This paper presents an optimal trajectory planning scheme for robotic capturing of a tumbling object. Motion planning of a space robot is much more complex than that of a fixed-based robot, due to the dynamic coupling between the manipulator and its base. In this work, the Path Independent Workspace (PIW), in which no dynamic singularity occurs, and Path Dependent Workspace (PDW) of the space robot are first calculated by the proposed algorithm. The motion equations of the tumbling object are formulated based on the Euler dynamics equations and the quaternion, which are used to predict the long-term motion of a grasping point on the tumbling object. Subsequently, the obtained PIW workspace and predicted motion trajectories are used to plan the trajectory of the end-effector to intercept the grasping point with zero relative velocity (to avoid impact) in an optimal way. In order to avoid dynamic singularity occurring at the capture moment, the optimal capture occasion is first determined by three proposed criterions guaranteeing the capture can be safely, reliably and rapidly performed, then the optimal trajectory of the end-effector is generated minimizing a cost function which acts as a constraint on acceleration magnitude. Simulations are presented to demonstrate the trajectory planning scheme for a space robot with a 3-degree of freedom (DOF) manipulator grasping a tumbling satellite, the results show that the manipulator end-effector can smoothly intercept the grasping point on the tumbling satellite with zero relative velocity.
