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

Liang Xu, Youfeng Su, He Cai

TL;DR

The paper addresses cooperative leader-following tracking of multiple nonholonomic mobile robots over directed communication graphs. It develops a distributed continuous feedback law with an explicit strict Lyapunov function, proving global ${\mathcal{K}}$-exponential stability, and extends to a practical sampled-data framework via emulation, valid for directed networks with a spanning tree. Theoretical guarantees are complemented by a numerical example validating formation tracking and centroid convergence to the leader trajectory. This work advances robustness and applicability of cooperative tracking in communication-constrained, directed-network environments with rigorous stability guarantees.

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.

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

TL;DR

The paper addresses cooperative leader-following tracking of multiple nonholonomic mobile robots over directed communication graphs. It develops a distributed continuous feedback law with an explicit strict Lyapunov function, proving global -exponential stability, and extends to a practical sampled-data framework via emulation, valid for directed networks with a spanning tree. Theoretical guarantees are complemented by a numerical example validating formation tracking and centroid convergence to the leader trajectory. This work advances robustness and applicability of cooperative tracking in communication-constrained, directed-network environments with rigorous stability guarantees.

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 -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.
Paper Structure (8 sections, 4 theorems, 71 equations, 3 figures, 1 table)

This paper contains 8 sections, 4 theorems, 71 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Problem formulation and Preliminaries
  3. Main Results
  4. Continuous Feedback Control Synthesis
  5. Exponential Convergence Rate of the Closed-Loop System
  6. Sampled-Data Feedback Control Synthesis
  7. Numerical example
  8. Conclusions

Key Result

Lemma 1

If $\bar{x}_{i}$, $\bar{y}_{i}$, and $\bar{\theta}_{i}$ of error-sys satisfy $\lim_{t \to \infty}[\bar{x}_{i}(t), \bar{y}_{i}(t),$$\bar{\theta}_{i}(t)]=0,~i=1,\dots, N,$ then, aim-00 holds.

Figures (3)

  • Figure 1: Communication topology graph $\mathcal{\bar{G}}$.
  • Figure 2: The trajectory of the center of four follower robots (cyan solid line), the trajectory of leader robot (red dotted line), and their formation pattern.
  • Figure 3: The formation errors between each follower and leader.

Theorems & Definitions (17)

  • Remark 1
  • Remark 2
  • Remark 3
  • Lemma 1
  • Theorem 1
  • Claim 1
  • Remark 4
  • Remark 5
  • Remark 6
  • Theorem 2
  • ...and 7 more