Optimal Trajectory Generation for Manipulator Robots under Thermal Constraints

We propose here to deal with the optimization of velocity profiles of manipulator robots with a minimum time criterion subject to thermal constraints. This paper deals with the real impact of thermal limitations on optimal velocity profiles and the methods to calculate the corresponding optimal trajectories. We first calculate analytically the optimal solution in a simple case in order to verify the validity of the numerical algorithm and also to present a general methodology to calculate optimal trajectories in robotics using results from the theory of calculus of variations and not from the theory of optimal control. We derive then a numerical algorithm based on the discretization of the time law through an interpolation with non uniform cubic splines. This algorithm shows robust and efficient convergence properties and the trajectories thus generated were executed successfully on a Staubli Rtimes90