中文摘要：

研究了一种优化的超精密点对点运动3阶轨迹规划算法及其精度补偿方法。首先阐述了超精密轨迹规划具有可实用性所必须具备的特征以及实现轨迹时间优化的基本要求。后以系统动力学限制为基础，考虑运动轨迹的全过程，提出了一种通过预处理以获得时间优化的3阶轨迹直接规划算法。提出了一种适当降低系统动力学限制的时间圆整方法，有效补偿了算法计算机离散实现时所带来的精度损失。实例证明了本文提出算法的有效性和可靠性。该算法也成功应用于纳米级精度的半导体加工装备的研发中。

英文摘要：

We study a third-order trajectory planning algorithm for ultra-precision point-to-point motion and its accuracy compensation method. First we explain the characteristics that have to be available for the applicability of the trajectory planning algorithm and the requirements for implementing the optimization of the trajectory time. Considering the whole process of the motion trajectory, we propose the third-order trajectory planning algorithm with time optimization through preprocessing. We also put forward the time roundness method for appropriately reducing the system dynamics constraints, which effectively compensates for the accuracy losses caused by time discretization implementation for the trajectory planning algorithm. A calculation instance verifies the effectiveness and reliability of the algorithm, which is successfully applied to the research and development of nano-level accuracy semiconductor manufacturing equipment.