Asymptotically-Optimal Motion Planning using Lower Bounds on Cost
This work addresses computational efficiency in motion planning for robotics, though it is incremental as it builds on the Fast Marching Trees (FMT*) algorithm.
The authors tackled the problem of speeding up sampling-based motion planning by introducing lower bounds on cost-to-go, similar to heuristics in graph search, resulting in the Motion Planning using Lower Bounds (MPLB) algorithm that reduces collision detection time to a negligible fraction in many cases.
Many path-finding algorithms on graphs such as A* are sped up by using a heuristic function that gives lower bounds on the cost to reach the goal. Aiming to apply similar techniques to speed up sampling-based motion-planning algorithms, we use effective lower bounds on the cost between configurations to tightly estimate the cost-to-go. We then use these estimates in an anytime asymptotically-optimal algorithm which we call Motion Planning using Lower Bounds (MPLB). MPLB is based on the Fast Marching Trees (FMT*) algorithm recently presented by Janson and Pavone. An advantage of our approach is that in many cases (especially as the number of samples grows) the weight of collision detection in the computation is almost negligible with respect to nearest-neighbor calls. We prove that MPLB performs no more collision-detection calls than an anytime version of FMT*. Additionally, we demonstrate in simulations that for certain scenarios, the algorithmic tools presented here enable efficiently producing low-cost paths while spending only a small fraction of the running time on collision detection.