BIT*: Batch Informed Trees for Optimal Sampling-based Planning via Dynamic Programming on Implicit Random Geometric Graphs

Path planning in continuous spaces has traditionally been divided between discrete and sampling-based techniques. Discrete techniques use the principles of dynamic programming to solve a discretized approximation of the problem, while sampling-based techniques use random samples to perform a stochastic search on the continuous state space. In this paper, we use the fact that stochastic planners can be viewed as a search of an implicit random geometric graph (RGG) to propose a general class of planners named Bellman random trees (BRTs) and derive an anytime optimal samplingbased algorithm, batch informed trees (BIT*). BIT* searches for a solution to the continuous planning problem by efficiently building and searching a series of implicit RGGs in a principled manner. In doing so, it strikes a balance between the advantages of discrete methods and sampling-based planners. By using the implicit RGG representation, defined as set of random samples and successor function, BIT* is able to scale more effectively to high dimensions than other optimal sampling-based planners. By using heuristics and intelligently reusing existing connections, like discrete lifelong planning algorithms, BIT* is able to focus its search in a principled and efficient manner. In simulations, we show that BIT* consistently outperforms optimal RRT (RRT*), informed RRT* and fast marching trees (FMT*) on random-world problems in R and R. We also present preliminary theoretical analysis demonstrating that BIT* is probabilistically complete and asymptotically optimal and conjecture that it may be optimally efficient under some probabilistic conditions.