Path Planning of Space Robots by Using Nonlinear Optimization Technique

A space robot, which consists of a satellite base and a manipulator mounted on it, is expected to perform various tasks involved in the construction and maintenance of space structures. Since the angular momentum of a space robot system is conserved, the motion of the system is subject to nonholonomic constraints. When the manipulator makes motion from an initial position to a desired position, variation of the base orientation depends on the trajectory of the motion owing to the nonholonomic property of the system. Since the satellite base is desired to have a constant orientation, we seek such a trajectory of the manipulator that a given motion is attained, that the base orientation is unchanged before and after the motion, and that the integral of the sum of the squares of accelerations of the joint angles is minimized during motion. First, we derive the equations of motion of the space robot, where the orientation of the satellite base is expressed in terms of Euler quaternions. We express the motion of joint angles in terms of the truncated Fourier series, and apply a nonlinear programming technique using a sequential quadratic programming algorithm to determine the optimal coefficients of the Fourier series. Some results of numerical computations are shown.