arXiv subjects

Vasileios Tzoumas

Publications and source records attributed to Vasileios Tzoumas.

At least 37 records · Page 2Linked to original sources

arXiv2023

Leveraging Untrustworthy Commands for Multi-Robot Coordination in Unpredictable Environments: A Bandit Submodular Maximization Approach

We study the problem of multi-agent coordination in unpredictable and partially-observable environments with untrustworthy external commands. The commands are actions suggested to the robots, and are untrustworthy in that their performance guarantees, if any, are unknown. Such commands may be generated by human operators or machine learning algorithms and, although untrustworthy, can often increase the robots' performance in complex multi-robot tasks. We are motivated by complex multi-robot tasks such as target tracking, environmental mapping, and area monitoring. Such tasks are often modeled as submodular maximization problems due to the information overlap among the robots. We provide an algorithm, Meta Bandit Sequential Greedy (MetaBSG), which enjoys performance guarantees even when the external commands are arbitrarily bad. MetaBSG leverages a meta-algorithm to learn whether the robots should follow the commands or a recently developed submodular coordination algorithm, Bandit Sequential Greedy (BSG) [1], which has performance guarantees even in unpredictable and partially-observable environments. Particularly, MetaBSG asymptotically can achieve the better performance out of the commands and the BSG algorithm, quantifying its suboptimality against the optimal time-varying multi-robot actions in hindsight. Thus, MetaBSG can be interpreted as robustifying the untrustworthy commands. We validate our algorithm in simulated scenarios of multi-target tracking.

eess.SY↗

arXiv2023

Safe Non-Stochastic Control of Linear Dynamical Systems

We study the problem of \textit{safe control of linear dynamical systems corrupted with non-stochastic noise}, and provide an algorithm that guarantees (i) zero constraint violation of convex time-varying constraints, and (ii) bounded dynamic regret, \ie bounded suboptimality against an optimal clairvoyant controller that knows the future noise a priori. The constraints bound the values of the state and of the control input such as to ensure collision avoidance and bounded control effort. We are motivated by the future of autonomy where robots will safely perform complex tasks despite real-world unpredictable disturbances such as wind and wake disturbances. To develop the algorithm, we capture our problem as a sequential game between a linear feedback controller and an adversary, assuming a known upper bound on the noise's magnitude. Particularly, at each step $t=1,\ldots, T$, first the controller chooses a linear feedback control gain $K_t \in \calK_t$, where $\calK_t$ is constructed such that it guarantees that the safety constraints will be satisfied; then, the adversary reveals the current noise $w_t$ and the controller suffers a loss $f_t(K_t)$ -- \eg $f_t$ represents the system's tracking error at $t$ upon the realization of the noise. The controller aims to minimize its cumulative loss, despite knowing $w_t$ only after $K_t$ has been chosen. We validate our algorithm in simulated scenarios of safe control of linear dynamical systems in the presence of bounded noise

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arXiv2023

Bandit Submodular Maximization for Multi-Robot Coordination in Unpredictable and Partially Observable Environments

We study the problem of multi-agent coordination in unpredictable and partially observable environments, that is, environments whose future evolution is unknown a priori and that can only be partially observed. We are motivated by the future of autonomy that involves multiple robots coordinating actions in dynamic, unstructured, and partially observable environments to complete complex tasks such as target tracking, environmental mapping, and area monitoring. Such tasks are often modeled as submodular maximization coordination problems due to the information overlap among the robots. We introduce the first submodular coordination algorithm with bandit feedback and bounded tracking regret -- bandit feedback is the robots' ability to compute in hindsight only the effect of their chosen actions, instead of all the alternative actions that they could have chosen instead, due to the partial observability; and tracking regret is the algorithm's suboptimality with respect to the optimal time-varying actions that fully know the future a priori. The bound gracefully degrades with the environments' capacity to change adversarially, quantifying how often the robots should re-select actions to learn to coordinate as if they fully knew the future a priori. The algorithm generalizes the seminal Sequential Greedy algorithm by Fisher et al. to the bandit setting, by leveraging submodularity and algorithms for the problem of tracking the best action. We validate our algorithm in simulated scenarios of multi-target tracking.

