Novel Reaction Control Techniques for Redundant Space Manipulators: Theory and Simulated Microgravity Tests

This paper presents two novel redundancy resolution schemes aimed at locally minimizing the reaction transferred to the spacecraft during manipulator manoeuvres. The subject is of particular interest in space robotics because reduced reactions result in reduced energy consumption and longer operating life of the Reaction Control System. The first presented solution is based on a weighted Jacobian pseudoinverse and is derived using Lagrangian multipliers. The weight matrix is defined by means of the generalized inertia matrix, which appears in the spacecraft reaction dynamics. The second one is based on a Least Squares formulation of the minimization problem. In this formulation the linearity of the forward kinematics and of the reaction dynamics equations with respect to the joint accelerations is used, since the joint variables and their derivatives are considered as state variables. A weighting matrix is introduced in both the formulations in order to take into account the relative importance of reaction forces and torques in the specific task. A closed-form solution is derived for both the presented methods, and the equivalence of these two solutions is analytically demonstrated. Two very important characteristics of the presented methods are that they are suitable for real time implementation and that they can take into account the robot physical/mechanical constraints in term of joint angle, velocity and acceleration limits directly inside the solution algorithm. A software simulator has been developed in order to verify the equivalence of the presented inverse kinematics solutions and to simulate their performance for the selected test cases. The proposed solutions have then been experimentally tested using a 3D free-flying robot previously tested in an ESA Parabolic Flight Campaign. In the test campaign the robot has been converted in a planar robot taking advantage of its modular structure, suspended by means of air-bearings on a granite plane, and fixed on ground by means of a custom design dynamometer in order to measure the reaction forces and torques. In this way it is possible to perform simulated microgravity tests without time constraints. The experimental validation of the presented inverse kinematics solutions has been carried out, and the experimental results confirmed the good performance of the proposed methods. In particular, two test cases have been analyzed in order to validate and evaluate the performances of both the unconstrained solution and the solution which takes into account the robot physical limits.