Abstract: This paper discusses the control of a free-floating space-based robot system with time delay to track the desired trajectory in inertial space when both the attitude and location of the base are uncontrolled. Combining the relationship of the linear momentum conservation and the Lagrange approach, the full-controlled dynamic equation and the Jacobian relation of the space-based robot system are analyzed and established. Based on the above results, for the case of a space-based robot system with time delay, mathematical models suitable for the design of control systems under the situation of time delay are established by using the Taylor series predictive and approximation method. Using the said mathematical model, an improved nonlinear feedback control scheme of a space-based robot system with time delay is proposed. Meanwhile, Lyapunov's second method is employed in combination with the way of norms and graphical analysis to prove the whole closed-loop control system's asymptotic stability with the existence of time delay. The above control scheme can effectively control the end-effector of a space-based robot to stably track the desired trajectory in inertial space. The effect of the controllers is testified by computer simulation.

Key words: free-floating space-based robot system, time delay, Taylor series expansion, inertial space, nonlinear feedback control