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arXiv2023

Safe Control of Partially-Observed Linear Time-Varying Systems with Minimal Worst-Case Dynamic Regret

We present safe control of partially-observed linear time-varying systems in the presence of unknown and unpredictable process and measurement noise. We introduce a control algorithm that minimizes dynamic regret, i.e., that minimizes the suboptimality against an optimal clairvoyant controller that knows the unpredictable future a priori. Specifically, our algorithm minimizes the worst-case dynamic regret among all possible noise realizations given a worst-case total noise magnitude. To this end, the control algorithm accounts for three key challenges: safety constraints; partially-observed time-varying systems; and unpredictable process and measurement noise. We are motivated by the future of autonomy where robots will autonomously perform complex tasks despite unknown and unpredictable disturbances leveraging their on-board control and sensing capabilities. To synthesize our minimal-regret controller, we formulate a constrained semi-definite program based on a System Level Synthesis approach for partially-observed time-varying systems. We validate our algorithm in simulated scenarios, including trajectory tracking scenarios of a hovering quadrotor collecting GPS and IMU measurements. Our algorithm is observed to have better performance than either or both the $\mathcal{H}_2$ and $\mathcal{H}_\infty$ controllers, demonstrating a Best of Both Worlds performance.

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arXiv2023

Efficient Online Learning with Memory via Frank-Wolfe Optimization: Algorithms with Bounded Dynamic Regret and Applications to Control

Projection operations are a typical computation bottleneck in online learning. In this paper, we enable projection-free online learning within the framework of Online Convex Optimization with Memory (OCO-M) -- OCO-M captures how the history of decisions affects the current outcome by allowing the online learning loss functions to depend on both current and past decisions. Particularly, we introduce the first projection-free meta-base learning algorithm with memory that minimizes dynamic regret, i.e., that minimizes the suboptimality against any sequence of time-varying decisions. We are motivated by artificial intelligence applications where autonomous agents need to adapt to time-varying environments in real-time, accounting for how past decisions affect the present. Examples of such applications are: online control of dynamical systems; statistical arbitrage; and time series prediction. The algorithm builds on the Online Frank-Wolfe (OFW) and Hedge algorithms. We demonstrate how our algorithm can be applied to the online control of linear time-varying systems in the presence of unpredictable process noise. To this end, we develop a controller with memory and bounded dynamic regret against any optimal time-varying linear feedback control policy. We validate our algorithm in simulated scenarios of online control of linear time-invariant systems.

cs.LG↗

arXiv2023

Online Submodular Coordination with Bounded Tracking Regret: Theory, Algorithm, and Applications to Multi-Robot Coordination

We enable efficient and effective coordination in unpredictable environments, i.e., in environments whose future evolution is unknown a priori and even adversarial. We are motivated by the future of autonomy that involves multiple robots coordinating in dynamic, unstructured, and adversarial environments to complete complex tasks such as target tracking, environmental mapping, and area monitoring. Such tasks are often modeled as submodular maximization coordination problems. We introduce the first submodular coordination algorithm with bounded tracking regret, i.e., with bounded suboptimality with respect to optimal time-varying actions that know the future a priori. The bound gracefully degrades with the environments' capacity to change adversarially. It also quantifies how often the robots must re-select actions to "learn" to coordinate as if they knew the future a priori. The algorithm requires the robots to select actions sequentially based on the actions selected by the previous robots in the sequence. Particularly, the algorithm generalizes the seminal Sequential Greedy algorithm by Fisher et al. to unpredictable environments, leveraging submodularity and algorithms for the problem of tracking the best expert. We validate our algorithm in simulated scenarios of target tracking.

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arXiv2022

Visual Navigation for Autonomous Vehicles: An Open-source Hands-on Robotics Course at MIT

This paper reports on the development, execution, and open-sourcing of a new robotics course at MIT. The course is a modern take on "Visual Navigation for Autonomous Vehicles" (VNAV) and targets first-year graduate students and senior undergraduates with prior exposure to robotics. VNAV has the goal of preparing the students to perform research in robotics and vision-based navigation, with emphasis on drones and self-driving cars. The course spans the entire autonomous navigation pipeline; as such, it covers a broad set of topics, including geometric control and trajectory optimization, 2D and 3D computer vision, visual and visual-inertial odometry, place recognition, simultaneous localization and mapping, and geometric deep learning for perception. VNAV has three key features. First, it bridges traditional computer vision and robotics courses by exposing the challenges that are specific to embodied intelligence, e.g., limited computation and need for just-in-time and robust perception to close the loop over control and decision making. Second, it strikes a balance between depth and breadth by combining rigorous technical notes (including topics that are less explored in typical robotics courses, e.g., on-manifold optimization) with slides and videos showcasing the latest research results. Third, it provides a compelling approach to hands-on robotics education by leveraging a physical drone platform (mostly suitable for small residential courses) and a photo-realistic Unity-based simulator (open-source and scalable to large online courses). VNAV has been offered at MIT in the Falls of 2018-2021 and is now publicly available on MIT OpenCourseWare (OCW).

