Nonlinear trajectory optimization with path constraints applied to spacecraft reconfiguration maneuvers

Abstract

Future space assembly and science missions (e.g., Terrestrial Planet Finder) will typically require complex reconfiguration maneuvers involving well coordinated 6 DOF motions of the entire fleet of spacecraft. The motions must also satisfy constraints such as collision avoidance and pointing restrictions on some of the instruments. This problem is particularly difficult due to the nonlinearity of the attitude dynamics and the non-convexity of some of the constraints. The coupling of the positions and attitudes of the N spacecraft by some of the constraints adds a significant complication because it requires that the trajectory optimization be solved as a single 6N DOF problem. This thesis presents a method to solve this problem by first concentrating on finding a feasible solution, then developing improvements to it. The first step is posed as a path planning problem without differential constraints and solved using Rapidly-exploring Random Trees (RRT's). The improvement step is posed as a feasible nonlinear optimization problem and solved by an iterative optimization similar to a sequential linear programming method. The primary contribution of the thesis is an improvement to the basic RRT algorithm that replaces the connection step with a more complex function that takes into account local information about the constraints. Two functions are proposed, one based on artificial potential functions, and another based on a random search. The results show that the new RRT with either of these connection functions is faster and more reliable for a difficult sample problem.

(cont.) The combination of an RRT with the new connection functions, and the improvement step, is also demonstrated on several challenging spacecraft reconfiguration problems with up to 16 spacecraft (96 DOF). The solution technique is shown to be robust and with computation times fast enough to embed in a real-time optimization algorithm as part of an autonomous onboard control system.