach performs a random walk over the space of inputs guided by a robustness metric defined by the MTL property. Robustness can be used to guide our search for a falsifying trajectory by exploring trajectories with smaller robustness values. We show that the notion of robustness can be generalized to consider hybrid system trajectories. The resulting testing framework can be applied to non-linear hybrid systems with external inputs. We show through numerous experiments on complex systems that using our framework can help automatically falsify properties with more consistency as compared to other means such as uniform sampling.

This paper describes the synthesis of correct robot control from high-level tasks that include non-projective locative prepositions. Here, locative prepositions such as `near' and `between' are used to refer to regions in the robot's workspace and are part of a high-level task description such as “Always stay near room 1” or “Visit the area between room 2 and room 3”. These prepositions induce a discrete abstraction of the workspace which, together with the rest of the task, is used to synthesize a correct-by-construction robot controller such that the robot is guaranteed to behave as expected, if the task is feasible. This work presents an important step towards allowing linguistic control of robots that is both intuitive and provably correct.

In this paper, we propose an optimization-based framework for path planning for multiple robots in presence of obstacles. The objective is to find multiple fixed length paths for multiple robots that satisfy the following constraints: (i) bounded curvature, (ii) obstacle avoidance, (iii) and collision avoidance. First, we formulate a relaxation of the path planning problem using polygonal approximations. We show that path planning problem for multiple robots under various constraints and missions, such as curvature and obstacle avoidance constraints as well as rendezvous and maximal total area coverage, can be cast as a nonconvex optimization problem. Then, we propose an alternative dual formulation that results in no duality gap. We show that the alternative dual function can be interpreted as minimum potential energy of a multi-particle system with discontinuous spring-like forces. Finally, we show that using the proposed duality-based framework, an approximation of the minimal length path planning problem (also known as Dubins' problem) in presence of obstacles can be solved efficiently using primal-dual interior-point methods.

In this paper, we describe how signaling networks and actuation in bacterial cells and biomolecular networks of bacteria can be used to develop an integrated micro-bio-robotic system. SU8 microstructures blotted with swarmer cells of Serratia Marcescens in a monolayer are propelled by the bacteria in the absence of any environmental stimulus. We call such microstructures with bacteria Micro Bio Robots (MBRs) and the uncontrolled motion in the absence of stimuli self actuation. Our paper has two primary contributions. First, we demonstrate the control of MBRs using self-actuation, DC electric fields and ultra-violet radiation, and develop experimentally validated mathematical model for the MBRs. This model allows us to use self-actuation and electrokinetic actuation to steer the MBR to any position and orientation in a planar micro channel. Second, we describe the development of biosensors for the MBRs. This is done by attaching genetically engineered Escherichia coli cells that are capable of sensing nonmetabolizable lactose analog methyl-β-D-thiogalactoside (TMG). We describe the fabrication process for MBRs and show experimental results demonstrating sensing, actuation and control.

In this paper, we propose a path planning method for nonholonomic multi-vehicle system in presence of moving obstacles. The objective is to find multiple fixed length paths for multiple vehicles with the following properties: (i) bounded curvature (ii) obstacle avoidant (iii) collision free. Our approach is based on polygonal approximation of a continuous curve. Using this idea, we formulate an arbitrarily fine relaxation of the path planning problem as a nonconvex feasibility optimization problem. Then, we propound a nonsmooth dynamical systems approach to find feasible solutions of this optimization problem. It is shown that the trajectories of the nonsmooth dynamical system always converge to some equilibria that correspond to the set of feasible solutions of the relaxed problem. The proposed framework can handle more complex mission scenarios for multi-vehicle systems such as rendezvous and area coverage.

This paper presents a systematic analysis of the motion of microscale structures actuated by flagellated bacteria. We perform the study both experimentally and theoretically. We use a blotting procedure to attach flagellated bacteria to a buoyancy-neutral plate called a microbarge. The motion of the plate depends on the distribution of the cells on the plate and the stimuli from the environment. We construct a stochastic mathematical model for the system, based on the assumption that the behavior of each bacterium is random and independent of that of its neighbors. The main finding of the paper is that the motion of the barge plus bacteria system is a function of a very small set of parameters. This reduced-dimensional model can be easily estimated using experimental data. We show that the simulation results obtained from the model show an excellent match with the experimentally-observed motion of the barge.

