Rapid path-planning algorithms for autonomous proximity operations of satellites

Autonomous proximity operations (APOs) can be bifurcated into two phases: (i) close-range rendezvous and (ii) final approach or endgame. For each APO phase, algorithms capable of real-time path planning provide the greatest ability to react to “unmodeled” events, thus enabling the highest level of autonomy. This manuscript explores methodologies for real-time computation of APO trajectories for both APO phases.;For the close-range rendezvous trajectories, an Adaptive Artificial Potential Function (AAPF) methodology is developed. The AAPF method is a modification of the Artificial Potential Function (APF) methodology which has favorable convergence characteristics. Building on these characteristics, the modification involves embedding the system dynamics and a performance criterion into the APF formulation resulting in a tunable system. Near-minimum time and/or near-minimum fuel trajectories are obtained by selecting the tuning parameter. Monte Carlo simulations are performed to assess the performance of the AAPF methodology.;For the final approach or endgame trajectories, two methodologies are considered: a Picard Iteration (PI) and a Homotopy Continuation (HC). Problems in this APO phase are typically solved as a finite horizon linear quadratic (LQ) problem, which essentially are solved as a final value problem with a Differential Riccati Equation (DRE). The PI and HC methods are well known tools for solving differential equations and are utilized in this effort to provide solutions to the DRE which are amenable to real-time implementations; i.e., they provide solutions which are functionals to be evaluated real-time. Several cases are considered and compared to the classical DRE solution.