Minimal length multi-segment clothoid return paths for vehicles with turn rate constraints

Continuous curvature recovery paths are needed to accurately return a fixed wing autonomous vehicle with turn rate constraints back to a missions path in the correct direction after collision avoidance. Clothoid paths where curvature is linearly dependent to arc length can be used to make multi-segment splines with continuous curvature, but require optimization to ensure that the path is of minimal length while meeting curvature and sharpness limits. The present work considers the problem of returning a fixed wing aircraft back to its original path facing the correct direction after a leaving it during collision avoidance by presenting a method of optimizing a three segment clothoid spline to be of minimal length while meeting fixed wing turn rate constraints and targeting a path function. The impact of this work is enabling accurate path recovery after collision avoidance with minimal length paths that minimize the time spent off a missions planned route, giving better control over time of arrival for the planned route and more time to complete mission objectives.