We propose a mathematical framework, inspired by the Wireless HART specification, for modeling and analyzing multi-hop communication networks. The framework is designed for systems consisting of multiple control loops closed over a multi-hop communication network. We separate control, topology, routing, and scheduling and propose formal syntax and semantics for the dynamics of the composed system. The main technical contribution of the paper is an explicit translation of multi-hop control networks to switched systems. We describe a Mathematica notebook that automates the translation of multihop control networks to switched systems, and use this tool to show how techniques for analysis of switched systems can be used to address control and networking co-design challenges.

This paper provides a frameworkto automaticallygenerate a hybrid controller thatguaranteesthat the robot can achieve its task when a robot model, a class of admissible environments, and a high-level task or behavior for the robot are provided. The desired task specifications, which are expressed in a fragment of linear temporal logic (LTL), can capture complex robot behaviors such as search and rescue, coverage, and collision avoidance. In addition, our framework explicitly captures sensor specifications that depend on the environment with which the robot is interacting, which results in a novel paradigm for sensor-based temporal-logic-motion planning. As one robot is part of the environment of another robot, our sensor-based framework very naturally captures multirobot specifications in a decentralized manner. Our computational approach is based on first creating discrete controllers satisfying specific LTL formulas. If feasible, the discrete controller is then used to guide the sensor-based composition of continuous controllers, which results in a hybrid controller satisfying the high-level specification but only if the environment is admissible.

This paper deals with vision-based localization for leader–follower formation control. Each unicycle robot is equipped with a panoramic camera that only provides the view angle to the other robots. The localization problem is studied using a new observability condition valid for general nonlinear systems and based on the extended output Jacobian. This allows us to identify those robot motions that preserve the system observability and those that render it nonobservable. The state of the leader–follower system is estimated via the extended Kalman filter, and an input-state feedback control law is designed to stabilize the formation. Simulations and real-data experiments confirm the theoretical results and show the effectiveness of the proposed formation control.

Distributed task assignment for multiple agents raises fundamental and novel problems in control theory and robotics. A new challenge is the development of distributed algorithms that dynamically assign tasks to multiple agents, not relying on a priori assignment information. We address this challenge using market-based coordination protocols where the agents are able to bid for task assignment with the assumption that every agent has knowledge of the maximum number of agents that any given task can accommodate. We show that our approach always achieves the desired assignment of agents to tasks after exploring at most a polynomial number of assignments, dramatically reducing the combinatorial nature of discrete assignment problems. We verify our algorithm through both simulation and experimentation on a team of non-holonomic robots performing distributed formation stabilization and group splitting and merging.

Distributed motion planning of multiple agents raises fundamental and novel problems in control theory and robotics. In particular, in applications such as coverage by mobile sensor networks or multiple target tracking, a great new challenge is the development of motion planning algorithms that dynamically assign targets or destinations to multiple homogeneous agents, not relying on any a priori assignment of agents to destinations. In this paper, we address this challenge using two novel ideas. First, distributed multidestination potential fields are developed that are able to drive every agent to any available destination. Second, nearest neighbor coordination protocols are developed ensuring that distinct agents are assigned to distinct destinations. Integration of the overall system results in a distributed, multiagent, hybrid system for which we show that the mutual exclusion property of the final assignment is guaranteed for almost all initial conditions. Furthermore, we show that our dynamic assignment algorithm will converge after exploring at most a polynomial number of assignments, dramatically reducing the combinatorial nature of purely discrete assignment problems. Our scalable approach is illustrated with nontrivial computer simulations.