cs.RO↗

arXiv2022

Distributed Attack-Robust Submodular Maximization for Multi-Robot Planning

In this paper, we design algorithms to protect swarm-robotics applications against sensor denial-of-service (DoS) 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 ones. Such applications are central in large-scale robotic applications, such as multi-robot motion planning for target tracking. But the current attack-robust algorithms are centralized. 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 cliques of robots. Then, the cliques optimize in parallel, independently of each other. We prove DRM achieves a close-to-optimal performance. We demonstrate DRM's performance in both Gazebo and MATLAB simulations, in scenarios of active target tracking with swarms of robots. In the simulations, DRM achieves computational speed-ups, being 1-2 orders faster than the centralized algorithms; yet, it nearly matches the tracking performance of the centralized counterparts. Since, DRM overestimates the number of attacks in each clique, in this paper we also introduce an Improved Distributed Robust Maximization (IDRM) algorithm. IDRM infers the number of attacks in each clique less conservatively than DRM by leveraging 3-hop neighboring communications. We verify IDRM improves DRM's performance in simulations.

cs.RO↗

arXiv2021

Outlier-Robust Estimation: Hardness, Minimally Tuned Algorithms, and Applications

Nonlinear estimation in robotics and vision is typically plagued with outliers due to wrong data association, or to incorrect detections from signal processing and machine learning methods. This paper introduces two unifying formulations for outlier-robust estimation, Generalized Maximum Consensus (G-MC) and Generalized Truncated Least Squares (G-TLS), and investigates fundamental limits, practical algorithms, and applications. Our first contribution is a proof that outlier-robust estimation is inapproximable: 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 in quasi-polynomial time). As a second contribution, we review and extend two general-purpose algorithms. The first, Adaptive Trimming (ADAPT), is combinatorial, and is suitable for G-MC; the second, Graduated Non-Convexity (GNC), is based on homotopy methods, and is suitable for G-TLS. We extend ADAPT and 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 RANSAC). We propose the first minimally tuned algorithms for outlier rejection, that 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. ADAPT and GNC execute in real-time, are deterministic, outperform 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.

cs.CV↗

arXiv2021

Resilient Active Information Acquisition with Teams of Robots

Emerging applications of collaborative autonomy, such as Multi-Target Tracking, Unknown Map Exploration, and Persistent Surveillance, require robots plan paths to navigate an environment while maximizing the information collected via on-board sensors. In this paper, 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 multi-robot planning against any number of attacks, which we call Resilient Active Information acquisitioN (RAIN). RAIN calls, in an online fashion, a Robust Trajectory Planning (RTP) subroutine which plans attack-robust control inputs over a look-ahead planning horizon. We quantify RTP's performance by bounding its suboptimality. We base our theoretical analysis on notions of curvature introduced in combinatorial optimization. We evaluate RAIN in three information acquisition scenarios: Multi-Target Tracking, Occupancy Grid Mapping, and Persistent Surveillance. The scenarios are simulated in C++ and a Unity-based simulator. In all simulations, RAIN runs 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 demonstrate RAIN's robustness and effectiveness against varying models of attacks (worst-case and random), as well as, varying replanning rates.

cs.RO↗

arXiv2020

Resilient Monotone Sequential Maximization

Applications in machine learning, optimization, and control require the sequential selection of a few system elements, such as sensors, data, or actuators, to optimize the system performance across multiple time steps. However, in failure-prone and adversarial environments, sensors get attacked, data get deleted, and actuators fail. Thence, traditional sequential design paradigms become insufficient and, in contrast, resilient sequential designs that adapt against system-wide attacks, deletions, or failures become important. In general, resilient sequential design problems are computationally hard. Also, even though they often involve objective functions that are monotone and (possibly) submodular, no scalable approximation algorithms are known for their solution. In this paper, we provide the first scalable algorithm, that achieves the following characteristics: system-wide resiliency, i.e., the algorithm is valid for any number of denial-of-service attacks, deletions, or failures; adaptiveness, i.e., at each time step, the algorithm selects system elements based on the history of inflicted attacks, deletions, or failures; and provable approximation performance, i.e., the algorithm guarantees for monotone objective functions a solution close to the optimal. We quantify the algorithm's approximation performance using a notion of curvature for monotone (not necessarily submodular) set functions. Finally, we support our theoretical analyses with simulated experiments, by considering a control-aware sensor scheduling scenario, namely, sensing-constrained robot navigation.

