Optimal Control for Robot Manipulators

Abstract

A trajectory planning method based on the dynamic model of robot manipulators is presented. First the problem of the optimal trajectography is discussed by considering several sub-problems related to the structural and modelling singularities, obstacle avoidance and technological constraints. The trajectory is then obtained through the optimization of a time-energy criterion and the identification of the conditions governing all singular configurations of a six degrees of freedom manipulator whose inverse kinematic position problem has a closed form solution. This general solution is applicable to a large class of robotic systems and takes into account constraints on the torques, non linearities and non convexities in the state space equations. The discrete augmented Lagrangian (DAL) technique is used to obtain a controller that caters for constraints on the state, as well as for system inputs, task specification and environnement modelling. The penalty coefficient asssociated with the equality and inequality constraints of the DAL is considered as a variable which is adjusted during the iterative procedure in order to improve the conditioning and the constraints satisfaction. The method was programmed on a PC-AT and some simulation results are given. The method was also used as a CAD tool for the trajectory planning of the modular assembly robot PAMIR developed at the Control Laboratory of ESIEE.