We consider motion planning problems for a vehicle with
kinodynamic constraints, where there is partial
knowledge about the environment and replanning is
required. We present a new tree-based planner that
explicitly deals with kinodynamic constraints and
addresses the safety issues when planning under finite
computation times, meaning that the vehicle avoids
collisions in its evolving configuration space. In
order to achieve good performance we incrementally
update a tree data-structure by retaining information
from previous steps and we bias the search of the
planner with a greedy, yet probabilistically complete
state space exploration strategy. Moreover, the number
of collision checks required to guarantee safety is
kept to a minimum. We compare our technique with
alternative approaches as a standalone planner and show
that it achieves favorable performance when planning
with dynamics. We have applied the planner to solve a
challenging replanning problem involving the mapping of
an unknown workspace with a non-holonomic platform.