The objective of this paper is to solve the minimum time trajectory planning problem of a robotic manipulator under average heat generation restriction. The solving procedure is divided into two stages. In the first stage, the motion trajectory is determined so as to minimize the cost function including both control time and average heat generation of all motors with different Lagrangian multipliers: In the second stage, the optimal Lagrangian multipliers are chosen so as to minimize the control time. To obtain the optimal trajectory in the first stage, we propose a new approach, by which the trajectory is approximated by 5th-order spline function and the optimization is performed with respect to not the spline function coefficients, but to the motion state variables at prescribed node points. To carry out the second stage, two methods are considered. In one method we assume that the control time can be minimized when all actuators generate the respective limited average heat at the same time. In the other we assume that the control time can be minimized when only one of them generates its limited average heat. This method is applied to the trajectory planning problems of a two-degrees-of freedom robotic manipulator with rotary joints and two typical calculated examples are presented.
