On Higher Order Inverse Kinematics Methods in Time-Optimal Trajectory Planning for Kinematically Redundant Manipulators

Time-optimal motion control will only find industrial applications if the optimal motions can actually be performed by standard industrial robots. This is not ensured by any optimal motion planning scheme proposed up to now. The limiting aspect rendering all these schemes impractical is the insufficient continuity of the motion trajectories. In this paper, a time-optimal path following along a predefined end-effector path is addressed for kinematically redundant robots, where nonredundant robots are included as special cases. As prerequisite explicit expressions for the higher order inverse kinematics are presented. Kinematic redundancy is resolved and exploited within the trajectory planning using the joint space decomposition and a novel pseudoinverse-based solution of the higher order inverse kinematics. The approaches are demonstrated for two examples of kinematically redundant manipulators performing time-optimal motions along prescribed end-effector paths in compliance with technological constraints. The optimization results are experimentally validated.