Optimal Trajectories for Propellant-Free Rendezvous Missions

TL;DR

This paper introduces a novel method for propellant-free spacecraft rendezvous by leveraging space environmental forces, optimizing trajectories through direct control methods considering nonlinear dynamics and multiple force effects.

Contribution

It presents a new optimal control framework that incorporates differential drag and Lorentz forces for energy- and time-efficient rendezvous without propellant use.

Findings

Differential drag's impact varies with altitude on control input and cost.

Lorentz forces can reduce rendezvous time when combined with differential drag.

Weighted cost functions enable balancing between differential drag and Lorentz forces for optimal energy use.

Abstract

The paper provides a new approach to utilizing space environmental forces in time- and energy-optimal, propellant-less spacecraft rendezvous missions. Considering the nonlinear form of the relative dynamic equations, rendezvous missions are posed as optimal control problems subject to input saturation. We conduct a direct optimal control approach to obtain optimal trajectories and control inputs. Initially, we consider the differential drag only and conduct a comprehensive analysis of the effect of altitude on the required control input and achieved cost function. Lorentz forces are then utilized with the differential drag, reducing the time required for time-optimal missions. For energy-optimal missions with combined differential drag and Lorentz forces, a weighting matrix in the cost function is introduced to adjust the relative contributions of these forces.