arXiv subjects

Magnus Egerstedt

Publications and source records attributed to Magnus Egerstedt.

At least 55 records · Page 3Linked to original sources

arXiv2020

A Sequential Composition Framework for Coordinating Multi-Robot Behaviors

A number of coordinated behaviors have been proposed for achieving specific tasks for multi-robot systems. However, since most applications require more than one such behavior, one needs to be able to compose together sequences of behaviors while respecting local information flow constraints. Specifically, when the inter-agent communication depends on inter-robot distances, these constraints translate into particular configurations that must be reached in finite time in order for the system to be able to transition between the behaviors. To this end, we develop a distributed framework based on finite-time convergence control barrier functions that enables a team of robots to adjust its configuration in order to meet the communication requirements for the different tasks. In order to demonstrate the significance of the proposed framework, we implemented a full-scale scenario where a team of eight planar robots explore an urban environment in order to localize and rescue a subject.

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arXiv2020

Inferring and Learning Multi-Robot Policies by Observing an Expert

We present a technique for learning how to solve a multi-robot mission that requires interaction with an external environment by observing an expert system executing the same mission. We define the expert system as a team of robots equipped with a library of controllers, each designed to solve a specific task, supervised by an expert policy that appropriately selects controllers based on the states of robots and environment. The objective is for an un-trained team of robots (i.e., imitator system) equipped with the same library of controllers, but agnostic to the expert policy, to execute the mission, with performances comparable to those of the expert system. From un-annotated observations of the expert system, a multi-hypothesis filtering technique is used to estimate individual controllers executed by the expert policy. Then, the history of estimated controllers and environmental states is used to train a neural network policy for the imitator system. Considering a perimeter protection scenario on a team of differential-drive robots, we show that the learned policy endows the imitator system with performances comparable to those of the expert system.

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arXiv2019

Persistification of Robotic Tasks

In this paper we propose a control framework that enables robots to execute tasks persistently, i.e., over time horizons much longer than robots' battery life. This is achieved by ensuring that the energy stored in the batteries of the robots is never depleted. This is framed as a set invariance constraint in an optimization problem whose objective is that of minimizing the difference between the robots' control inputs and nominal control inputs corresponding to the task that is to be executed. We refer to this process as the persistification of a robotic task. Forward invariance of subsets of the state space of the robots is turned into a control input constraint by using control barrier functions. The solution of the formulated optimization problem with energy constraints ensures that the robotic task is persistent. To illustrate the operation of the proposed framework, we consider two tasks whose persistent execution is particularly relevant: environment exploration and environment surveillance. We show the persistification of these two tasks both in simulation and on a team of wheeled mobile robots on the Robotarium.

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arXiv2019

Tracking Control by the Newton-Raphson Method with Output Prediction and Controller Speedup

This paper presents a control technique for output tracking of reference signals in continuous-time dynamical systems. The technique is comprised of the following three elements: (i) output prediction which has to track the reference signal, (ii) a controller based on an integrator with variable gain, and (iii) a speedup of the control action for enhancing the tracker's accuracy and, in some cases, guaranteeing stability of the closed-loop system. The technique is suitable for linear and nonlinear systems, implementable by simple algorithms, can track reference points as well as time-dependent reference signals, and may have large, even global domains of attraction. The derived theoretical results include convergence of the tracking controller and error analysis, and are supported by illustrative simulation and laboratory experiments.

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arXiv2019

Path Planning in Unknown Environments Using Optimal Transport Theory

This paper introduces a graph-based, potential-guided method for path planning problems in unknown environments, where obstacles are unknown until the robots are in close proximity to the obstacle locations. Inspired by optimal transport theory, the proposed method generates a graph connecting the initial and target configurations, and then finds a path over the graph using the available environmental information. The graph and path are updated iteratively when newly encountered obstacle information becomes available. The resulting method is a deterministic procedure proven to be complete, i.e., it is guaranteed to find a feasible path, when one exists, in a finite number of iterations. The method is scalable to high-dimensional problems. In addition, our method does not search the entire domain for the path, instead, the algorithm only explores a sub-region that can be described by the evolution of the Fokker-Planck equation. We demonstrate the performance of our algorithm via several numerical examples with different environments and dimensions, including high-dimensional cases.

