基于核心函数的机器人系统自适应跟踪控制

Adaptive Tracking Control of Robot Systems Based on Core Functions

摘要: 实际运行中的单关节机器人系统往往面临模型参数摄动及未知外部扰动等非精确建模因素的影响，这给高精度轨迹跟踪控制带来了挑战。针对这一问题，本文提出了一种基于反步法的鲁棒自适应跟踪控制策略。首先，建立了考虑外部扰动的严格反馈非线性系统模型。随后，针对系统中存在的未知非线性动态，引入一个未知常数作为其上界的核心参数，并设计自适应律对其进行在线估计，以补偿不确定性对系统的影响。在控制器设计过程中，结合Lyapunov稳定性理论，逐步构造虚拟控制律与实际控制律，并利用不等式放缩技巧处理非线性耦合项。理论分析证明，所提方法能保证闭环系统中所有信号一致最终有界，且通过调节设计参数可使跟踪误差收敛至原点任意小的邻域内。最后，仿真结果表明，系统输出能够快速、准确地跟踪期望轨迹，验证了该控制策略在处理模型不确定性方面的有效性和可行性。

Abstract: In practical operation, single-joint robotic systems often face challenges posed by imprecise modeling, such as parameter perturbations and unknown external disturbances, which pose difficulties for high-precision trajectory tracking control. To address this issue, this paper proposes a robust adaptive tracking control strategy based on backstepping. First, a strict-feedback nonlinear system model accounting for external disturbances is established. Subsequently, to handle the unknown nonlinear dynamics in the system, an unknown constant is introduced as the core parameter that defines an upper bound for it, and an adaptive law is designed to estimate it online, compensating for the impact of uncertainties. During controller design, the Lyapunov stability theory is employed to construct virtual and actual control laws step by step, while inequality techniques are used to manage nonlinear coupling terms. Theoretical analysis demonstrates that the proposed method ensures that all signals in the closed-loop system are uniformly ultimately bounded, and by adjusting design parameters, the tracking error can be made to converge to an arbitrarily small neighborhood of the origin. Finally, simulation results show that the system output can quickly and accurately track the desired trajectory, validating the effectiveness and feasibility of this control strategy in handling model uncertainties.