Angles-Only Robust Trajectory Optimization for NRHO Rendezvous

This study demonstrates a robust trajectory optimization approach for rendezvous and proximity operations with angles-only navigation measurements. Often, sensors that directly measure relative range and velocity require communication or coordination between the chaser and target vehicle and can have limiting pointing accuracy, mass, or power requirements compared to angle measurement sensors. Thus, the capability to perform a rendezvous with only angle measurements can be advantageous for vehicle design and to improve robustness to failures. However, the well studied limitation of angles-only navigation in measuring range results in large uncertainties in the navigation system that must be reduced with chaser vehicle thrust maneuvers to induce observability in range for the navigation filter. This analysis presents a trajectory optimization problem for a lunar ascent rendezvous during a crewed lunar mission in a Near-Rectilinear Halo Orbit (NRHO) that is limited to only angle measurements. The objective of this study is to show that an angles-only rendezvous is feasible in an NRHO and to present the sensitivity to an assortment of constraints generated from a systematic optimization process using linear covariance analysis and particle swarm optimization. Linearized NRHO dynamics and linearized relative targeting are applied to use linear covariance analysis to determine the expected delta-v and trajectory dispersions due to initial state uncertainty, sensor errors, maneuver execution errors, and unmodeled dynamics. The delta-v and trajectory dispersions are passed into a particle swarm optimization algorithm to find the optimized maneuver profile that minimizes fuel use while satisfying constraints such as free drift and underburn to 3-sigma certainty. The trajectory constraints including time available, desired final uncertainty, and initial uncertainty are varied to ascertain sensitivity and desirable engineering trades.