Least Squares Based Reaction Control of Space Manipulators

This paper presents a novel solution for the inverse kinematics of redundant space manipulators, which is aimed at locally minimizing the dynamic disturbances transferred to the spacecraft during trajectory tracking maneuvers. The solution is based on a constrained least-squares approach and is suitable for real-time implementation. To formulate the problem as a function of dynamic variables, the inverse kinematics at the acceleration level is considered. The proposed solution is introduced in the context of a more general theory, including the classical pseudoinverse, the extended task-space, and the task priority solutions. Moreover, the introduction of joint acceleration constraints in order to take into account the physical limits of the manipulator joints and the relaxing of the end-effector tracking requirements have been studied, and their influence on the minimization performance has been assessed. The experimental validation of the proposed solutions, with an insight on the effect of joint flexibility on their performance, has been carried out for a planar three-degrees-of-freedom manipulator. Two test cases have been considered, in which the number of force and torque reaction components to be controlled are equal to or greater than the available degree of redundancy.