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In this paper, the adaptive control of free-floating dual-arm space robot system is studied. Firstly, in order to overcome the difficulty that the dynamic equations of dual-arm space robot system can not be linearly parameterized, the system is modeled as under-actuated robot system. And then with the augmentation approach, we demonstrate that the dynamic equations of the system can be linearly dependent on inertial parameters. Based on the results, an adaptive control scheme of dual-arm space robot system is developed. The asymptotic stability of the control scheme is proved with Lyapunov method. A planar free-floating dual-arm space robot system with two objects is simulated to verify the proposed control scheme.