Lyapunov-Based $\mathcal{L}_2$-Stable PI-Like Control of a Four-Wheel Independently Driven and Steered Robot

TL;DR

This paper presents a Lyapunov-based method for designing a PI-like controller that ensures $\\mathcal{L}_2$-stability and robust motion control of a four-wheel robot, with experimental validation demonstrating effectiveness.

Contribution

It introduces a systematic Lyapunov-based synthesis approach for a PI-like controller with explicit stability guarantees for a four-wheel robot.

Findings

Controller achieves $\\mathcal{L}_2$-stability in experiments.

Design reduces configuration-dependent effects.

Robust real-time control demonstrated on a physical robot.

Abstract

In this letter, Lyapunov-based synthesis of a PI-like controller is proposed for $\mathcal{L}_2$-stable motion control of an independently driven and steered four-wheel mobile robot. An explicit, structurally verified model is used to enable systematic controller design with stability and performance guarantees suitable for real-time operation. A Lyapunov function is constructed to yield explicit bounds and $\mathcal{L}_2$ stability results, supporting feedback synthesis that reduces configuration dependent effects. The resulting control law maintains a PI-like form suitable for standard embedded implementation while preserving rigorous stability properties. Effectiveness and robustness are demonstrated experimentally on a real four-wheel mobile robot platform.