arXiv subjects

Magnus Egerstedt

Publications and source records attributed to Magnus Egerstedt.

At least 73 records · Page 4Linked to original sources

arXiv2019

A Study of a Class of Vibration-Driven Robots: Modeling, Analysis, Control and Design of the Brushbot

In this paper we present a study of a specific class of vibration-driven robots: the brushbots. In a bottom-up fashion, we start by deriving dynamic models of the brushes and we discuss the conditions under which these models can be employed to describe the motion of brushbots. Then, we present two designs of brushbots: a fully-actuated platform and a differential-drive-like one. The former is employed to experimentally validate both the developed theoretical models and the devised motion control algorithms. Finally, a coordinated-control algorithm is implemented on a swarm of differential-drive-like brushbots in order to demonstrate the design simplicity and robustness that can be achieved employing a vibration-based locomotion strategy.

cs.RO↗

arXiv2018

Fault Tolerant Control for Networked Mobile Robots

Teams of networked autonomous agents have been used in a number of applications, such as mobile sensor networks and intelligent transportation systems. However, in such systems, the effect of faults and errors in one or more of the sub-systems can easily spread throughout the network, quickly degrading the performance of the entire system. In consensus-driven dynamics, the effects of faults are particularly relevant because of the presence of unconstrained rigid modes in the transfer function of the system. Here, we propose a two-stage technique for the identification and accommodation of a biased-measurements agent, in a network of mobile robots with time invariant interaction topology. We assume these interactions to only take place in the form of relative position measurements. A fault identification filter deployed on a single observer agent is used to estimate a single fault occurring anywhere in the network. Once the fault is detected, an optimal leader-based accommodation strategy is initiated. Results are presented by means of numerical simulations and robot experiments.

eess.SY↗

arXiv2018

Control of Multi-Agent Systems with Finite Time Control Barrier Certificates and Temporal Logic

In this paper, a method to synthesize controllers using finite time convergence control barrier functions guided by linear temporal logic specifications for continuous time multi-agent dynamical systems is proposed. Finite time convergence to a desired set in the state space is guaranteed under the existence of a suitable finite time convergence control barrier function. In addition, these barrier functions also guarantee forward invariance once the system converges to the desired set. This allows us to formulate a theoretical framework which synthesizes controllers for the multi-agent system. These properties also enable us to solve the reachability problem in continuous time by formulating a theorem on the composition of multiple finite time convergence control barrier functions. This approach is more flexible than existing methods and also allows for a greater set of feasible control laws. Linear temporal logic is used to specify complex task specifications that need to be satisfied by the multi-agent system. With this solution methodology, a control law is synthesized that satisfies the given temporal logic task specification. Robotic experiments are provided which were performed on the Robotarium multi-robot testbed at Georgia Tech.

eess.SY↗

arXiv2018

A Distributed Version of the Hungarian Method for Multi-Robot Assignment

In this paper, we propose a distributed version of the Hungarian Method to solve the well known assignment problem. In the context of multi-robot applications, all robots cooperatively compute a common assignment that optimizes a given global criterion (e.g. the total distance traveled) within a finite set of local computations and communications over a peer-to-peer network. As a motivating application, we consider a class of multi-robot routing problems with "spatio-temporal" constraints, i.e. spatial targets that require servicing at particular time instants. As a means of demonstrating the theory developed in this paper, the robots cooperatively find online, suboptimal routes by applying an iterative version of the proposed algorithm, in a distributed and dynamic setting. As a concrete experimental test-bed, we provide an interactive "multi-robot orchestral" framework in which a team of robots cooperatively plays a piece of music on a so-called orchestral floor.

eess.SY↗

arXiv2018

Herdable Systems Over Signed, Directed Graphs

This paper considers 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. The basic theory of herdable systems is presented, including a necessary and sufficient condition for herdability. This paper then considers the impact of the underlying graph structure of a linear system on the herdability of the system, for the case where the graph is represented as signed and directed. By classifying nodes based on the length and sign of walks from an input, we find a class of completely herdable systems as well as provide a complete characterization of nodes that can be herded in systems with an underlying graph that is a directed out-branching rooted at a single input.

eess.SY↗

arXiv2018

Coverage Control for Wire-Traversing Robots

In this paper we consider the coverage control problem for a team of wire-traversing robots. The two-dimensional motion of robots moving in a planar environment has to be projected to one-dimensional manifolds representing the wires. Starting from Lloyd's descent algorithm for coverage control, a solution that generates continuous motion of the robots on the wires is proposed. This is realized by means of a Continuous Onto Wires (COW) map: the robots' workspace is mapped onto the wires on which the motion of the robots is constrained to be. A final projection step is introduced to ensure that the configuration of the robots on the wires is a local minimizer of the constrained locational cost. An algorithm for the continuous constrained coverage control problem is proposed and it is tested both in simulation and on a team of mobile robots.

