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Trajectory planning method has been proved to be an effective way to suppress robot vibration in multiple experiments, which can be divided into off-line trajectory planning for repetitive task and online trajectory modified for uncertain task. Particle swarm optimization (PSO) is a typical optimization algorithm, which can be used in offline joint trajectory planning, but classical PSO is incapable of optimizing a joint trajectory with variable constraints. Thus, in this paper, a novel compression factor PSO with penalty function named CP-PSO is proposed to modify joint trajectory, thereby achieve minimum residual elastic potential energy in the case of joint angle constraint. However, CP-PSO algorithm still needs plenty of computation time, which is unsuitable for online optimizing uncertain operational task's trajectory. To solve this issue, trajectory modified based on vibration prediction criteria is put forward to suppress manipulator vibration. Particularly, vibration prediction criteria is based on torque error between theoretical joint torque and actual joint torque, as well as the modified trajectory is named as DKA trajectory by the reason of it is composed of three sections, namely, smooth decelerating process, low velocity keeping process, and accelerating process. When vibration is predicted to occur via vibration prediction criteria, DKA trajectory is switched ON to suppress vibration. Finally, experiments are performed on manipulator to verify the proposed methods.

Trajectory Modified in Joint Space for Vibration Suppression of Manipulator