  We consider time-optimal motion planning for dynamical systems that are
translation-invariant, a property that holds for many mobile robots, such as
differential-drives, cars, airplanes, and multirotors. Our key insight is that
we can extend graph-search algorithms to the continuous case when used
symbiotically with optimization. For the graph search, we introduce
discontinuity-bounded A* (db-A*), a generalization of the A* algorithm that
uses concepts and data structures from sampling-based planners. Db-A* reuses
short trajectories, so-called motion primitives, as edges and allows a maximum
user-specified discontinuity at the vertices. These trajectories are locally
repaired with trajectory optimization, which also provides new improved motion
primitives. Our novel kinodynamic motion planner, kMP-db-A*, has almost surely
asymptotic optimal behavior and computes near-optimal solutions quickly. For
our empirical validation, we provide the first benchmark that compares search-,
sampling-, and optimization-based time-optimal motion planning on multiple
dynamical 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.
