The control of an orbital space robot is challenging due to the strong nonlinear dynamic coupling between the floating base spacecraft and the equipped manipulator. To address this problem effectively, this paper develops a geometric control framework by identifying and exploiting the Lie group structures of the space robot. The paper shows how to formulate the system momentum evolution equations as a set of first-order ordinary differential equations. Then, it discusses the designs of the Lie-algebra proportional-integral controller and the manifold model predictive controller to perform the three-dimensional pose trajectory tracking task. For the manifold model predictive controller, the paper presents the structure-preserving direct-collocation method to enforce the discrete dynamic constraints in a finite-horizon optimal control problem. Furthermore, it presents the performance comparisons of the above two controllers in numerical simulations, and emphasizes the significance of computational accuracy and efficiency, momentum shaping and prediction horizon selection for the manifold model predictive controller, with detailed benchmarks against the classic Euclidean model predictive controller. Finally, the paper demonstrates the trajectory tracking and object capturing experiments in a three-dimensional space via an air-bearing space robot simulator.
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