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

Discrete and sampling-based methods have traditionally been popular techniques for path planning in continuous spaces. 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 (BRT) and derive an anytime optimal sampling-based 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 $\mathbb{R}^2$ and $\mathbb{R}^8$ . 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.

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