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.

翻译：本文提出了一种基于李雅普诺夫综合的类PI控制器，用于实现独立驱动与转向四轮移动机器人的鲁棒轨迹跟踪。针对所考虑的机器人，采用显式结构验证的数学模型，使控制器设计具有严格的稳定性保证，适用于实时实现。针对内环速度误差与积分误差的联合动力学，建立了增广李雅普诺夫实用稳定性分析，给出了实用稳定性与联合速度-误差及积分误差状态一致最终有界的显式界限和充分条件。所得控制律保留类PI结构并包含基于模型的前馈补偿，使其适用于标准嵌入式平台，同时提高对构型相关残余动力学及未建模效应的鲁棒性。通过四轮独立转向与独立驱动移动机器人平台，在水平和垂直工况下进行实验，验证了所提设计的有效性和鲁棒性，并与PI控制器和滑模控制器进行了对比。