This paper introduces a motion planning method for capture of tumbling objects using a free-floating space robot. The proposed approach incorporates an improved Rapidly Exploring Random Tree Star (RRT*) algorithm enabling obstacle avoidance and generating desired trajectories for the robot's end-effectors. Additionally, a multi-layer optimization process and a greedy policy are proposed to achieve singularity avoidance, joint velocity, and acceleration optimization by leveraging the robot arm's joint energy distribution, torque, and manipulability. By adopting this motion planning strategy, the space robotic system demonstrates improved performance in obstacle and singularity avoidance, without the need for inverse Jacobian matrix calculations. Furthermore, the multi-layer optimization process enhances trajectory smoothness and reduces end-effector vibration through energy and torque optimization. This research contributes to advancing space robotic systems by enhancing the entire energy and torque consumption on motion planning to make the end-effector move smooth and reduce the vibration.