Hill-Clohessy-Wiltshire-Based Multi-Objective Optimization (MOP) for Relative Positioning in Small Groups of Interacting Objects

This research presents a performance analysis of a multi-objective optimization (MOP) strategy designed for managing relative positioning within small groups of interacting objects in orbit. Our study addresses the challenges of proximity navigation and formation maintenance by leveraging the analytical framework of the Hill-Clohessy-Wiltshire (HCW) equations. Using the MATLAB environment, we developed a mathematical model of the relative dynamics of bodies in the local reference frame (LVLH), providing a unified framework for describing the coupled trajectories of multiple interacting agents.
The research methodology was executed using a rigorous three-step approach. First, we formulated the HCW equations of motion within a multi-objective optimization algorithm to simultaneously minimize fuel consumption (Δv) and relative positioning error. Secondly, we implemented a classical single-objective control structure as a performance benchmark to evaluate the trade-offs offered by the Pareto front of the MOP solution. Finally, the architecture was validated by a high-fidelity simulation reproducing a flight scenario involving a formation of interacting objects, taking into account collision safety constraints and J2 orbital perturbations.
Our results demonstrate that while the single-objective approach allows for rapid target acquisition, the Hill-Clohessy-Wiltshire-based MOP strategy offers greater decision-making flexibility, enabling an optimal balance between energy efficiency and the accuracy of maintaining the geometric configuration of the group.