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In this paper, we propose an adaptive controller for a space robot system with unknown payload parameters. The dynamic equations of dual-arm space robot system are derived through the Lagrangian formulation. The obtained dynamic equation can be represented by a group of inertial parameters. Based on the results and considered unknown payload parameters, we design an adaptive controller for the robot system to track the desired trajectory. And the numerical simulation is carried out, which confirms the controller proposed is feasible and effective.