Mobile robotic manipulators (MRMs), which integrate mobility and manipulation capabilities, present significant control challenges due to their nonlinear dynamics, underactuation, and coupling between the base and manipulator subsystems. This paper proposes a novel homogeneous Proportional-Integral-Derivative (hPID) control strategy tailored for MRMs to achieve robust and coordinated motion control. Unlike classical PID controllers, the hPID controller leverages the mathematical framework of homogeneous control theory to systematically enhance the stability and convergence properties of the closed-loop system, even in the presence of dynamic uncertainties and external disturbances involved into a system in a homogeneous way. A homogeneous PID structure is designed, ensuring improved convergence of tracking errors through a graded homogeneity approach that generalizes traditional PID gains to nonlinear, state-dependent functions. Stability analysis is conducted using Lyapunov-based methods, demonstrating that the hPID controller guarantees global asymptotic stability and finite-time convergence under mild assumptions. Experimental results on a representative MRM model validate the effectiveness of the hPID controller in achieving high-precision trajectory tracking for both the mobile base and manipulator arm, outperforming conventional linear PID controllers in terms of response time, steady-state error, and robustness to model uncertainties. This research contributes a scalable and analytically grounded control framework for enhancing the autonomy and reliability of next-generation mobile manipulation systems in structured and unstructured environments.

翻译：移动机器人操作臂（MRMs）集成了移动性与操作能力，由于其非线性动力学特性、欠驱动特性以及基座与操作臂子系统间的耦合作用，带来了显著的控制挑战。本文提出了一种专为MRMs设计的新型齐次比例-积分-微分（hPID）控制策略，以实现鲁棒且协调的运动控制。与经典PID控制器不同，hPID控制器利用齐次控制理论的数学框架，系统性地提升闭环系统的稳定性和收敛特性，即使在动态不确定性和外部扰动以齐次方式作用于系统时亦然。所设计的齐次PID结构通过分级齐次化方法，将传统PID增益推广为非线性、状态相关的函数，从而确保跟踪误差的收敛性得到改善。基于李雅普诺夫方法进行稳定性分析，证明在温和假设下，hPID控制器能保证全局渐近稳定性和有限时间收敛性。在典型MRM模型上的实验结果表明，hPID控制器在实现移动基座和操作臂的高精度轨迹跟踪方面具有显著效果，在响应时间、稳态误差及对模型不确定性的鲁棒性方面均优于传统线性PID控制器。本研究为增强结构化与非结构化环境中新一代移动操作系统的自主性与可靠性，提供了一个可扩展且具有分析依据的控制框架。