Cooperative Global $\mathcal{K}$-exponential Tracking Control of Multiple Mobile Robots -- Extended Version

TL;DR

This paper develops a distributed control strategy for multiple mobile robots that guarantees global exponential stability and robustness, validated through numerical simulations.

Contribution

It introduces a novel cooperative control law ensuring global $ extbf{K}$-exponential stability for multi-robot systems with directed communication networks.

Findings

Proves global asymptotic and exponential stability of the system.

Designs a practical sampled-data control law based on Lyapunov functions.

Validates effectiveness through numerical simulations.

Abstract

This paper studies the cooperative tracking control problem for multiple mobile robots over a directed communication network. First, it is shown that the closed-loop system is uniformly globally asymptotically stable under the proposed distributed continuous feedback control law, where an explicit strict Lyapunov function is constructed. Then, by investigating the convergence rate, it is further proven that the closed-loop system is globally $\mathcal{K}$-exponentially stable. Moreover, to make the proposed control law more practical, the distributed continuous feedback control law is generalized to a distributed sampled-data feedback control law using the emulation approach, based on the strong integral input-to-state stable Lyapunov function. Numerical simulations are presented to validate the effectiveness of the proposed control methods.