Control of mobile networks raises fundamental and novel problems in controlling the structure of the resulting dynamic graphs. In particular, in applications involving mobile sensor networks and multiagent systems, a great new challenge is the development of distributed motion algorithms that guarantee connectivity of the overall network. Motivated by the inherently discrete nature of graphs as combinatorial objects, we address this challenge using a key control decomposition. First, connectivity control of the network structure is performed in thediscretespace of graphs and relies on local estimates of the network topology used, along with algebraic graph theory, to verify link deletions with respect to connectivity. Tie breaking, when multiple such link deletions can violate connectivity, is achieved by means of gossip algorithms and distributed market-based control. Second, motion control is performed in thecontinuousconfiguration space, where nearest-neighbor potential fields are used to maintain existing links in the network. Integration of the earlier controllers results in a distributed, multiagent, hybrid system, for which we show that the resulting motion always ensures connectivity of the network, while it reconfigures toward certain secondary objectives. Our approach can also account for communication time delays as well as collision avoidance and is illustrated in nontrivial computer simulations.

Classical path planning does not address many of the challenges of robotic systems subject to differential constraints. While there have been many recent efforts to develop motion planning algorithms for systems with differential constraints (MPD), very little has been said about the existence of exact algorithms. In other words, the decidability of MPD problems is still an open question. In this paper, we propose a partial answer to this question limiting ourselves to special cases where the trajectory functions of the systems under the finite-dimensional piecewise-continuous controls have a closed-form polynomial formulation. We define an abstract formulation for the MPD problem based on the concept of a control space. We provide an incremental decision algorithm to answer the decidability question and present sufficient conditions for problems to which this algorithm can be applied. Decidability results for several non trivial MPD problems are presented. For example, we show that the question of existence of a trajectory for a Dubin's car with a polygonal rigid body between two specified positions and orientations in a polygonal environment with a fixed and finite number of discontinuities in curvature is decidable.

Given a robot model and a class of admissible environments, this paper provides a framework for automatically and verifiably composing controllers that satisfy high level task specifications expressed in suitable temporal logics. The desired task specifications can express complex robot behaviors such as search and rescue, coverage, and collision avoidance. In addition, our framework explicitly captures sensor specifications that depend on the environment with which the robot is interacting, resulting in a novel paradigm for sensor-based temporal logic motion planning. As one robot is part of the environment of another robot, our sensor-based framework very naturally captures multi-robot specifications. Our computational approach is based on first creating discrete controllers satisfying so-called general reactivity formulas. If feasible, the discrete controller is then used in order to guide the sensor-based composition of continuous controllers resulting in a hybrid controller satisfying the high level specification, but only if the environment is admissible.

This paper focuses on leader-follower formations of mobile robots equipped with panoramic cameras and extend earlier works in the literature addressing both the vision-based localization and control problems. First, a new sufficient analytical condition for localizability is proved and used to shed light on the geometrical meaning of formation localization using uncalibrated vision sensors, here performed with the unscented Kalman filter. Second, we design a feedback control law based on dynamic extension in order to extend the applicability of our control scheme also to the case of distant robots.

Distributed motion planning of multiple agents raises fundamental and novel problems in control theory and robotics. Recently, one such great challenge has been the development of motion planning algorithms that dynamically assign targets or destinations to multiple homogeneous agents, not relying on any a priori assignment of agents to destinations. In this paper, we address this challenge using two novel ideas. First, we develop distributed multi-destination potential fields able to drive every agent to any available destination for almost all initial conditions. Second, we propose sensor-based coordination protocols that ensure that distinct agents are assigned to distinct destinations. Integration of the overall system results in a distributed, multi-agent, hybrid system for which we show that the mutual exclusion property of the final assignment is guaranteed for almost all initial conditions. Moreover, we show that our dynamic assignment algorithm converges after exploring at most a polynomial number of assignments, dramatically reducing the combinatorial nature of purely discrete assignment problems. Our scalable approach is illustrated with nontrivial computer simulations.

