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We consider time-optimal motion planning for dynamical systems that aretranslation-invariant, a property that holds for many mobile robots, such asdifferential-drives, cars, airplanes, and multirotors. Our key insight is thatwe can extend graph-search algorithms to the continuous case when usedsymbiotically with optimization. For the graph search, we introducediscontinuity-bounded A* (db-A*), a generalization of the A* algorithm thatuses concepts and data structures from sampling-based planners. Db-A* reusesshort trajectories, so-called motion primitives, as edges and allows a maximumuser-specified discontinuity at the vertices. These trajectories are locallyrepaired with trajectory optimization, which also provides new improved motionprimitives. Our novel kinodynamic motion planner, kMP-db-A*, has almost surelyasymptotic optimal behavior and computes near-optimal solutions quickly. Forour empirical validation, we provide the first benchmark that compares search-,sampling-, and optimization-based time-optimal motion planning on multipledynamical systems in different settings. Compared to the baselines, kMP-db-A*consistently solves more problem instances, finds lower-cost initial solutions,and converges more quickly.

db-A*: Discontinuity-bounded Search for Kinodynamic Mobile Robot Motion Planning