Dynamic Modelling and Continuous Trajectory Tracking Control of Space Robots Based on Lie Group SE(3)

For space robots, it is difficult to track continuous time-varying manifolds on SE(3) by using traditional closed-loop control strategies, which are designed to track the position and the attitude separately. Therefore, the dynamics model should be rebuilt, and the corresponding control strategy should be redesigned. Firstly, the dynamics equations for a space robot in the joint space and workspace are established separately in the framework of Lie group SE(3) and screw theory based on the Lagrange principle. Secondly, based on the proposed feedback form, a PD (proportional derivative) control law of output force on the end-effector is designed, and a closed-loop continuous tracking control strategy is proposed using the force Jacobian matrix and the kinematic model. The simulation results show that the control scheme has good performance when the system state changes gently. Furthermore, a robust sliding mode tracking control scheme is designed. The simulation results show that the proposed robust control law has better accuracy than the PD control law because the system state changes wildly. Finally, a robust fuzzy sliding mode tracking control scheme is designed to deal with the chattering phenomenon. The simulation results show that the proposed robust fuzzy control law can eliminate the chattering well and decrease the joint control torque significantly. The robustness of the proposed robust fuzzy control law is also verified by numerical simulation.