In modern process industries, data-driven models are important tools for real-time monitoring when key performance indicators are difficult to measure directly. While accurate predictions are essential, reliable uncertainty quantification (UQ) is equally critical for safety, reliability, and decision-making, but remains a major challenge in current data-driven approaches. In this work, we introduce a diffusion-based posterior sampling framework that inherently produces well-calibrated predictive uncertainty via faithful posterior sampling, eliminating the need for post hoc calibration. In extensive evaluations on synthetic distributions, the Raman-based phenylacetic acid soft sensor benchmark, and a real ammonia synthesis case study, our method achieves practical improvements over existing UQ techniques in both uncertainty calibration and predictive accuracy. These results highlight diffusion samplers as a principled and scalable paradigm for advancing uncertainty-aware modeling in industrial applications.

Human cognitive states, such as mental workload, play a pivotal role in decision making processes within human automation teams. Although subjective measures of mental workload can be obtained using standard questionnaires, such as the NASA-TLX, their administration is often impractical as it interferes with the primary tasks of the human operator. Therefore, it is of interest to estimate these subjective measures from less intrusive observations. Evidence suggests that mental workload is a dynamic process so incorporating historical measurements could reduce its estimation error. In addition, the estimation of operator performance in human automation teams is essential in optimizing task effectiveness and facilitating efficient resource allocation. In this work, we consider a scenario where a human and an automation solve binary classification tasks under time constraints. We present and compare different dynamic schemes to estimate the operator’s performance, i.e., classification accuracy, and its subjective ratings on subscales of the NASA-TLX questionnaire, which measure mental workload across multiple dimensions. These schemes differ in the information available for estimation. We test these schemes on data collected from a scenario, where a human and an automation perform a series of classification tasks for simulated mobile objects. Our analysis of the interaction data and the estimation schemes indicates that employing dynamic estimation for certain NASA-TLX subscale ratings leads to decreased estimation errors.

For many automated perception and decision tasks, state-of-the-art performance may be obtained by algorithms that are too complex for their behavior to be completely understandable or predictable by human users, e.g., because they employ large machine learning models. To integrate these algorithms into safety-critical decision and control systems, it is particularly important to develop methods that can promote trust into their decisions and help explore their failure modes. In this article, we combine the anchors methodology with Monte Carlo Tree Search to provide local model-agnostic explanations for the behaviors of a given black-box model making decisions by processing time-varying input signals. Our approach searches for descriptive explanations for these decisions in the form of properties of the input signals, expressed in Signal Temporal Logic, which are highly likely to reproduce the observed behavior. To illustrate the methodology, we apply it in simulations to the analysis of a hybrid (continuous-discrete) control system and a collision avoidance system for unmanned aircraft (ACAS Xu) implemented by a neural network.

This paper introduces a set of customizable and novel cost functions that enable the user to easily specify desirable robot formations, such as a "high-coverage" infrastructure-inspection formation, while maintaining high relative pose estimation accuracy. The overall cost function balances the need for the robots to be close together for good ranging-based relative localization accuracy and the need for the robots to achieve specific tasks, such as minimizing the time taken to inspect a given area. The formations found by minimizing the aggregated cost function are evaluated in a coverage path planning task in simulation and experiment, where the robots localize themselves and unknown landmarks using a simultaneous localization and mapping algorithm based on the extended Kalman filter. Compared to an optimal formation that maximizes ranging-based relative localization accuracy, these formations significantly reduce the time to cover a given area with minimal impact on relative pose estimation accuracy.

Ultra-wideband (UWB) systems are becoming increasingly popular as a means of inter-robot ranging and communication. A major constraint associated with UWB is that only one pair of UWB transceivers can range at a time to avoid interference, hence hindering the scalability of UWBbased localization. In this paper, a ranging protocol is proposed that allows all robots to passively listen on neighbouring communicating robots without any hierarchical restrictions on the role of the robots. This is utilized to allow each robot to obtain more range measurements and to broadcast preintegrated inertial measurement unit (IMU) measurements for relative extended pose state estimation directly on$SE_{2}(3)$. Consequently, a simultaneous clock-synchronization and relative-pose estimator (CSRPE) is formulated using an on-manifold extended Kalman filter (EKF) and is evaluated in simulation using Monte-Carlo runs for up to 7 robots. The ranging protocol is implemented in C on custom-made UWB boards fitted to 3 quadcopters, and the proposed filter is evaluated over multiple experimental trials, yielding up to 48% improvement in localization accuracy.

