  We present a motion planner for planning through space-time with dynamic
obstacles, velocity constraints, and unknown arrival time. Our algorithm,
Space-Time RRT* (ST-RRT*), is a probabilistically complete, bidirectional
motion planning algorithm, which is asymptotically optimal with respect to the
shortest arrival time. We experimentally evaluate ST-RRT* in both abstract (2D
disk, 8D disk in cluttered spaces, and on a narrow passage problem), and
simulated robotic path planning problems (sequential planning of 8DoF mobile
robots, and 7DoF robotic arms). The proposed planner outperforms RRT-Connect
and RRT* on both initial solution time, and attained final solution cost. The
code for ST-RRT* is available in the Open Motion Planning Library (OMPL).
