Linear Programming Trajectory Optimization vs. Artificial Potential Function Methods for Rendezvous and Proximity Operations
Benjamin P. Pritchard, Daniel Doyle, Jonathan T. Black · ASCEND 2020 · 2020
Over the past decade, there has been an increasing desire and need for rendezvous and proximity operations. The number of missions that perform proximity operations in the presence of non-cooperative objects is expected to increase, such as orbital debris mitigation and satellite servicing and repair. The scientific and technical communities have been well aware of this trend in mission design and have produced many autonomous path planning and trajectory optimization methods optimized for rendezvous and proximity operations. However, there seems to be a lack of comparison between these methods. New mission designers are left without any starting point for selecting an autonomous path planning algorithm for their mission. The goal of this study is to perform a comparison between two path planning algorithms. The first method to be explored in this study is Linear Programming Trajectory Optimization (LPTO). LPTO generates a path through optimizing a trajectory under the Hill Clohessy Wiltshire equations with constrained initial and final states. The second path planning method is an Artificial Potential Function Method (APFM). APFMs generate a path in real time through gradient descent based on an artificial potential function superimposed in the operating space of the mission. Preliminary investigation, through one-dimensional path planning problems, has shown that LPTO may be best suited to well defined and controlled operating environments, such as when one is attempting to dock a pair of cooperative spacecraft. This is due to the relatively large computation time required for an optimal solution. APFM may be best suited to poorly defined or controlled environments, such as attempting to inspect or capture a piece of orbital debris. Because the path is generated in real time, the system may easily react to changes in the environment. However, the path is generally sub-optimal. This report documents the development procedure of LPTO and APFM path planning methods. A preliminary investigation using a 1-dimensional example is shown, and the results are analyzed. Then, this example is compared with the results of a two-dimensional, relative orbital motion example. This study compares computation time and optimality of each method.