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Ultra-Wideband (UWB) systems are becoming increasingly popular for indoor localization, where range measurements are obtained by measuring the time-of-flight of radio signals. However, the range measurements typically suffer from a systematic error or bias that must be corrected for high-accuracy localization. In this paper, a ranging protocol is proposed alongside a robust and scalable antenna-delay calibration procedure to accurately and efficiently calibrate antenna delays for many UWB tags. Additionally, the bias and uncertainty of the measurements are modelled as a function of the received-signal power. The full calibration procedure is presented using experimental training data of 3 aerial robots fitted with 2 UWB tags each, and then evaluated on 2 test experiments. A localization problem is then formulated on the experimental test data, and the calibrated measurements and their modelled uncertainty are fed into an extended Kalman filter (EKF). The proposed calibration is shown to yield an average of 46% improvement in localization accuracy. Lastly, the paper is accompanied by an open-source UWB-calibration Python library, which can be found at https://github.com/decargroup/uwb_calibration.

In robotic networks relying on noisy range measurements between agents for cooperative localization, the achievable positioning accuracy strongly depends on the network geometry. This motivates the problem of planning robot trajectories in such multirobot systems in a way that maintains high localization accuracy. We present potential-based planning methods, where localizability potentials are introduced to characterize the quality of the network geometry for cooperative position estimation. These potentials are based on Cramér Rao lower bounds (CRLB) and provide a theoretical lower bound on the error covariance achievable by any unbiased position estimator. In the process, we establish connections between CRLBs and the theory of graph rigidity, which has been previously used to plan the motion of robotic networks. We develop decentralized deployment algorithms appropriate for large networks, and we use equality-constrained CRLBs to extend the concept of localizability to scenarios where additional information about the relative positions of the ranging sensors is known. We illustrate the resulting robot deployment methodology through simulated examples and an experiment.

Accurate and real-time position estimates are cru-cial for mobile robots. This work focuses on ranging-based positioning systems, which rely on distance measurements between known points, called anchors, and a tag to localize. The topology of the network formed by the anchors strongly influences the tag's localizability, i.e., its ability to be accurately localized. Here, the tag and some anchors are supposed to be carried by robots, which allows enhancing the positioning accuracy by planning the anchors' motions. We leverage Bayesian Cramer-Rao Lower Bounds (CRLBs) on the estimates' covariance in order to quantify the tag's localizability. This class of CRLBs can capture prior information on the tag's position and take it into account when deploying the anchors. We propose a method to decrease a potential function based on the Bayesian CRLB in order to maintain the localizability of the tag while having some prior knowledge about its position distribution. Then, we present a new experiment highlighting the link between the localizability potential and the precision expected in practice. Finally, two real-time anchor motion planners are demonstrated with ranging measurements in the presence or absence of prior information about the tag's position.

Position estimation in Multi-Robot Systems (MRS) relies on relative angle or distance measurements between the robots, which generally deteriorate as distances increase. Moreover, the localization accuracy is strongly influenced both by the quality of the raw measurements but also by the overall geometry of the network. In this paper, we design a cost function that accounts for these two issues and can be used to develop motion planning algorithms that optimize the localizability in MRS, i.e., the ability of individual robots to localize themselves accurately. This cost function is based on computing new Cramér Rao Lower Bounds characterizing the achievable positioning performance with range and angle measurements that deteriorate with increasing distances. We describe a gradient-based motion-planning algorithm for MRS deployment that can be implemented in a distributed manner, as well as a non-myopic strategy to escape local minima. Finally, we test the proposed methodology experimentally for range measurements obtained using ultra-wide band transceivers and illustrate the improvements resulting from leveraging the more accurate measurement model in the robot placement algorithms.

In multi-robot missions, relative position and attitude information between robots is valuable for a variety of tasks such as mapping, planning, and formation control. In this paper, the problem of estimating relative poses from a set of inter-robot range measurements is investigated. Specifically, it is shown that the estimation accuracy is highly dependent on the true relative poses themselves, which prompts the desire to find multi-robot formations that provide the best estimation performance. By direct maximization of Fischer information, it is shown in simulation and experiment that large improvements in estimation accuracy can be obtained by optimizing the formation geometry of a team of robots.