What would it be like if we could give our robot high level commands and it would automatically execute them in a verifiably correct fashion in dynamically changing environments? This work demonstrates a method for generating continuous feedback control inputs that satisfy high-level specifications. Using a collection of continuous local feedback control policies in concert with a synthesized discrete automaton, this paper demonstrates the approach on an Ackermann-steered vehicle that satisfies the command "drive around until you find an empty parking space, then park." The system reacts to changing environmental conditions using only local information, while guaranteeing the correct high level behavior. The local policies consider the vehicle body shape as well as bounds on drive and steering velocities. The discrete automaton that invokes the local policies guarantees executions that satisfy the high-level specification based only on information about the current availability of the nearest parking space. This paper also demonstrates coordination of two vehicles using the approach.

Recently, Linear Temporal Logic (LTL) has been successfully applied to high-level task and motion planning problems for mobile robots. One of the main attributes of LTL is its close relationship with fragments of natural language. In this paper, we take the first steps toward building a natural language interface for LTL planning methods with mobile robots as the application domain. For this purpose, we built a structured English language which maps directly to a fragment of LTL.

The control of mobile networks of multiple agents raises fundamental and novel problems in controlling the structure of the resulting dynamic graphs. In this paper, we consider the problem of controlling a network of agents so that the resulting motion always preserves the connectivity property of the network. In particular, the connectivity condition is translated to differentiable constraints on individual agent motion by considering the dynamics of the Laplacian matrix and its spectral properties. Artificial potential fields are then used to drive the agents to configurations away from the undesired space of disconnected networks while avoiding collisions with each other. We conclude by illustrating a class of interesting problems that can be achieved while preserving connectivity constraints.

Bridging the gap between model-based design and platform-based implementation is one of the critical challenges for embedded software systems.In the context of embedded control systems that interact with an environment, a variety of errors due to quantization, delays, and scheduling policies may generate executable code that does not faithfully implement the model-based design. In this paper, we show that the performance gap between the model-level semantics of proportional-integral-derivative (PID) controllers and their implementation-level semantics can be rigorously quantified if the controller implementation is executed on a predictable time-triggered architecture. Our technical approach uses lifting techniques for periodic, time-varying linear systems in order to compute the exact error between the model semantics and the execution semantics. Explicitly computing the impact of the implementation on overall system performance allows us to compare and partially order different implementations with various scheduling or timing characteristics.

In this paper, we consider the problem of robot motion planning in order to satisfy formulas expressible in temporal logics. Temporal logics naturally express traditional robot specifications such as reaching a goal or avoiding an obstacle, but also more sophisticated specifications such as sequencing, coverage, or temporal ordering of different tasks. In order to provide computational solutions to this problem, we first construct discrete abstractions of robot motion based on some environmental decomposition. We then generate discrete plans satisfying the temporal logic formula using powerful model checking tools, and finally translate the discrete plans to continuous trajectories using hybrid control. Critical to our approach is providing formal guarantees ensuring that if the discrete plan satisfies the temporal logic formula, then the continuous motion also satisfies the exact same formula.

This paper concerns the problem of actively searching for and localizing ground features by a coordinated team of air and ground robotic sensor platforms. The approach taken builds on well known Decentralized Data Fusion (DDF) methodology. In particular, it brings together established representations developed for identification and linearized estimation problems to jointly address feature detection and localization. This provides transparent and scalable integration of sensor information from air and ground platforms. As in previous studies, an Information-theoretic utility measure and local control strategy drive the robots to uncertainty reducing team configurations. Complementary characteristics in terms of coverage and accuracy are revealed through analysis of the observation uncertainty for air and ground on-board cameras. Implementation results for a detection and localization example indicate the ability of this approach to scalably and efficiently realize such collaborative potential.

Mapping a set of feedback control components to executable code introduces errors due to a variety of factors such as discretization, computational delays, and scheduling policies. We argue that the gap between the model and the implementation can be rigorously quantified leading to predictability if the implementation is viewed as a sequence of control blocks executed in statically allocated time slots on a time-triggered platform. For linear systems controlled by linear controllers, we show how to calculate the exact error between the model-level semantics and the execution semantics of an implementation, allowing us to compare different implementations. The calculated error of different implementations is demonstrated using simulations on illustrative examples

In this paper, we present a computational framework for automatic generation of provably correct control laws for planar robots in polygonal environments. Using polygon triangulation and discrete abstractions, we map continuous motion planning and control problems, specified in terms of triangles, to computationally inexpensive problems on finite-state-transition systems. In this framework, discrete planning algorithms in complex environments can be seamlessly linked to automatic generation of feedback control laws for robots with underactuation constraints and control bounds. We focus on fully actuated kinematic robots with velocity bounds and (underactuated) unicycles with forward and turning speed bounds.

