Trajectory optimization using mixed-integer linear programming

Abstract

This thesis presents methods for finding optimal trajectories for vehicles subjected to avoidance and assignment requirements. The former include avoidance of collisions with obstacles or other vehicles and avoidance of thruster plumes from spacecraft. Assignment refers to the inclusion of decisions about terminal constraints in the optimization, such as assignment of waypoints to UAVs and the assignment of spacecraft to positions in a formation. These requirements lead to non-convex constraints and difficult optimizations. However, they can be formulated as mixed-integer linear programs (MILP) that can be solved for global optimality using powerful, commercial software. This thesis provides several extensions to previous work using MILP. The constraints for avoidance are extended to prevent plume impingement, which occurs when one spacecraft fire thrusters towards another. Methods are presented for efficient simplifications to complex problems, allowing solutions to be obtained in practical computation times. An approximation is developed to enable the inclusion of aircraft dynamics in a linear optimization, and also to include a general form of waypoint assignment suitable for UAV problems. Finally, these optimizations are used in model predictive control, running in real-time to incorporate feedback and compensate for uncertainty. Two major application areas are considered: spacecraft and aircraft. Spacecraft problems involve minimum fuel optimizations, and include ISS rendezvous and satellite cluster configuration. Aircraft problems are solved for minimum flight-time, or in the case of UAV problems with assignment, waypoint values and vehicle capabilities are included. Aircraft applications include air traffic management and coordination of autonomous UAVs. The results in this thesis provide a direct route to globally-optimal solutions of these non-convex trajectory optimizations.