  This paper presents methods for dramatically improving the performance of
sampling-based kinodynamic planners. The key component is the first-known
complete, exact steering method that produces a time-optimal trajectory between
any states for a vector of synchronized double integrators. This method is
applied in three ways: 1) to generate RRT edges that quickly solve the
two-point boundary-value problems, 2) to produce a (quasi)metric for more
accurate Voronoi bias in RRTs, and 3) to iteratively time-optimize a given
collision-free trajectory. Experiments are performed for state spaces with up
to 2000 dimensions, resulting in improved computed trajectories and orders of
magnitude computation time improvements over using ordinary metrics and
constant controls.
