Abstract
Space robots, which consist of a satellite base and a manipulator mounted on it, are expected to perform various tasks for construction and maintenance of space structures. Since the angular momentum of the 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 squares of accelerations of the joint angles during motion is minimized.
First, the equations of motion of the space robot are derived, where the orientation of the satellite base is expressed in terms of Euler quaternions. We parameterize the motion of joint angles by expressing it in terms of the truncated Fourier series, and a nonlinear programming technique using sequential quadratic programming algorithm is applied to determine the optimal coefficients of the Fourier series. Some results of the numerical computation are shown.
