Abstract: A trajectory planning method is proposed to regulate the manipulator to track the target with the desired velocity. The proposed method can achieve the obstacle avoidance while satisfying joint limits. Based on the trajectory planning method, an adaptive control strategy is designed, by which the free-floating space robot can track and capture a nutational and rotational satellite. In addition, the optimal energy-consumption, measurement errors and optimization errors are considered in the control strategy. Firstly, in order to minimize the end-effector tracking error and manipulator energy-consumption, the space robot control strategy is described as an optimization problem with inequality constraints about the joint velocity, torques and the distance from the obstacles. Then, an explicit state equation with a lower triangular matrix is derived, and the objective function is decoupled and linearized. A piecewise optimization method for the joint velocity and torque is designed to replace the traditional convex quadratic programming method to solve the optimal problem, which demonstrates high computational efficiency. The convergence of the proposed control strategy is verified by Lyapunov stability theory.