Formations of multi-agent systems, such as mobile robots, satellites and aircraft, require individual agents to satisfy their kinematic equations while constantly maintaining interagent constraints. In this paper, we develop a systematic framework for studying formation motion feasibility of multi-agent systems. In particular, we consider formations wherein all the agents cooperate to enforce the formation. We determine algebraic conditions that guarantee formation feasibility given the individual agent kinematics. Our framework also enables us to obtain lower dimensional control systems describing the group kinematics while maintaining all formation constraints.

Pursuit-evasion games in complex environments have a rich but disconnected history. Continuous or differential pursuit-evasion games focus on optimal control methods, and rely on very intense computations in order to provide locally optimal controls. Discrete pursuit-evasion games on graphs are algorithmically much more appealing, but completely ignore the physical dynamics of the players, resulting in possibly infeasible motions. In this paper, we present a provable and algorithmically feasible solution for visibility-based pursuit-evasion games in simply-connected environments, for players with dynamic constraints. This is achieved by combining two recent but distant results.

The paper investigates the stability properties of mobile agent formations which are based on leader following. We derive nonlinear gain estimates that capture how leader behavior affects the interconnection errors observed in the formation. Leader-to-formation stability (LFS) gains quantify error amplification, relate interconnection topology to stability and performance, and offer safety bounds for different formation topologies. Analysis based on the LFS gains provides insight to error propagation and suggests ways to improve the safety, robustness, and performance characteristics of a formation.

This paper describes the modeling language CHARON for modular design of interacting hybrid systems. The language allows specification of architectural as well as behavioral hierarchy and discrete as well as continuous activities. The modular structure of the language is not merely syntactic, but is exploited by analysis tools and is supported by a formal semantics with an accompanying compositional theory of refinement. We illustrate the benefits of CHARON in the design of embedded control software using examples from automated highways concerning vehicle coordination.

A new type of stability of leader follower formations is defined, based on input-to-state stability (ISS) properties of cascade interconnections. Formation ISS links leader input to internal state of the formation and characterizes the way this input affects performance. The effect of feedforward and feedback inter-agent communication is then investigated in this framework and it is indicated how the structure of interconnections and the amount of available information can affect stability performance.

A hybrid system is a dynamical system with both discrete and continuous state changes. For analysis purposes, it is often useful to abstract a system in a way that preserves the properties being analysed while hiding the details that are of no interest. We show that interesting classes of hybrid systems can be abstracted to purely discrete systems while preserving all properties that are definable in temporal logic. The classes that permit discrete abstractions fall into two categories. Either the continuous dynamics must be restricted, as is the case for timed and rectangular hybrid systems, or the discrete dynamics must be restricted, as is the case for o-minimal hybrid systems. In this paper, we survey and unify results from both areas.

We explore the use of distributed online motion planning algorithms for multiple mobile agents, in air traffic management systems (ATMS). The work is motivated by current trends in ATMS to move towards decentralized air traffic management, in which the aircraft operate in "free flight" mode instead of following prespecified "sky freeways". Conflict resolution strategies are an integral part of the free flight setting. The purpose of this paper is to obtain a set of manoeuvres to cover all possible conflict scenarios involving multiple agents. A distributed motion planning algorithm based on potential and vortex fields is used. While the algorithm is not always guaranteed to generate flyable trajectories, the obtained trajectories can serve as qualitative prototypes for coordination manoeuvres between multiple aircraft. The actual manoeuvres are generated by approximating these prototypes with trajectories made zip of straight lines and are further verified using hybrid verification techniques.