  Path planning is a crucial algorithmic approach for designing robot
behaviors. Sampling-based approaches, like rapidly exploring random trees
(RRTs) or probabilistic roadmaps, are prominent algorithmic solutions for path
planning problems. Despite its exponential convergence rate, RRT can only find
suboptimal paths. On the other hand, $\textrm{RRT}^*$, a widely-used extension
to RRT, guarantees probabilistic completeness for finding optimal paths but
suffers in practice from slow convergence in complex environments. Furthermore,
real-world robotic environments are often partially observable or with poorly
described dynamics, casting the application of $\textrm{RRT}^*$ in complex
tasks suboptimal. This paper studies a novel algorithmic formulation of the
popular Monte-Carlo tree search (MCTS) algorithm for robot path planning.
Notably, we study Monte-Carlo Path Planning (MCPP) by analyzing and proving, on
the one part, its exponential convergence rate to the optimal path in fully
observable Markov decision processes (MDPs), and on the other part, its
probabilistic completeness for finding feasible paths in partially observable
MDPs (POMDPs) assuming limited distance observability (proof sketch). Our
algorithmic contribution allows us to employ recently proposed variants of MCTS
with different exploration strategies for robot path planning. Our experimental
evaluations in simulated 2D and 3D environments with a 7 degrees of freedom
(DOF) manipulator, as well as in a real-world robot path planning task,
demonstrate the superiority of MCPP in POMDP tasks.
