Model Predictive Framework for Guidance and Control of a Multi-Satellite Assembly in Elliptic Orbit

Abstract

In this paper, a guidance and control system for multi-satellite assembly missions in proximity operations is proposed. Utilizing the Tschauner-Hempel relative motion equations, the system is developed within the framework of model predictive control. Linear inequality constraints are employed to handle control input saturation of thrusters and to ensure collision avoidance between satellites. Additionally, a new line-of-sight constraint method is introduced to facilitate smooth docking while simplifying the optimization problem. The proposed algorithm aims to minimize a predefined cost function, which is a weighted sum of state errors and control efforts. At each sampling time, an online quadratic optimization problem is solved to determine the optimal control action that satisfies all mission constraints. Nonlinear numerical simulations in MATLAB are used to demonstrate that the proposed guidance and control system achieves the desired performance. The algorithm is tested for various multi-satellite assembly configurations (cubic and hexagonal) in elliptic orbits of arbitrary eccentricity. A comparative study is conducted between the proposed algorithm and a linear model predictive control algorithm based on the Clohessy-Wiltshire linear model. The results show that the proposed algorithm achieves superior performance in terms of constraint satisfaction and control efforts.