Bidirectional Sampling Based Search Without Two Point Boundary Value Solution
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Bidirectional path and motion planning approaches decrease planning time, on average, compared to their unidirectional counterparts. In the context of single-query feasible motion planning, using bidirectional search to find a continuous motion plan requires an explicit connection between the forward search tree and the reverse search tree. Such a tree-tree connection requires solving a two-point Boundary Value Problem (BVP). However, two-point BVP solution can be difficult or impossible to calculate for many types of vehicles (using numerical methods to find a solution, such as shooting approaches may be computationally expensive and is sometimes numerically unstable). To overcome this challenge, we present a generalized bidirectional search algorithm that does not require solving two-point BVP. Instead of connecting the two trees directly, our algorithm uses the cost information of the reverse tree as a guiding heuristic for forward search. This enables the forward search to quickly converge to a full feasible solution without an explicit tree-tree connection and without the solution to a two-point BVP. We run multiple software simulations in different environments and using dynamics of different vehicles along with real-world hardware experiments to show that our approach performs very close or better than existing state of the art approaches in terms of quickly converging to an initial feasible solution.
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