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arXiv2019

A Reinforcement Learning Framework for Sequencing Multi-Robot Behaviors

Given a list of behaviors and associated parameterized controllers for solving different individual tasks, we study the problem of selecting an optimal sequence of coordinated behaviors in multi-robot systems for completing a given mission, which could not be handled by any single behavior. In addition, we are interested in the case where partial information of the underlying mission is unknown, therefore, the robots must cooperatively learn this information through their course of actions. Such problem can be formulated as an optimal decision problem in multi-robot systems, however, it is in general intractable due to modeling imperfections and the curse of dimensionality of the decision variables. To circumvent these issues, we first consider an alternate formulation of the original problem through introducing a sequence of behaviors' switching times. Our main contribution is then to propose a novel reinforcement learning based method, that combines Q-learning and online gradient descent, for solving this reformulated problem. In particular, the optimal sequence of the robots' behaviors is found by using Q-learning while the optimal parameters of the associated controllers are obtained through an online gradient descent method. Finally, to illustrate the effectiveness of our proposed method we implement it on a team of differential-drive robots for solving two different missions, namely, convoy protection and object manipulation.

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arXiv2019

Robust Barrier Functions for a Fully Autonomous, Remotely Accessible Swarm-Robotics Testbed

The Robotarium, a remotely accessible swarm-robotics testbed, has provided free, open access to robotics and controls research for hundreds of users in thousands of experiments. This high level of usage requires autonomy in the system, which mainly corresponds to constraint satisfaction in the context of users' submissions. In other words, in case that the users' inputs to the robots may lead to collisions, these inputs must be altered to avoid these collisions automatically. However, these alterations must be minimal so as to preserve the users' objective in the experiment. Toward this end, the system has utilized barrier functions, which admit a minimally invasive controller-synthesis procedure. However, barrier functions are yet to be robustified with respect to unmodeled disturbances (e.g., wheel slip or packet loss) in a manner conducive to real-time synthesis. As such, this paper formulates robust barrier functions for a general class of disturbed control-affine systems that, in turn, is key for the Robotarium to operate fully autonomously (i.e., without human supervision). Experimental results showcase the effectiveness of this robust formulation in a long-term experiment in the Robotarium.

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arXiv2019

Passivity-Based Decentralized Control of Multi-Robot Systems With Delays Using Control Barrier Functions

In this paper, we present a solution to the problem of coordinating multiple robots across a communication channel that experiences delays. The proposed approach leverages control barrier functions in order to ensure that the multi-robot system remains dissipative. This is achieved by encoding the dissipativity-preserving condition as a set invariance constraint. This constraint is then included in an optimization problem, whose objective is that of modifying, in a minimally invasive fashion, the nominal input to the robots. The formulated optimization problem is decentralized in the sense that, in order to be solved, it does not require the individual robots to have access to global information. Moreover, thanks to its convexity, each robot can solve it using fast and efficient algorithms. The effectiveness of the proposed control framework is demonstrated through the implementation of a formation control algorithm in presence of delays on a team of mobile robots.

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arXiv2019

Constraint-Driven Coordinated Control of Multi-Robot Systems

In this paper we present a reformulation--framed as a constrained optimization problem--of multi-robot tasks which are encoded through a cost function that is to be minimized. The advantages of this approach are multiple. The constraint-based formulation provides a natural way of enabling long-term robot autonomy applications, where resilience and adaptability to changing environmental conditions are essential. Moreover, under certain assumptions on the cost function, the resulting controller is guaranteed to be decentralized. Furthermore, finite-time convergence can be achieved, while using local information only, and therefore preserving the decentralized nature of the algorithm. The developed control framework has been tested on a team of ground mobile robots implementing long-term environmental monitoring.

