Reduced Complexity Multi-Scale Path-Planning on Probabilistic Maps

TL;DR

This paper improves the MSPP multi-scale path-planning algorithm by introducing methods to reduce computational complexity, including faster neighbor computation, delayed calculations, and sampling-based map approximation with probabilistic guarantees.

Contribution

The paper presents novel modifications to the MSPP algorithm that significantly speed up execution and reduce complexity through new neighbor computation, delayed processing, and sampling techniques.

Findings

Neighbor computation complexity reduced from O(|V|^2) to O(|V| log |V|)

Delayed computations save processing time by avoiding unnecessary calculations

Sampling-based map approximation provides probabilistic bounds on failure

Abstract

We present several modifications to the previously proposed MSPP algorithm that can speed-up its execution considerably. The MSPP algorithm leverages a multiscale representation of the environment in $n$ dimensions. The information of the environment is stored in a tree data structure representing a recursive dyadic partitioning of the search space. The information used by the algorithm is the probability that a node in the tree corresponds to an obstacle in the search space. Such trees are often created from mainstream perception algorithms, and correspond to quadtrees and octrees in two and three dimensions, respectively. We first present a new method to compute the graph neighbors in order to reduce the complexity of each iteration, from $O(| V|^2)$ to $O(| V| \log |V|)$. We then show how to delay expensive intermediate computations until we know that new information will be required, hence saving time by not operating on information that is never used during the search. Finally, we present a way to remove the very expensive need to calculate a full multi-scale map with the use of sampling and derive an theoretical upperbound of the probability of failure as a function of the number of samples.