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We address the problem of optimal path planning for a simple nonholonomicvehicle in the presence of obstacles. Most current approaches are either splithierarchically into global path planning and local collision avoidance, orneglect some of the ambient geometry by assuming the car is a point mass. Wepresent a Hamilton-Jacobi formulation of the problem that resolves time-optimalpaths and considers the geometry of the vehicle.

A Hamilton-Jacobi Formulation for Time-Optimal Paths of Rectangular Nonholonomic Vehicles