Ranging systems can provide inexpensive, accurate, energy- and computationally-efficient navigation solutions for mobile robots. This work focuses on location and pose estimation in ranging networks composed of anchors with known positions as well as mobile robots modeled as rigid bodies, each carrying multiple tags to localize. Noisy distance measurements can be obtained between a subset of the nodes (anchors and tags), and the robots can move in order to improve the accuracy of the localization process, which depends on the geometry of the network. We propose a method to find trajectories for the robots leading to configurations that locally optimize this localization accuracy. These trajectories minimize a cost function based on the constrained Cramér-Rao Lower Bound (CRLB), where the constraints capture the information about the known distances between tags carried by the same robot. A primal-dual optimization scheme aims to enforce these distance constraints between tags in the motion planner as well. An important feature of the approach is that the gradient terms necessary to plan the motion can be computed essentially in closed form, thereby simplifying the implementation. We compare the proposed method to a naive two-stage algorithm that optimizes the positions and orientations of the robots independently. Simulation results illustrate the benefits of using the constrained optimization approach.

In mixed-initiative systems where teams of humans and automated agents collaborate to perform decision-making tasks, determining factors of joint performance include human cognitive workload and the level of trust placed by the operators in the automation. Both workload and trust are dynamic variables that change over time based on current task allocation and on the result of past interactions. In this paper, we propose a methodology leveraging quantitative models of trust and workload to automatically and dynamically suggest efficient task allocations in mixed human-machine systems. Our approach is based on a Markov decision process framework and is presented for concreteness in the context of a human-machine team performing repeated binary decision-making tasks. Simulation results show the emergence of interesting automation behaviors such as seeking trust, attempting to repair trust after an error and adjusting human workload for optimal performance. Overall, the human-aware dynamic task allocation strategy shows the potential of significant team performance improvement compared to a static task distribution, even in the presence of significant errors in the trust and workload models used.

The ability to accurately measure signal time-of-flight between ultra-wideband (UWB) wireless communication transceivers, even in multipath environments, makes this technology ideally suited to develop ranging-based positioning systems, especially for indoor applications where GPS signals are not available. In recent years, low-cost commercial UWB transceivers have become more easily available and increasingly used to develop custom robot positioning systems. In this paper, we focus in particular on positioning techniques requiring the synchronization of base stations such as Time of Arrival (TOA) and Time Difference of Arrival (TDOA). We present a protocol based on Kalman filtering for simultaneous synchronization of multiple UWB base stations and positioning of an arbitrary number of passive UWB receivers. We illustrate experimentally using our protocol and an EKF-based navigation system design the level of accuracy achievable with small low-power UWB modules for mobile robot positioning. We discuss in details measurement errors and system tuning issues applicable to popular commercial UWB transceivers.

This paper presents a strategy to guide a mobile ground robot equipped with a camera or depth sensor, in order to autonomously map the visible part of a bounded 3-D structure. We describe motion planning algorithms that determine appropriate successive viewpoints and attempt to fill holes automatically in a point cloud produced by the sensing and perception layer. The emphasis is on accurately reconstructing a 3-D model of a structure of moderate size rather than mapping large open environments, with applications for example in architecture, construction, and inspection. The proposed algorithms do not require any initialization in the form of a mesh model or a bounding box, and the paths generated are well adapted to situations where the vision sensor is used simultaneously for mapping and for localizing the robot, in the absence of additional absolute positioning system. We analyze the coverage properties of our policy, and compare its performance with the classic frontier-based exploration algorithm. We illustrate its efficacy for different structure sizes, levels of localization accuracy, and range of the depth sensor, and validate our design on a real-world experiment.

Road traffic estimation systems can rely nowadays on an increasing number and variety of sensors and data sources to provide better coverage and accuracy, from standard static detectors to, more recently, location traces obtained possibly from individual drivers' smartphones. Motivated by privacy concerns raised by such systems, this paper discusses a methodology for estimating the macroscopic traffic state (density, velocity) along a road segment in real-time, while providing formal differential privacy guarantees to the individual drivers, a state-of-the-art notion of privacy that protects against adversaries with arbitrary side-information. The impact of the privacy constraint on estimation performance is mitigated by the use of a nonlinear model of the traffic dynamics, fused with the sensor measurements via an Ensemble Kalman Filter, a classical method for data assimilation.

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.

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.

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.

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.