Development and Real-Time Validation of GNC Systems for Multi-Satellite Assembly

This paper presents a novel real-time validation method for guidance, navigation, and control (GNC) systems of multi-satellite assemblies in proximity operations. The proposed study employs Linear Quadratic Regulator (LQR) and Model Predictive Control (MPC) to track the optimal trajectory while ensuring collision avoidance between the satellites, achieving a relative positioning accuracy of within 0.01 m. Additionally, it introduces a new state-estimation method using the Unscented Kalman Filter (UKF) for the navigation system, which demonstrates a 13.8% improvement in estimation accuracy compared to traditional methods. To optimize fuel consumption, the guidance system is designed using the Lagrange method to achieve the simultaneous assembly of the satellites within a finite time, reducing fuel consumption by 43.6% compared to the standard LQR and MPC methods. The integrated GNC systems are numerically simulated using a high-fidelity 6-DOF (six degrees of freedom) mathematical model of satellite relative motion. The communication topology of the satellites is effectively modeled using Graph Theory, enabling efficient information exchange among them during the assembly process. The proposed systems are verified in real-time using the dSPACE^® SCALAXIO Lab Box, which implements and executes the systems on the target board to verify the feasibility and performance of the proposed algorithms. The GNC systems are initially developed in a MATLAB^®/Simulink environment using code generation mode. A model-in-the-loop (MIL) test is conducted to validate their functionality. Subsequently, the ConfigurationDesk software from dSPACE^® generates optimized C/C++ code, which is then uploaded to the Lab Box for real-time testing. The key contributions of this research include the development and implementation of GNC systems in MATLAB^®/Simulink and their validation through real-time testing, demonstrating their applicability on target boards.