Coordinated Motion Control of Multiple Manipulator Space Free-flyers

In this paper, coordination between a spacecraft and its several manipulators is investigated, during a capture maneuver of a moving object in space. Using a general Lagrangian formulation, the dynamics model of the system is derived, and the results are summarized in an explicit dynamics model of multiple manipulator space free-flyers. The system dynamics is also formulated on the basis of choosing Euler parameters for orientation representation. This selection introduces algebraic constraints to the system, and the Natural Orthogonal Complement Method is applied to obtain independent system of equations of motion. Two model-based control algorithms, based on an Euler angle and an Euler parameter description of the orientation, are developed that allow coordinated control of the manipulators and the spacecraft, to track the planned trajectories. These trajectories ensure smooth operation, and reduce disturbances on the spacecraft and on the object just before grasping. The performance of the two model-based algorithms is compared to that of a transposed Jacobian controller, by a 3D simulation. It is shown that both model-based algorithms result in smaller errors, as long as model uncertainties are limited. However, the Euler angle model-based control algorithm (MB1) presents the inconvenience of representational singularities at some orientations, while the one based on Euler parameters (MB2) overcomes this problem.