Workspace Control of Free-Floating Space Manipulators with Non-Zero Momentum on Lie Groups

This paper develops an output-tracking controller to control the end-effector pose of an N-link free-floating space manipulator, with non-zero momentum. The space manipulator is modelled as an open-chain multi-body system and its kinematics and dynamics are derived on the Special Euclidean group SE(3). Using the conservation of linear and angular momentum of the system, the dynamics of the space manipulator is carefully reduced. The input-output linearization of the system is performed on the Lie algebra .se(3), without adopting any local coordinate chart for the SE(3). Coordinate-free pose and velocity error functions on SE(3) are then employed to define a modified feedforward, feedback PID control law to stabilize the end-effector pose to a feasible trajectory. A simulation example is provided to demonstrate the tracking capabilities of the proposed controller.