stat.ML↗

arXiv2020

Robust and Adaptive Sequential Submodular Optimization

Emerging applications of control, estimation, and machine learning, ranging from target tracking to decentralized model fitting, pose resource constraints that limit which of the available sensors, actuators, or data can be simultaneously used across time. Therefore, many researchers have proposed solutions within discrete optimization frameworks where the optimization is performed over finite sets. By exploiting notions of discrete convexity, such as submodularity, the researchers have been able to provide scalable algorithms with provable suboptimality bounds. In this paper, we consider such problems but in adversarial environments, where in every step a number of the chosen elements in the optimization is removed due to failures/attacks. Specifically, we consider for the first time a sequential version of the problem that allows us to observe the failures and adapt, while the attacker also adapts to our response. We call the novel problem Robust Sequential submodular Maximization (RSM). Generally, the problem is computationally hard and no scalable algorithm is known for its solution. However, in this paper we propose Robust and Adaptive Maximization (RAM), the first scalable algorithm. RAM runs in an online fashion, adapting in every step to the history of failures. Also, it guarantees a near-optimal performance, even against any number of failures among the used elements. Particularly, RAM has both provable per-instance a priori bounds and tight and/or optimal a posteriori bounds. Finally, we demonstrate RAM's near-optimality in simulations across various application scenarios, along with its robustness against several failure types, from worst-case to random.

math.OC↗

arXiv2020

Graduated Non-Convexity for Robust Spatial Perception: From Non-Minimal Solvers to Global Outlier Rejection

Semidefinite Programming (SDP) and Sums-of-Squares (SOS) relaxations have led to certifiably optimal non-minimal solvers for several robotics and computer vision problems. However, most non-minimal solvers rely on least-squares formulations, and, as a result, are brittle against outliers. While a standard approach to regain robustness against outliers is to use robust cost functions, the latter typically introduce other non-convexities, preventing the use of existing non-minimal solvers. In this paper, we enable the simultaneous use of non-minimal solvers and robust estimation by providing a general-purpose approach for robust global estimation, which can be applied to any problem where a non-minimal solver is available for the outlier-free case. To this end, we leverage the Black-Rangarajan duality between robust estimation and outlier processes (which has been traditionally applied to early vision problems), and show that graduated non-convexity (GNC) can be used in conjunction with non-minimal solvers to compute robust solutions, without requiring an initial guess. Although GNC's global optimality cannot be guaranteed, we demonstrate the empirical robustness of the resulting robust non-minimal solvers in applications, including point cloud and mesh registration, pose graph optimization, and image-based object pose estimation (also called shape alignment). Our solvers are robust to 70-80% of outliers, outperform RANSAC, are more accurate than specialized local solvers, and faster than specialized global solvers. We also propose the first certifiably optimal non-minimal solver for shape alignment using SOS relaxation.

cs.CV↗

arXiv2020

LQG Control and Sensing Co-Design

We investigate a Linear-Quadratic-Gaussian (LQG) control and sensing co-design problem, where one jointly designs sensing and control policies. We focus on the realistic case where the sensing design is selected among a finite set of available sensors, where each sensor is associated with a different cost (e.g., power consumption). We consider two dual problem instances: sensing-constrained LQG control, where one maximizes control performance subject to a sensor cost budget, and minimum-sensing LQG control, where one minimizes sensor cost subject to performance constraints. We prove no polynomial time algorithm guarantees across all problem instances a constant approximation factor from the optimal. Nonetheless, we present the first polynomial time algorithms with per-instance suboptimality guarantees. To this end, we leverage a separation principle, that partially decouples the design of sensing and control. Then, we frame LQG co-design as the optimization of approximately supermodular set functions; we develop novel algorithms to solve the problems; and we prove original results on the performance of the algorithms, and establish connections between their suboptimality and control-theoretic quantities. We conclude the paper by discussing two applications, namely, sensing-constrained formation control and resource-constrained robot navigation.

