A Hamilton-Jacobi Formulation for Time-Optimal Paths of Rectangular Nonholonomic Vehicles
We address the problem of optimal path planning for a simple nonholonomic vehicle in the presence of obstacles. Most current approaches are either split hierarchically into global path planning and local collision avoidance, or neglect some of the ambient geometry by assuming the car is a point mass and/or buffering obstacle boundaries. We present a Hamilton-Jacobi formulation of the problem which resolves time-optimal paths and considers the geometry of the vehicle. In doing so, we avert the need for a hierarchical path planner or other obstacle avoidance considerations. We design an upwind fast sweeping scheme to solve the Hamilton-Jacobi equation numerically, and we conclude by briefly discussing some generalizations.