Time-Optimal Paths for High-Speed Maneuvering

Abstract

Recent theoretical results have completely solved the problem of determining the minimal length path for a vehicle moving from an initial configuration to a final configuration. Time- optimal paths for a constant-speed vehicle are a subset of the minimum length paths. The time-optimal paths consist of sequences of arcs of circles and straight lines. The Pontrya gin Maximum Principle introduces concepts (dual variables, bang-bang solutions, singular solutions, and transversality conditions) that provide important insight into the nature of the time-optimal paths. We have created a module that finds the time-optimal path from an initial canfrguration to a final configuration. We have demonstrated that the paths can be followed by a large (820-kg) mobile robot.