math.OC↗

arXiv2020

Sensor Placement for Optimal Kalman Filtering: Fundamental Limits, Submodularity, and Algorithms

In this paper, we focus on sensor placement in linear dynamic estimation, where the objective is to place a small number of sensors in a system of interdependent states so to design an estimator with a desired estimation performance. In particular, we consider a linear time-variant system that is corrupted with process and measurement noise, and study how the selection of its sensors affects the estimation error of the corresponding Kalman filter over a finite observation interval. Our contributions are threefold: First, we prove that the minimum mean square error of the Kalman filter decreases only linearly as the number of sensors increases. That is, adding extra sensors so to reduce this estimation error is ineffective, a fundamental design limit. Similarly, we prove that the number of sensors grows linearly with the system's size for fixed minimum mean square error and number of output measurements over an observation interval; this is another fundamental limit, especially for systems where the system's size is large. Second, we prove that the logdet of the error covariance of the Kalman filter, which captures the volume of the corresponding confidence ellipsoid, with respect to the system's initial condition and process noise is a supermodular and non-increasing set function in the choice of the sensor set. Therefore, it exhibits the diminishing returns property. Third, we provide efficient approximation algorithms that select a small number sensors so to optimize the Kalman filter with respect to this estimation error ---the worst-case performance guarantees of these algorithms are provided as well. Finally, we illustrate the efficiency of our algorithms using the problem of surface-based monitoring of CO2 sequestration sites studied in Weimer et al. (2008).

math.OC↗

arXiv2020

Sensing-Constrained LQG Control

Linear-Quadratic-Gaussian (LQG) control is concerned with the design of an optimal controller and estimator for linear Gaussian systems with imperfect state information. Standard LQG assumes the set of sensor measurements, to be fed to the estimator, to be given. However, in many problems, arising in networked systems and robotics, one may not be able to use all the available sensors, due to power or payload constraints, or may be interested in using the smallest subset of sensors that guarantees the attainment of a desired control goal. In this paper, we introduce the sensing-constrained LQG control problem, in which one has to jointly design sensing, estimation, and control, under given constraints on the resources spent for sensing. We focus on the realistic case in which the sensing strategy has to be selected among a finite set of possible sensing modalities. While the computation of the optimal sensing strategy is intractable, we present the first scalable algorithm that computes a near-optimal sensing strategy with provable sub-optimality guarantees. To this end, we show that a separation principle holds, which allows the design of sensing, estimation, and control policies in isolation. We conclude the paper by discussing two applications of sensing-constrained LQG control, namely, sensing-constrained formation control and resource-constrained robot navigation.

math.OC↗

arXiv2019

Outlier-Robust Spatial Perception: Hardness, General-Purpose Algorithms, and Guarantees

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.

stat.ML↗

arXiv2018

Resilient Non-Submodular Maximization over Matroid Constraints

The control and sensing of large-scale systems results in combinatorial problems not only for sensor and actuator placement but also for scheduling or observability/controllability. Such combinatorial constraints in system design and implementation can be captured using a structure known as matroids. In particular, the algebraic structure of matroids can be exploited to develop scalable algorithms for sensor and actuator selection, along with quantifiable approximation bounds. However, in large-scale systems, sensors and actuators may fail or may be (cyber-)attacked. The objective of this paper is to focus on resilient matroid-constrained problems arising in control and sensing but in the presence of sensor and actuator failures. In general, resilient matroid-constrained problems are computationally hard. Contrary to the non-resilient case (with no failures), even though they often involve objective functions that are monotone or submodular, no scalable approximation algorithms are known for their solution. In this paper, we provide the first algorithm, that also has the following properties: First, it achieves system-wide resiliency, i.e., the algorithm is valid for any number of denial-of-service attacks or failures. Second, it is scalable, as our algorithm terminates with the same running time as state-of-the-art algorithms for (non-resilient) matroid-constrained optimization. Third, it provides provable approximation bounds on the system performance, since for monotone objective functions our algorithm guarantees a solution close to the optimal. We quantify our algorithm's approximation performance using a notion of curvature for monotone (not necessarily submodular) set functions. Finally, we support our theoretical analyses with numerical experiments, by considering a control-aware sensor selection scenario, namely, sensing-constrained robot navigation.

math.OC↗