cs.RO↗

arXiv2018

Permissive Barrier Certificates for Safe Stabilization Using Sum-of-squares

Motivated by the need to simultaneously guarantee safety and stability of safety-critical dynamical systems, we construct permissive barrier certificates in this paper that explicitly maximize the region where the system can be stabilized without violating safety constraints. An optimization strategy is developed to search for the maximum volume barrier certified region of safe stabilization. The barrier certified region, which is allowed to take any arbitrary shape, is proved to be strictly larger than safe regions generated with Lyapunov sublevel set based methods. The proposed approach effectively unites a Lyapunov function with multiple barrier functions that might not be compatible with each other. Iterative search algorithms are developed using sum-of-squares to compute the most permissive, that is, the maximum volume, barrier certificates. Simulation results of the iterative search algorithm demonstrate the effectiveness of the proposed method.

math.OC↗

arXiv2018

A Parametric MPC Approach to Balancing the Cost of Abstraction for Differential-Drive Mobile Robots

When designing control strategies for differential-drive mobile robots, one standard tool is the consideration of a point at a fixed distance along a line orthogonal to the wheel axis instead of the full pose of the vehicle. This abstraction supports replacing the non-holonomic, three-state unicycle model with a much simpler two-state single-integrator model (i.e., a velocity-controlled point). Yet this transformation comes at a performance cost, through the robot's precision and maneuverability. This work contains derivations for expressions of these precision and maneuverability costs in terms of the transformation's parameters. Furthermore, these costs show that only selecting the parameter once over the course of an application may cause an undue loss of precision. Model Predictive Control (MPC) represents one such method to ameliorate this condition. However, MPC typically realizes a control signal, rather than a parameter, so this work also proposes a Parametric Model Predictive Control (PMPC) method for parameter and sampling horizon optimization. Experimental results are presented that demonstrate the effects of the parameterization on the deployment of algorithms developed for the single-integrator model on actual differential-drive mobile robots.

cs.RO↗

arXiv2017

Safe Learning of Quadrotor Dynamics Using Barrier Certificates

To effectively control complex dynamical systems, accurate nonlinear models are typically needed. However, these models are not always known. In this paper, we present a data-driven approach based on Gaussian processes that learns models of quadrotors operating in partially unknown environments. What makes this challenging is that if the learning process is not carefully controlled, the system will go unstable, i.e., the quadcopter will crash. To this end, barrier certificates are employed for safe learning. The barrier certificates establish a non-conservative forward invariant safe region, in which high probability safety guarantees are provided based on the statistics of the Gaussian Process. A learning controller is designed to efficiently explore those uncertain states and expand the barrier certified safe region based on an adaptive sampling scheme. In addition, a recursive Gaussian Process prediction method is developed to learn the complex quadrotor dynamics in real-time. Simulation results are provided to demonstrate the effectiveness of the proposed approach.

cs.LG↗

arXiv2017

Differentially Private Cloud-Based Multi-Agent Optimization with Constraints

We present an optimization framework that solves constrained multi-agent optimization problems while keeping each agent's state differentially private. The agents in the network seek to optimize a local objective function in the presence of global constraints. Agents communicate only through a trusted cloud computer and the cloud also performs computations based on global information. The cloud computer modifies the results of such computations before they are sent to the agents in order to guarantee that the agents' states are kept private. We show that under mild conditions each agent's optimization problem converges in mean-square to its unique solution while each agent's state is kept differentially private. A numerical simulation is provided to demonstrate the viability of this approach.

math.OC↗

arXiv2017

Convergence Rate Estimates for Consensus over Random Graphs

Multi-agent coordination algorithms with randomized interactions have seen use in a variety of settings in the multi-agent systems literature. In some cases, these algorithms can be random by design, as in a gossip-like algorithm, and in other cases they are random due to external factors, as in the case of intermittent communications. Targeting both of these scenarios, we present novel convergence rate estimates for consensus problems solved over random graphs. Established results provide asymptotic convergence in this setting, and we provide estimates of the rate of convergence in two forms. First, we estimate decreases in a quadratic Lyapunov function over time to bound how quickly the agents' disagreement decays, and second we bound the probability of being at least a given distance from the point of agreement. Both estimates rely on (approximately) computing eigenvalues of the expected matrix exponential of a random graph's Laplacian, which we do explicitly in terms of the network's size and edge probability, without assuming that any relationship between them holds. Simulation results are provided to support the theoretical developments made.

math.OC↗

arXiv2017

Safe Open-Loop Strategies for Handling Intermittent Communications in Multi-Robot Systems

In multi-robot systems where a central decision maker is specifying the movement of each individual robot, a communication failure can severely impair the performance of the system. This paper develops a motion strategy that allows robots to safely handle critical communication failures for such multi-robot architectures. For each robot, the proposed algorithm computes a time horizon over which collisions with other robots are guaranteed not to occur. These safe time horizons are included in the commands being transmitted to the individual robots. In the event of a communication failure, the robots execute the last received velocity commands for the corresponding safe time horizons leading to a provably safe open-loop motion strategy. The resulting algorithm is computationally effective and is agnostic to the task that the robots are performing. The efficacy of the strategy is verified in simulation as well as on a team of differential-drive mobile robots.

