一种新型高阶连续的点对点运动轨迹规划算法

A novel high-order continuous point-to-point motion trajectory planning algorithm

摘要:

为解决机器人、数控机床、起重机等机械设备的运动状态变化对系统冲击过大的问题,利用两段双曲正切函数构造衔接点在匀速段的S型速度曲线,并将S型曲线与跟踪微分器结合,生成一种结构简单、高阶连续的点对点运动轨迹 (HCPPMT),通过调整HCPPMT的相关参数,可调节加、减速阶段的快慢程度、匀速阶段的最大速度、作业时间,使点对点运动过程中加速、匀速、减速过程的平滑程度、冲击强度可控、各阶段状态可调,减少了运动状态切换对机械设备的冲击,增强了运动平稳性。应用Lyapunov方法证明了HCPPMT的收敛性,并对HCPPMT具有的一些物理性质进行了严格的数学证明,通过与其他两种轨迹对比,以及在三自由度机械臂末端执行器轨迹规划上的应用,说明了HCPPMT的优越性。

Abstract:

In order to solve the problem of excessive impact on the system due to the movement state changes in robots, CNC machine tools, lifting machinery, and other equipment, two hyperbolic tangent functions were used to construct the S-type velocity curve with the junction point at uniform motion stage. Combined the S-type velocity curve with tracking differentiator, a high-order continuous point-to-point motion trajectory (HCPPMT) was obtained. By adjusting the relevant parameters of HCPPMT, the speed at acceleration and deceleration stages, as well as the maximum speed and operation time at constant speed stage could be adjusted, so that the smoothness and impact strength during the acceleration, constant speed, and deceleration processes could be controlled, and the states of each stage could be adjusted in the process of point-to-point motion. Therefore, the impact of motion state switching on the mechanical equipment could be reduced and the stability of the motion could be enhanced. The convergence of HCPPMT was proved by Lyapunov method, and the physical properties of HCPPMT were mathematically proved. The superiority of HCPPMT was illustrated by comparing with two other trajectories and the application of trajectory planning for end-effector of three-degree-of-freedom manipulator.