基于三阶速度和四阶位移的轨迹规划方法研究

Trajectory Planning Method of Motion Stage based on Hybrid Splicing of Third-order Velocity and Fourth-order Displacement Trajectory

针对超精密运动工作台在高速高精度运动过程中的小冲击、小残余振动等运动要求,研究了一种基于三阶速度轨迹和四阶位移轨迹混合拼接的超精密轨迹规划算法。阐述了精密运动工作台轨迹规划具备的实用性特点及约束条件;然后,以系统动力学为基础,结合运动工作台点对点场景运动全过程,提出了对其第二运动阶段的速度进行三阶轨迹规划,并根据运动工作台实际工作区域中稳定时间及工作时间累加结果,完成四阶轨迹特征组合;进而结合工作区域起始位置及三阶速度轨迹对应位移值,反推第一运动阶段终点坐标及位移,求得第一运动阶段特征参数组合;最后,根据第一运动阶段和第二运动阶段的时间切换矩阵特点,拼接形成时间切换矩阵并输出对应加加速度斜率序列,结合多重离散积分方法及精度控制策略,得出运动工作台运动规划轨迹。实例证明提出的算法精确和有效。

Aiming at the motion requirements of small impact,small residual vibration of equipment stage in high-speed and high-precision motion,an ultra-precision trajectory planning algorithm based on the hybrid splicing of third-order velocity trajectory and fourth-order displacement trajectory is studied.Firstly,the applicable characteristics and constraints of motion trajectory planning of the equipment stage are described;Then,based on system dynamics,combined with the whole process of point-to-point movement of equipment stage,a third-order trajectory planning for the second movement phase velocity is proposed,and combined with the actual accumulation results of stabilization time and working time in the actual work area of stage,the fourth-order trajectory feature parameters are obtained;Then,combined with the starting position of the work area and the corresponding displacement value of the third-order velocity trajectory,the end coordinates and displacement of the first movement phase are deduced,and the fourth-order motion feature parameters combination are obtained;Finally,according to the characteristics of time switching matrix of the first movement phase and the second movement phase,the time switching matrix is spliced and the corresponding djerk sequence is output.Combined with the multiple discrete integral method and precision control strategy,the motion planning trajectory of equipment stage is obtained.The simulation experiment show that the proposed algorithm is accurate and effective.