Optimal Path Planning for Space Robots with Joint Friction Torque

Abstract

This paper presents a method of optimal path planning for space robots to minimize the total accouter torque required for realizing the final position of the manipulator hand. The proposed method determines the optimum trajectory of joint angles that minimizes the total amount of the output torque to be applied at the joint actuators. In this paper, the nonlinear friction torque inherent to the joint actuator mechanism, as well as the dynamic torque used for the manipulator motion, is modeled in the equations of motion. The optimal control problem is solved by using Fourier series approximation of the trajectories. Thereby the original optimal control problem is reduced to a nonlinear parameter optimization problem, where the Rosenbrock method is used in the cost function minimization. The sequential conjugate gradient and restoration (SCGR) algorithm is also used for improving the Fourier series solutions. Numerical simulations are made for a twodimensional experimental model of free-flying space robot having a three-link rigid manipulator. The results show that the obtained optimum trajectory depends highly on the magnitude of the joint friction torque, which imply the fact that an accurate modeling of the joint friction torque is very important for the optimal path planning.