Sliding mode predictive guidance for terminal rendezvous in eccentric orbits

This paper presents a robust guidance algorithm for a chaser spacecraft to rendezvous with a target spacecraft in Earth orbit. The basis of the proposed guidance method is finding an appropriate set of states as close as possible to the current states that would lead the spacecraft to the target in the desired mission time. In order to provide the prediction of states, the relative dynamics equations of motion are solved analytically for the chaser spacecraft rendezvous considering constant acceleration. Although the equations are solved for rendezvous with circular orbit target, it is shown by several simulations that the proposed guidance algorithm is applicable in perturbed elliptical orbits rendezvous as well. The sliding mode method as a robust nonlinear method is utilized as the steering law. The robust steering law tracks the desired states computed by the predictive guidance method. The Lyapunov stability method proves the asymptotic stability of the integrated guidance and steering laws. Because the proposed closed-loop guidance is simple and computationally easy, it is suitable for implementation in real-time applications. Some numerical simulations are conducted to show the performance of the proposed guidance method in different conditions. It is illustrated that compared with other steering laws, the fuel consumption is reduced utilizing the proposed guidance approach. The results reveal that the sliding mode guarantees the tracking of the required states and minimum final errors even in the presence of uncertainties and disturbances.