Fast-BIT∗: Modified heuristic for sampling-based optimal planning with a faster first solution and convergence in implicit random geometric graphs

This paper presents Fast Batch Informed Trees (Fast-BIT∗), a modification to the asymptotically optimal path planner Batch Informed Trees (BIT∗). Fast-BIT∗ modifies the underlying heuristic that dictates the expansion and processing of vertex and edge queues. BIT∗ uses heuristics to guide the search of implicit Random Geometric Graphs (RGGs) to generate an explicit solutions, while minimizing highly computational tasks such as collision checking. Fast-BIT∗ builds on BIT∗ by biasing the search heuristic towards the goal, in a solution analogous to depth-first search, finding an initial solution of the implicit RGG at a faster rate, at the cost of decreasing initial optimality. Fast-BIT∗ requires additional procedures to reset expansion variables of affected areas in the graph, ensuring the bias is not lasting in the graph expansion. An earlier initial solution leads to a faster initial upper bound for use in informed graph pruning, allowing convergence of path cost to begin earlier in the planning procedure. We show that Fast-BIT∗ finds a first solution faster than BIT∗ as well as the commonly used RRT-Connect and similar methods, along with a faster overall convergence rate. This paper shows various random-world test examples, showing the benefits of similar algorithms, along with a robot path planning simulation.