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.

针对含黏滞与滑动摩擦等非光滑因素的机械臂系统轨迹跟踪任务中存在的精度下降与控制稳定性不足问题, 提出一种基于Udwadia-Kalaba (U-K)方法的伺服控制策略。在考虑法向及切向约束力耦合的U-K动力学拓展理论框架下, 将受控目标的期望轨迹转化为伺服约束条件, 显式地推导出主动控制力和被动约束力的解析表达式, 并研究相应的伺服控制方法, 有效地解决约束力耦合引发的系统震荡及控制精度降低问题。为进一步增强系统的稳定性, 引入Baumgarte稳定化方法来修正初始扰动导致的约束违约问题。同时, 结合光滑牛顿算法, 对法向支持力方向判断引发的绝对值求解问题进行光滑化处理, 提升数值计算的稳定性。基于MATLAB平台, 对多类复杂轨迹进行仿真验证, 结果表明, 该伺服控制策略能够有效地抑制摩擦带来的震荡, 同时保证轨迹的高精度和渐近稳定跟踪, 显示良好的鲁棒性和推广性。