Modeling and Real-Time Simulation of Spacecraft Berthing: Orbital Dynamics and Lumped Parameter Systems in Proximity Operations

The research, conducted within the Multi-Satellite Proximity Operations for Rendezvous and Docking Missions in Earth and Moon Orbits (MUSAPOEM) project funded by the Italian Space Agency (ASI), presents advanced mathematical models and algorithms for autonomous guidance, navigation, and control (GNC) in proximity operations in both terrestrial and lunar environments.Future collaborative missions such as lunar sample return, in-orbit assembly, and satellite servicing require precise modelling of the dynamics involved in berthing and docking manoeuvres.A hybrid modelling approach is proposed for berthing operations between a chaser and a target spacecraft, selecting the most suitable model depending on their relative distance.For distances above a critical threshold, the relative motion is described using orbital dynamics; for closer ranges, a detailed robotic system model is adopted to simulate the extension and positioning of the manipulator arm towards the docking point.Upon contact, a lumped parameter model (LPM) simulates the interaction phase, ensuring real-time computation where simulation time is always greater than computation time.This multi-phase modelling strategy enables complete mission simulation, including berthing and unberthing manoeuvres, with high fidelity representation of contact forces.These forces, derived from multibody simulations, include both normal and frictional components, where static and dynamic friction significantly influence docking stability.A Particle Swarm Optimization (PSO) algorithm is employed to tune the parameters of both the lumped parameter and multibody models, achieving accuracy and efficiency in real-time scenarios.The results demonstrate the framework's ability to simulate the full mission timeline while dynamically switching between modelling approaches according to mission phase requirements.This methodology contributes to robust, efficient, and autonomous GNC solutions, supporting future cooperative space missions in Earth and lunar orbits.