Nonlinear Model Predictive Control of J2-perturbed impulsive transfer trajectories in long-range rendezvous missions

Abstract

This paper develops a Nonlinear Model Predictive Control (NMPC) strategy for robust tracking of multi-impulse smooth transfer trajectories in J2-perturbed orbital environments. The reference trajectories are designed for long-range rendezvous of servicing satellites with orbiting targets. In the proposed NMPC, the control signals are velocity increments at the impulse times, and the prediction horizon is variable due to the impulsive nature of the reference trajectories. The reference control input and the impulse times are pre-specified by the reference trajectory. Then, the NMPC calculates the optimal correction control vector to track the trajectory with minimum deviation and control effort, during the time between two consecutive impulses. To arrive near the target at the end of the transfer, the optimization in the last horizon is modified to be free-final-time, with an added soft constraint to minimize the final distance between the servicer and the target satellite. To avoid singularities in the mean dynamics of the J2-perturbed servicer, the equinoctial orbital elements are used in the process model. We also include the first-order long-periodic effects in this model. We investigate the robustness of the proposed NMPC in a simulation environment that additionally models: (i) the first-order short-periodic effects, (ii) a bounded uncertain acceleration to capture unmodelled dynamics, and (iii) burning time for satellite thrusters. Finally, an evolutionary optimization algorithm is implemented and embedded in the controller to decrease the computational complexity and to handle impulsive control inputs. Simulation results are provided to illustrate the tracking effectiveness of the developed controller.