On time-optimal trajectory planning for a flexible link robot

Abstract

This article focuses on time-optimal trajectory planning for robots with flexible links. Minimum time trajectories along specified paths as well as time-optimal point-to-point motions, which avoid vibration excitation due to elastic deflections, are determined. This is achieved by additionally constraining parts of the generalized forces and generalized force derivatives, resulting from the elastic potential. Therefore, the dynamical robot model is obtained using the Projection Equation. In a further step, a reduced model with the most essential degrees of freedom and sufficient accuracy is introduced, resulting in a flat system. Utilizing this, a trajectory control with an exact feedforward linearization in combination with a feedback part, consisting of a motor joint as well as a joint torque control, is realized. This nearly ideal control is used for moving on the time-optimal trajectories. The optimization is conducted with respect to velocity, jerk and motor torques as well as the newly introduced constraints, computable due to the flatness of the system. Experimental results demonstrate the improvement concerning vibration avoidance of the considered robot. Furthermore, a comparison between the occurring bending stress and the maximum permissible bending stress shows that mechanical damage is prevented with the use of the additional constraints.