Magnus Egerstedt

Formation constrained multi-agent control

We propose a model independent coordination strategy for multi-agent formation control. The main theorem states that under a bounded tracking error assumption our method stabilizes the formation error. We illustrate the usefulness of the method by applying it to rigid body constrained motions, as well as to mobile manipulation.

Distributed Coordination Control of Multiagent Systems While Preserving Connectedness

This paper addresses the connectedness issue in multiagent coordination, i.e., the problem of ensuring that a group of mobile agents stays connected while achieving some performance objective. In particular, we study the rendezvous and the formation control problems over dynamic interaction graphs, and by adding appropriate weights to the edges in the graphs, we guarantee that the graphs stay connected.

Controllability of Multi-Agent Systems from a Graph-Theoretic Perspective

In this work, we consider the controlled agreement problem for multi-agent networks, where a collection of agents take on leader roles while the remaining agents execute local, consensus-like protocols. Our aim is to identify reflections of graph-theoretic notions on system-theoretic properties of such systems. In particular, we show how the symmetry structure of the network, characterized in terms of its automorphism group, directly relates to the controllability of the corresponding multi-agent system. Moreover, we introduce network equitable partitions as a means by which such controllability characterizations can be extended to the multileader setting.

A control Lyapunov function approach to multiagent coordination

In this paper, the multiagent coordination problem is studied. This problem is addressed for a class of robots for which control Lyapunov functions can be found. The main result is a suite of theorems about formation maintenance, task completion time, and formation velocity. It is also shown how to moderate the requirement that, for each individual robot, there exists a control Lyapunov function. An example is provided that illustrates the soundness of the method.

Containment Control in Mobile Networks

In this paper, the problem of driving a collection of mobile robots to a given target destination is studied. In particular, we are interested in achieving this transfer in an orderly manner so as to ensure that the agents remain in the convex polytope spanned by the leader-agents, while the remaining agents, only employ local interaction rules. To this aim we exploit the theory of partial difference equations and propose hybrid control schemes based on stop-go rules for the leader-agents. Non-Zenoness, liveness and convergence of the resulting system are also analyzed.

On the regularization of Zeno hybrid automata

Fundamental properties of hybrid automata, such as existence and uniqueness of executions, are studied. Particular attention is devoted to Zeno hybrid automata, which are hybrid automata that take infinitely many discrete transitions in finite time. It is shown that regularization techniques can be used to extend the Zeno executions of these automata to times beyond the Zeno time. Different types of regularization may, however, lead to different extensions. A water tank control problem and a bouncing ball system are used to illustrate the results.

Symbolic planning and control of robot motion [Grand Challenges of Robotics]

In this paper, different research trends that use symbolic techniques for robot motion planning and control are illustrated. As it often happens in new research areas, contributions to this topic started at about the same time by different groups with different emphasis, approaches, and notation. This article tries to describe a framework in which many of the current methods and ideas can be placed and to provide a coherent picture of what the authors want to do, what have they got so far, and what the main missing pieces are. Generally speaking, the aim of symbolic control as is envisioned in this article is to enable the usage of methods of formal logic, languages, and automata theory for solving effectively complex planning problems for robots and teams of robots. The results presented in this article can be divided in two groups: top-down approaches, whereby formal logic tools are employed on rather abstract models of robots; and bottom up approaches, whose aim is to provide means by which such abstractions are possible and effective. The two ends do not quite tie as yet, and much work remains to be done in both directions to obtain generally applicable methods. However, the prospects of symbolic control of robots are definitely promising, and the challenging nature of problems to be solved warrants for the interest of a wide community of researchers

Control of mobile platforms using a virtual vehicle approach

Two model independent solutions to the problem of controlling wheel-based mobile platforms are proposed. These two algorithms are based on a so called virtual vehicle approach, where the motion of the reference point on the desired trajectory is governed by a differential equation containing error feedback. This, combined with the fact that the proven stable control algorithms are basically proportional regulators with arbitrary positive gains, make the solutions robust with respect to errors and disturbances, as demonstrated by the experimental results.

Transition-time optimization for switched-mode dynamical systems

This note considers the problem of determining optimal switching times at which mode transitions should occur in multimodal, hybrid systems. It derives a simple formula for the gradient of the cost functional with respect to the switching times, and uses it in a gradient-descent algorithm. Much of the analysis is carried out in the setting of optimization problems involving fixed switching-mode sequences, but a possible extension is pointed out for the case where the switching-mode sequence is a part of the variable. Numerical examples testify to the viability of the proposed approach.

Distributed containment control with multiple stationary or dynamic leaders in fixed and switching directed networks

In this paper, we study the problem of distributed containment control of a group of mobile autonomous agents with multiple stationary or dynamic leaders under both fixed and switching directed network topologies. First, when the leaders are stationary and all followers share an inertial coordinate frame, we present necessary and sufficient conditions on the fixed or switching directed network topology such that all followers will ultimately converge to the stationary convex hull formed by the stationary leaders for arbitrary initial states in a space of any finite dimension. When the directed network topology is fixed, we partition the (nonsymmetric) Laplacian matrix and explore its properties to derive the convergence results. When the directed network topology is switching, the commonly adopted decoupling technique based on the Kronecker product in a high-dimensional space can no longer be applied and we hence present an important coordinate transformation technique to derive the convergence results. The proposed coordinate transformation technique also has potential applications in other high-dimensional distributed control scenarios and might be used to simplify the analysis of a high-dimensional system to that of a one-dimensional system when the decoupling technique based on the Kronecker product cannot be applied. Second, when the leaders are dynamic and all followers share an inertial coordinate frame, we propose a distributed tracking control algorithm without velocity measurements. When the directed network topology is fixed, we derive conditions on the network topology and the control gain to guarantee that all followers will ultimately converge to the dynamic convex hull formed by the dynamic leaders for arbitrary initial states in a space of any finite dimension. When the directed network topology is switching, we derive conditions on the network topology and the control gain such that all followers will ultimately converge to the minimal hyperrectangle that contains the dynamic leaders and each of its hyperplanes is normal to one axis of the inertial coordinate frame in any high-dimensional space. We also show via some counterexamples that it is, in general, impossible to find distribute containment control algorithms without velocity measurements to guarantee that all followers will ultimately converge to the convex hull formed by the dynamic leaders under a switching network topology in a high-dimensional space. Simulation results are presented as a proof of concept.