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.