AI 中文总结
该研究针对受非线性执行器约束的伺服系统，提出结合解析最优性与高计算效率的实时参考整形方法，搭配轨迹补偿器，可在近100kHz频率下实现实时最优运动规划，计算速度优于现有方法。
AI 中文摘要
本文研究受非线性、依赖状态的执行器约束的伺服系统的实时运动规划问题，提出一种结合解析最优性与高计算效率的参考整形方法。利用Karush-Kuhn-Tucker条件明确刻画问题结构，证明最优解位于有限候选点集合内，通过闭式表达式与小规模特征值问题构造完整解集，得到确定性算法，可恢复精确最优解，无需迭代优化或求根。针对激进指令引发的运动学失配，引入实时轨迹补偿器校正累积位置误差，同时保持可行性。仿真结果显示，该方法相较现有方法计算速度显著提升，可在接近100kHz的频率下实现实时运行。
英文摘要
This paper addresses real-time motion planning for servo systems subject to nonlinear, state-dependent actuator constraints. A reference reshaping method is proposed that combines analytical optimality with high computational efficiency. Using Karush-Kuhn-Tucker conditions, the problem structure is explicitly characterized, and it is shown that the optimal solution lies within a finite set of candidate points. The complete solution set is constructed via closed-form expressions and a small-scale eigenvalue problem, yielding a deterministic algorithm that recovers the exact optimal solution without iterative optimization or root-finding. To address kinematic mismatch induced by aggressive commands, a real-time trajectory compensator is introduced to correct accumulated position error while preserving feasibility. Simulation results demonstrate significant computational speed improvements over existing methods, enabling real-time implementation at frequencies approaching 100 kHz.