cs.MA↗

arXiv2017

Safe Certificate-Based Maneuvers for Teams of Quadrotors Using Differential Flatness

Safety Barrier Certificates that ensure collision-free maneuvers for teams of differential flatness-based quadrotors are presented in this paper. Synthesized with control barrier functions, the certificates are used to modify the nominal trajectory in a minimally invasive way to avoid collisions. The proposed collision avoidance strategy complements existing flight control and planning algorithms by providing trajectory modifications with provable safety guarantees. The effectiveness of this strategy is supported both by the theoretical results and experimental validation on a team of five quadrotors.

cs.RO↗

arXiv2016

Asynchronous Multi-Agent Primal-Dual Optimization

We present a framework for asynchronously solving convex optimization problems over networks of agents which are augmented by the presence of a centralized cloud computer. This framework uses a Tikhonov-regularized primal-dual approach in which the agents update the system's primal variables and the cloud updates its dual variables. To minimize coordination requirements placed upon the system, the times of communications and computations among the agents are allowed to be arbitrary, provided they satisfy mild conditions. Communications from the agents to the cloud are likewise carried out without any coordination in their timing. However, we require that the cloud keep the dual variable's value synchronized across the agents, and a counterexample is provided that demonstrates that this level of synchrony is indeed necessary for convergence. Convergence rate estimates are provided in both the primal and dual spaces, and simulation results are presented that demonstrate the operation and convergence of the proposed algorithm.

math.OC↗

arXiv2016

The Robotarium: A remotely accessible swarm robotics research testbed

This paper describes the Robotarium -- a remotely accessible, multi-robot research facility. The impetus behind the Robotarium is that multi-robot testbeds constitute an integral and essential part of the multi-robot research cycle, yet they are expensive, complex, and time-consuming to develop, operate, and maintain. These resource constraints, in turn, limit access for large groups of researchers and students, which is what the Robotarium is remedying by providing users with remote access to a state-of-the-art multi-robot test facility. This paper details the design and operation of the Robotarium and discusses the considerations one must take when making complex hardware remotely accessible. In particular, safety must be built into the system already at the design phase without overly constraining what coordinated control programs users can upload and execute, which calls for minimally invasive safety routines with provable performance guarantees.

cs.RO↗

arXiv2016

Hamiltonian-based Algorithm for Relaxed Optimal Control

This paper concerns a first-order algorithmic technique for a class of optimal control problems defined on switched-mode hybrid systems. The salient feature of the algorithm is that it avoids the computation of Fréchet or Gâteaux derivatives of the cost functional, which can be time consuming, but rather moves in a projected-gradient direction that is easily computable (for a class of problems) and does not require any explicit derivatives. The algorithm is applicable to a class of problems where a pointwise minimizer of the Hamiltonian is computable by a simple formula, and this includes many problems that arise in theory and applications. The natural setting for the algorithm is the space of continuous-time relaxed controls, whose special structure renders the analysis simpler than the setting of ordinary controls. While the space of relaxed controls has theoretical advantages, its elements are abstract entities that may not be amenable to computation. Therefore, a key feature of the algorithm is that it computes adequate approximations to relaxed controls without loosing its theoretical convergence properties. Simulation results, including cpu times, support the theoretical developments.

math.OC↗

arXiv2016

Safety Barrier Certificates for Heterogeneous Multi-Robot Systems

This paper presents a formal framework for collision avoidance in multi-robot systems, wherein an existing controller is modified in a minimally invasive fashion to ensure safety. We build this framework through the use of control barrier functions (CBFs) which guarantee forward invariance of a safe set; these yield safety barrier certificates in the context of heterogeneous robot dynamics subject to acceleration bounds. Moreover, safety barrier certificates are extended to a distributed control framework, wherein neighboring agent dynamics are unknown, through local parameter identification. The end result is an optimization-based controller that formally guarantees collision free behavior in heterogeneous multi-agent systems by minimally modifying the desired controller via safety barrier constraints. This formal result is verified in simulation on a multi-robot system consisting of both cumbersome and agile robots, is demonstrated experimentally on a system with a Magellan Pro robot and three Khepera III robots.

cs.RO↗

arXiv2016

Multi-objective Compositions for Collision-Free Connectivity Maintenance in Teams of Mobile Robots

Compositional barrier functions are proposed in this paper to systematically compose multiple objectives for teams of mobile robots. The objectives are first encoded as barrier functions, and then composed using AND and OR logical operators. The advantage of this approach is that compositional barrier functions can provably guarantee the simultaneous satisfaction of all composed objectives. The compositional barrier functions are applied to the example of ensuring collision avoidance and static/dynamical graph connectivity of teams of mobile robots. The resulting composite safety and connectivity barrier certificates are verified experimentally on a team of four mobile robots.

cs.RO↗