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In this paper, the dynamics and control of Space Walking Robot (SWR) is considered.The SWR can be regarded as a satellite with a dual-arm manipulator system.The dynamics of SWR with 7 Joint-Rotation-DOFs in each arm is derived by an improved Kane's method.A controller based on feedback linearization and PID control is employed to drive the SWR to follow the desired trajectories.Numerical simulations show that the SWR is capable of tracking the prescribed trajectories to achieve the walking task.