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We present an algorithm for non-holonomic motion planning (or 'parking acar') that is as computationally efficient as a simple approach to solving thefamous Piano-mover's problem, where the non-holonomic constraints are ignored.The core of the approach is a graph-discretization of the problem. Thegraph-discretization is provably accurate in modeling the non-holonomicconstraints, and yet is nearly as small as the straightforward regular griddiscretization of the Piano-mover's problem into a 3D volume of 2D positionplus angular orientation. Where the Piano mover's graph has one vertex andedges to six neighbors each, we have three vertices with a total of ten edges,increasing the graph size by less than a factor of two, and this factor doesnot depend on spatial or angular resolution. The local edge connections areorganized so that they represent globally consistent turn and straightsegments. The graph can be used with Dijkstra's algorithm, A*, value iterationor any other graph algorithm. Furthermore, the graph has a structure that lendsitself to processing with deterministic massive parallelism. The turn andstraight curves divide the configuration space into many parallel groups. Weuse this to develop a customized 'kernel-style' graph processing method. Itresults in an N-turn planner that requires no heuristics or load balancing andis as efficient as a simple solution to the Piano mover's problem even insequential form. In parallel form it is many times faster than the sequentialprocessing of the graph, and can run many times a second on a consumer gradeGPU while exploring a configuration space pose grid with very high spatial andangular resolution. We prove approximation quality and computational complexityand demonstrate that it is a flexible, practical, reliable, and efficientcomponent for a production solution.

Nonholonomic Motion Planning as Efficient as Piano Mover's