We present an efficient anytime motion planner for mobile robots that considers both other dynamic obstacles and uncertainty caused by various sensors and low-level controllers. Our planning algorithm, which is an anytime extension of the Rapidly-exploring Random Belief Tree (RRBT), maintains the best possible path throughout the robot execution, and the generated path gets closer to the optimal one as more computation resources are allocated. We propose a branch-and-bound method to cull out unpromising areas by considering path lengths and uncertainty. We also propose an uncertainty-aware velocity obstacle as a simple local analysis to avoid dynamic
obstacles efficiently by finding a collision-free velocity. We have tested our method with three benchmarks that have non-linear measurement regions or potential collisions with dynamic obstacles. By using the proposed methods, we achieve up to five times faster performance given a fixed path cost.