基于李雅普诺夫理论设计鲁棒控制律，实现四轮独立驱动转向机器人精准轨迹跟踪。
Lyapunov-Based PI-Like Control for Robust Trajectory Tracking of a Four-Wheel Independently Driven and Steered Robot: Design and Experimental Validation
- 采用李雅普诺夫方法构建带前馈补偿的类PI控制结构，保证实时性与稳定性。
- 在水平与垂直工况下实验验证，相比传统PI和滑模控制更具鲁棒性。
- 适用于嵌入式平台，可应对参数变化与未建模干扰，适合高精度移动机器人场景。
本文针对四轮独立驱动与转向移动机器人，提出一种基于李雅普诺夫理论的类PI控制器设计方法，用于实现鲁棒轨迹跟踪。通过显式且结构验证的数学模型，系统化地设计控制器，并提供严格的稳定性保证，适用于实时实现。针对内环速度误差与积分误差动态，发展了增强型李雅普诺夫实用稳定性分析，获得联合状态的实际稳定性和一致最终有界性的显式边界及充分条件。所提控制律保持类PI结构并引入基于模型的前馈补偿，可在标准嵌入式平台上实施，同时提升对依赖配置的残余动态和未建模效应的鲁棒性。在四轮独立转向与驱动移动机器人平台上，通过水平与垂直工况下的实验验证了该设计的有效性与鲁棒性，对比了经典PI控制器与滑模控制器，结果表明其性能更优。
原文摘要 · Abstract (English)
In this paper, a Lyapunov-based synthesis of a PI-like controller is proposed for robust trajectory tracking of an independently driven and steered four-wheel mobile robot. For the robot considered in this work, an explicit structurally verified mathematical model is used to enable systematic controller design with rigorous stability guarantees suitable for real time implementation. An augmented Lyapunov-based practical stability analysis is developed for the combined velocity-error and integral-error dynamics of the inner loop, yielding explicit bounds and sufficient conditions for practical stability and uniform ultimate boundedness of the combined velocity-error and integral-error state. The resulting control law retains a PI-like structure with model-based feedforward compensation, making it suitable for implementation on standard embedded platforms while improving robustness against configuration dependent residual dynamics and unmodelled effects. The effectiveness and robustness of the proposed design are demonstrated experimentally on a four-wheel independently steered and independently driven mobile robot platform, under both horizontal and vertical operating conditions and benchmarked against a PI controller and a sliding-mode controller.
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