Modelling and Optimal Control of a Docking Maneuver with an Uncontrolled Satellite

TL;DR

This paper models and solves an optimal control problem for docking a controlled satellite with an uncontrolled target, ensuring collision avoidance and successful rendezvous, demonstrated through simulations of capturing tumbling satellites.

Contribution

It introduces a comprehensive modeling and optimal control framework for satellite rendezvous with constraints, solved via full discretization in AMPL/IpOpt, applied to tumbling satellite capture.

Findings

Successful simulation of capturing tumbling satellites

Effective avoidance of collision during rendezvous

Validated control strategy for satellite docking

Abstract

Capturing disused satellites in orbit and their controlled reentry is the aim of the DEOS space mission. Satellites that ran out of fuel or got damaged pose a threat to working projects in orbit. Additionally, the reentry of such objects endangers the population as the place of impact cannot be controlled anymore. This paper demonstrates the modelling of a rendezvous szenario between a controlled service satellite and an uncontrolled target. The situation is modelled via first order ordinary differental equations where a stable target is considered. In order to prevent a collision of the two spacecrafts and to ensure both satellites are docked at the end of the maneuver, additional state constraints, box contraints for the control and a time dependent rendezvous condition for the final time are added. The problem is formulated as an optimal control problem with Bolza type cost functional and solved using a full discretization approach in AMPL/IpOpt. Last, simulation results for capturing a tumbling satellite are given.