  This work presents an efficient method to solve a class of continuous-time,
continuous-space stochastic optimal control problems of robot motion in a
cluttered environment. The method builds upon a path integral representation of
the stochastic optimal control problem that allows computation of the optimal
solution through sampling and estimation process. As this sampling process
often leads to a local minimum especially when the state space is highly
non-convex due to the obstacle field, we present an efficient method to
alleviate this issue by devising a proposed topological motion planning
algorithm. Combined with a receding-horizon scheme in execution of the optimal
control solution, the proposed method can generate a dynamically feasible and
collision-free trajectory while reducing concern about local optima.
Illustrative numerical examples are presented to demonstrate the applicability
and validity of the proposed approach.
