北京大学学报（自然科学版）2026，Vol.62Issue(5)：941-949,9.DOI:10.13209/j.0479-8023.2025.100
基于改进的 Udwadia-Kalaba 方法对含非光滑机械臂系统轨迹控制的研究
Trajectory Control of Non-smooth Robotic Arms Based on the Modified Udwadia-Kalaba Method
摘要
Abstract
To address the degradation of tracking accuracy and insufficient control stability in robotic manipulator systems involving nonsmooth effects,such as viscous and sliding friction,a servo control strategy based on the Udwadia-Kalaba(U-K)method is proposed.Within an extended U-K dynamics framework that accounts for the coupling between normal and tangential constraint forces,the desired trajectory of the controlled system is formulated as a set of servo constraints.Analytical expressions for the active control forces and passive constraint forces are then explicitly derived,based on which a corresponding servo control method is developed.This method effectively mitigates system oscillations and tracking accuracy degradation caused by the coupling of constraint forces.To further enhance system stability,the Baumgarte stabilization method is introduced to correct constraint violations induced by initial perturbations.In addition,a smoothing Newton algorithm is employed to regularize the absolute-value term arising from the determination of the normal support-force direction,thereby improving numerical stability.Simulations of various complex trajectories are conducted in MATLAB.The results demonstrate that the proposed servo control strategy effectively suppresses friction-induced oscillations while ensuring high-precision and asymptotically stable trajectory tracking,exhibiting favorable robustness and generalizability.关键词
非光滑机械臂系统/Udwadia-Kalaba(U-K)方法/伺服控制策略/轨迹跟踪Key words
non-smooth manipulator system/Udwadia-Kalaba(U-K)method/servo control strategy/trajectory tracking引用本文复制引用
荣斯琦,姚文莉,张欣刚,张树翠..基于改进的 Udwadia-Kalaba 方法对含非光滑机械臂系统轨迹控制的研究[J].北京大学学报（自然科学版）,2026,62(5):941-949,9.基金项目
国家自然科学基金(12272197,12202224)和山东省自然科学基金(ZR2022MA066)资助 （12272197,12202224）
