A control Lyapunov function approach to multiagent coordination

Abstract

Abstract-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.

On the controllability of nearest neighbor interconnections

“…One class focuses on the effect of interconnection topology on the type of formation equilibrium configurations [1], [2], where it was shown that the rigidity of the interconnection graph plays a crucial role. Another class of coordination algorithms uses potential functions to express the group task [3], [4], [5]. Potential fields have been combined with synchronization control inputs to yield coordinated formation and decentralized flocking and swarming motion [6], [7], [8], [9].…”

Stability Analysis and Implementation of a Decentralized Formation Control Strategy for Unmanned Vehicles

“…In [24], a formation Lyapunov stability function is defined as a weighted sum of the control Lyapunov function for each vehicle to support the formation stability analysis. In [25], the idea of relative-position-based formation stability was proposed and the Lyapunov method was also used to design the decentralized controllers, along with an extended linear matrix inequality (LMI) to analyze the conditions required for formation stability.…”

Performance Evaluation of Potential Field Based Distributed Motion Planning Methods for Robot Collectives

“…While considerable literature exists for motion planning of individual mobile agents, the renewed challenge lies in creating motion plans for the entire team while incorporating notions such as cooperation. The "formation" paradigm has emerged as a convenient mechanism for abstraction and coordination with approaches ranging from leader-following (Wang, 1991;Desai et al, 2001), virtual structures (Lewis and Tan, 1997;Beard et al, 2001) and virtual leaders (Leonard and Fiorelli, 2001;Ogren et al, 2002). The group control problem now reduces to a well-known single-agent control problem from which the other agents derive their control laws but requires communication of some coordination information.…”

“…The formation paradigm has evolved to allow prescription of parameterized formation maneuvers and group feedback (Egerstedt and Hu, 2001;Young et al, 2001;Ogren et al, 2002). From these seemingly disparate approaches, a dynamic system-theoretic perspective has emerged for examining the decentralized multiagent "behavioral control" in the context of "formations" (Lawton et al, 2000;Egerstedt and Hu, 2001;Leonard and Fiorelli, 2001;Young et al, 2001;Ogren et al, 2002;Olfati-Saber and Murray, 2006). "Behavioral" control laws, derived implicitly as gradients of limited-range artificial potentials, can be implemented in a decentralized manner while permitting a Lyapunov-based analysis of formation maintenance.…”