Optimal SUAS Path Planning in Three-Dimensional Constrained Environments

Small Unmanned Aircraft Systems have grown in autonomy and capability and continue to complement Department of Defense mission objectives. Teaming unmanned aircraft with manned vehicles can expand mission profiles and reduce risk to human life. To fully leverage unmanned systems, vehicles must be efficient and autonomous in path planning development. The work herein explores direct orthogonal collocation optimal control techniques combined with fast geometric path planning algorithms to reduce computation time and increase solution accuracy for small unmanned aircraft systems path planning missions. Previous work in the two-dimensional plane demonstrated a methodology to provide optimal flight paths through defined simplex corridors and simplified the optimal control parameter bounds by formulating the problem in the barycentric coordinate system. These methodologies are extended in this paper for three-dimensional flight and are solved with two different formulations for flight in an urban environment. The first formulation solves the constrained optimal control problem using a single phase while modeling the building constraints with superquadric functions. The second formulation implements the simplex methodology, eliminating polygonal constraints from the search domain, and solving the optimal path in a multiple phase approach. Results illustrate the benefits gained in computation time and accuracy when implementing simplex methods into the optimal control design and provide a foundation for closing the gap to real-time, onboard operations for unmanned vehicle path planning.