Global Optimum Path Planning for a Redundant Space Robot

Abstract

Robotic manipulators will play a significant role in the maintenance and repair of space stations and satellites, and other future space missions. Robot path planning and control for the above applications should be optimum, since any inefficiency in the planning may considerably risk the success of the space mission. This paper presents a global optimum path planning scheme for redundant space robotic manipulators to be used in such missions. In this formulation, a variational approach is used to minimize the objective functional. Two optimum path planning problems are considered: first, given the end-effector trajectory, find the optimum trajectories of the joints, and second, given the terminal conditions of the end-effector, find the optimum trajectories for the end-effector and the joints. It is explicitly assumed that the gravity is zero in, and the robotic manipulator is mounted on a completely free-flying base (spacecraft) and the attitude control (reaction wheels or thrust jets) is off. Linear and angular momentum conditions for this system lead to a set of mixed holonomic an nonholonomic constraints. These equations are adjoined to the objective functional using a Lagrange multiplier technique. The formulation leads to a system of Differential and Algebraic Equations (DAEs) and a set of terminal conditions. A numerical scheme is presented for forward integration of the above system of DAEs, and an iterative shooting method is used to satisfy the terminal conditions. This approach is significant since most space robots that have been developed so far are redundant. The kinematic redundancy of space robots offers efficient control and provides the necessary dexterity for extra-vehicular activity or avoidance of potential obstacles in space stations.