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arXiv2019

An Optimal Task Allocation Strategy for Heterogeneous Multi-Robot Systems

For a team of heterogeneous robots executing multiple tasks, we propose a novel algorithm to optimally allocate tasks to robots while accounting for their different capabilities. Motivated by the need that robot teams have in many real-world applications of remaining operational for long periods of time, we allow each robot to choose tasks taking into account the energy consumed by executing them, besides the global specifications on the task allocation. The tasks are encoded as constraints in an energy minimization problem solved at each point in time by each robot. The prioritization of a task over others -- effectively signifying the allocation of the task to that particular robot -- occurs via the introduction of slack variables in the task constraints. Moreover, the suitabilities of certain robots towards certain tasks are also taken into account to generate a task allocation algorithm for a team of robots with heterogeneous capabilities. The efficacy of the developed approach is demonstrated both in simulation and on a team of real robots.

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arXiv2019

Multi-Objective Policy Generation for Multi-Robot Systems Using Riemannian Motion Policies

In many applications, multi-robot systems are required to achieve multiple objectives. For these multi-objective tasks, it is oftentimes hard to design a single control policy that fulfills all the objectives simultaneously. In this paper, we focus on multi-objective tasks that can be decomposed into a set of simple subtasks. Controllers for these subtasks are individually designed and then combined into a control policy for the entire team. One significant feature of our work is that the subtask controllers are designed along with their underlying manifolds. When a controller is combined with other controllers, their associated manifolds are also taken into account. This formulation yields a policy generation framework for multi-robot systems that can combine controllers for a variety of objectives while implicitly handling the interaction among robots and subtasks. To describe controllers on manifolds, we adopt Riemannian Motion Policies (RMPs), and propose a collection of RMPs for common multi-robot subtasks. Centralized and decentralized algorithms are designed to combine these RMPs into a final control policy. Theoretical analysis shows that the system under the control policy is stable. Moreover, we prove that many existing multi-robot controllers can be closely approximated by the framework. The proposed algorithms are validated through both simulated tasks and robotic implementations.

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arXiv2019

Stable, Concurrent Controller Composition for Multi-Objective Robotic Tasks

Robotic systems often need to consider multiple tasks concurrently. This challenge calls for controller synthesis algorithms that fulfill multiple control specifications while maintaining the stability of the overall system. In this paper, we decompose multi-objective tasks into subtasks, where individual subtask controllers are designed independently and then combined to generate the overall control policy. In particular, we adopt Riemannian Motion Policies (RMPs), a recently proposed controller structure in robotics, and, RMPflow, its associated computational framework for combining RMP controllers. We re-establish and extend the stability results of RMPflow through a rigorous Control Lyapunov Function (CLF) treatment. We then show that RMPflow can stably combine individually designed subtask controllers that satisfy certain CLF constraints. This new insight leads to an efficient CLF-based computational framework to generate stable controllers that consider all the subtasks simultaneously. Compared with the original usage of RMPflow, our framework provides users the flexibility to incorporate design heuristics through nominal controllers for the subtasks. We validate the proposed computational framework through numerical simulation and robotic implementation.

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arXiv2019

Barrier-Certified Adaptive Reinforcement Learning with Applications to Brushbot Navigation

This paper presents a safe learning framework that employs an adaptive model learning algorithm together with barrier certificates for systems with possibly nonstationary agent dynamics. To extract the dynamic structure of the model, we use a sparse optimization technique. We use the learned model in combination with control barrier certificates which constrain policies (feedback controllers) in order to maintain safety, which refers to avoiding particular undesirable regions of the state space. Under certain conditions, recovery of safety in the sense of Lyapunov stability after violations of safety due to the nonstationarity is guaranteed. In addition, we reformulate an action-value function approximation to make any kernel-based nonlinear function estimation method applicable to our adaptive learning framework. Lastly, solutions to the barrier-certified policy optimization are guaranteed to be globally optimal, ensuring the greedy policy improvement under mild conditions. The resulting framework is validated via simulations of a quadrotor, which has previously been used under stationarity assumptions in the safe learnings literature, and is then tested on a real robot, the brushbot, whose dynamics is unknown, highly complex and nonstationary.

