Integer-order calculus fails to capture the long-range dependence (LRD) and memory effects found in many complex systems. Fractional calculus addresses these gaps through fractional-order integrals and derivatives, but fractional-order dynamical systems pose substantial challenges in system identification and optimal control tasks. In this paper, we theoretically derive the optimal control via linear quadratic regulator (LQR) for fractional-order linear time-invariant (FOLTI) systems and develop an end-to-end deep learning framework based on this theoretical foundation. Our approach establishes a rigorous mathematical model, derives analytical solutions, and incorporates deep learning to achieve data-driven optimal control of FOLTI systems. Our key contributions include: (i) proposing a novel method for system identification and optimal control strategy in FOLTI systems, (ii) developing the first end-to-end data-driven learning framework, Fractional-Order Learning for Optimal Control (FOLOC), that learns control policies from observed trajectories, and (iii) deriving theoretical bounds on the sample complexity for learning accurate control policies under fractional-order dynamics. Experimental results indicate that our method accurately approximates fractional-order system behaviors without relying on Gaussian noise assumptions, pointing to promising avenues for advanced optimal control.

We provide a communication- and computation-efficient method for distributed submodular optimization in robot mesh networks. Submodularity is a property of diminishing returns that arises in active information gathering such as mapping, surveillance, and target tracking. Our method, Resource- Aware distributed Greedy (RAG), introduces a new distributed optimization paradigm that enables scalable and near-optimal action coordination. To this end, RAG requires each robot to make decisions based only on information received from and about their neighbors. In contrast, the current paradigms allow the relay of information about all robots across the network. As a result, RAG's decision-time scales linearly with the network size, while state-of-the-art near-optimal submodular optimization algorithms scale cubically. We also characterize how the designed mesh network topology affects RAG's approximation performance. Our analysis implies that sparser networks favor scalability without proportionally compromising approximation performance: while RAG's decision time scales linearly with network size, the gain in approximation performance scales sublinearly. We demonstrate RAG's performance in simulated scenarios of area detection with up to 45 robots, simulating realistic robot-to-robot (r2r) communication speeds such as the 0.25 Mbps speed of the Digi XBee 3 Zigbee 3.0. In the simulations, RAG enables real-time planning, up to three orders of magnitude faster than competitive near-optimal algorithms, while also achieving superior mean coverage performance. To enable the simulations, we extend the high-fidelity and photorealistic simulator AirSim by integrating a scalable collaborative autonomy pipeline to tens of robots and simulating r2r communication delays.

We provide an algorithm for the simultaneous sys- tem identification and model predictive control of nonlinear systems. The algorithm has finite-time near-optimality guarantees and asymptotically converges to the optimal (non-causal) controller. Particularly, the algorithm enjoys sublineardynamic regret, defined herein as the suboptimality against an optimal clairvoyant controller that knows how the unknown disturbances and system dynamics will adapt to its actions. The algorithm is self-supervised and applies to control-affine systems with unknown dynamics and disturbances that can be expressed in reproducing kernel Hilbert spaces. Such spaces can model external disturbances and modeling errors that can even be adaptive to the system's state and control input. For example, they can model wind and wave disturbances to aerial and marine vehicles, or inaccurate model parameters such as inertia of mechanical systems. We are motivated by the future of autonomy where robots will autonomously perform complex tasks despite real-world unknown disturbances such as wind gusts. The algorithm first generates random Fourier features that are used to approximate the unknown dynamics or disturbances. Then, it employs model predictive control based on the current learned model of the unknown dynamics (or disturbances). The model of the unknown dynamics is updated online using least squares based on the data collected while controlling the system. We validate our algorithm in both hardware experiments and physics-based simulations. The simulations include (i) a cart-pole aiming to maintain the pole upright despite inaccurate model parameters, and (ii) a quadrotor aiming to track reference trajectories despite unmodeled aerodynamic drag effects. The hardware experiments include a quadrotor aiming to track a circular trajectory despite unmodeled aerodynamic drag effects, ground effects, and wind disturbances. The code is open-sourced athttps://github.com/UM-iRaL/SSI-MPChttps://github.com/UM-iRaL/SSI-MPC.

Nonlinear estimation in robotics and vision is typically plagued with outliers due to wrong data association or incorrect detections from signal processing and machine learning methods. This article introduces two unifying formulations for outlier-robust estimation,generalized maximum consensus($\text{G}$-$\text{MC}$) andgeneralized truncated least squares($\text{G-TLS}$), and investigates fundamental limits, practical algorithms, and applications. Our first contribution is a proof that outlier-robust estimation isinapproximable:In the worst case, it is impossible to (even approximately) find the set of outliers, even with slower-than-polynomial-time algorithms (particularly, algorithms running inquasi-polynomialtime). As a second contribution, we review and extend two general-purpose algorithms. The first,adaptive trimming($\text{ADAPT}$), is combinatorial and is suitable for$\text{G}$-$\text{MC}$; the second,graduated nonconvexity($\text{GNC}$), is based on homotopy methods and is suitable for$\text{G-TLS}$. We extend$\text{ADAPT}$and$\text{GNC}$to the case where the user does not have prior knowledge of the inlier-noise statistics (or the statistics may vary over time) and is unable to guess a reasonable threshold to separate inliers from outliers (as the one commonly used in RANdom SAmple Consensus$(\text{RANSAC})$. We propose the firstminimally tunedalgorithms for outlier rejection, which dynamically decide how to separate inliers from outliers. Our third contribution is an evaluation of the proposed algorithms on robot perception problems: mesh registration, image-based object detection (shape alignment), and pose graph optimization.$\text{ADAPT}$and$\text{GNC}$execute in real time, are deterministic, outperform$\text{RANSAC}$, and are robust up to 80–90% outliers. Their minimally tuned versions also compare favorably with the state of the art, even though they do not rely on a noise bound for the inliers.

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.

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.

Spatial perception is the backbone of many robotics applications, and spans a broad range of research problems, including localization and mapping, point cloud alignment, and relative pose estimation from camera images. Robust spatial perception is jeopardized by the presence of incorrect data association, and in general, outliers. Although techniques to handle outliers do exist, they can fail in unpredictable manners (e.g., RANSAC, robust estimators), or can have exponential runtime (e.g., branch-and-bound). In this paper, we advance the state of the art in outlier rejection by making three contributions. First, we show that even a simple linear instance of outlier rejection is inapproximable: in the worst-case one cannot design a quasi-polynomial time algorithm that computes an approximate solution efficiently. Our second contribution is to provide the first per-instance sub-optimality bounds to assess the approximation quality of a given outlier rejection outcome. Our third contribution is to propose a simple general-purpose algorithm, named adaptive trimming, to remove outliers. Our algorithm leverages recently-proposed global solvers that are able to solve outlier-free problems, and iteratively removes measurements with large errors. We demonstrate the proposed algorithm on three spatial perception problems: 3D registration, two-view geometry, and SLAM. The results show that our algorithm outperforms several state-of-the-art methods across applications while being a general-purpose method.

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.