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arXiv2019

Herdability of Linear Systems Based on Sign Patterns and Graph Structures

We consider the notion of herdability, a set-based reachability condition, which asks whether the state of a system can be controlled to be element-wise larger than a non-negative threshold. First a number of foundational results on herdability of a continuous time, linear time invariant system are presented. These show that the herdability of a linear system can be determined based on certain matrices, such as the controllability matrix, which arise in the study of controllability of linear systems. Second, the relationship between the sign pattern of the underlying graph structure of a system and the herdability properties of the system is investigated. In doing so the notion of sign herdability is introduced which captures classes of systems whose sign pattern determines their herdability. We identify a set of conditions, first on the sign pattern of the controllability matrix and then on the underlying graph structure, that ensure that the system is sign herdable.

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arXiv2019

Control Barrier Functions: Theory and Applications

This paper provides an introduction and overview of recent work on control barrier functions and their use to verify and enforce safety properties in the context of (optimization based) safety-critical controllers. We survey the main technical results and discuss applications to several domains including robotic systems.

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arXiv2019

Voluntary Retreat for Decentralized Interference Reduction in Robot Swarms

In densely-packed robot swarms operating in confined regions, spatial interference -- which manifests itself as a competition for physical space -- forces robots to spend more time navigating around each other rather than performing the primary task. This paper develops a decentralized algorithm that enables individual robots to decide whether to stay in the region and contribute to the overall mission, or vacate the region so as to reduce the negative effects that interference has on the overall efficiency of the swarm. We develop this algorithm in the context of a distributed collection task, where a team of robots collect and deposit objects from one set of locations to another in a given region. Robots do not communicate and use only binary information regarding the presence of other robots around them to make the decision to stay or retreat. We illustrate the efficacy of the algorithm with experiments on a team of real robots.

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arXiv2019

Tracking Control by the Newton-Raphson Flow: Applications to Autonomous Vehicles

This paper concerns applications of a recently-developed output-tracking technique to trajectory control of autonomous vehicles. The technique is based on three principles: Newton-Raphson flow for solving algebraic equations,output prediction, and controller speedup. Early applications of the technique, made to simple systems of an academic nature,were implemented by simple algorithms requiring modest computational efforts. In contrast, this paper tests it on commonly-used dynamic models to see if it can handle more complex control scenarios. Results are derived from simulations as well as a laboratory setting, and they indicate effective tracking convergence despite the simplicity of the control algorithm.

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arXiv2019

Non-Uniform Robot Densities in Vibration Driven Swarms Using Phase Separation Theory

In robot swarms operating under highly restrictive sensing and communication constraints, individuals may need to use direct physical proximity to facilitate information exchange. However, in certain task-related scenarios, this requirement might conflict with the need for robots to spread out in the environment, e.g., for distributed sensing or surveillance applications. This paper demonstrates how a swarm of minimally-equipped robots can form high-density robot aggregates which coexist with lower robot densities in the domain. We envision a scenario where a swarm of vibration-driven robots---which sit atop bristles and achieve directed motion by vibrating them---move somewhat randomly in an environment while colliding with each other. Theoretical techniques from the study of far-from-equilibrium collectives and statistical mechanics clarify the mechanisms underlying the formation of these high and low density regions. Specifically, we capitalize on a transformation that connects the collective properties of a system of self-propelled particles with that of a well-studied molecular fluid system, thereby inheriting the rich theory of equilibrium thermodynamics. This connection is a formal one and is a relatively recent result in studies of motility induced phase separation; it is previously unexplored in the context of robotics. Real robot experiments as well as simulations illustrate how inter-robot collisions can precipitate the formation of non-uniform robot densities in a closed and bounded region.

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