Directional Sampling-Based Generalized Shape Expansion for Accelerated Motion Planning in 2-D Obstacle-Cluttered Environments

TLDR: This letter proposes two sampling schemes - basic and augmented directional sampling - and presents GSE-D andGSE-AD algorithms, respectively, as expansion over the GSE, in terms of computational time efficiency and shortest path cost.

Abstract: Recently proposed Generalized Shape Expansion (GSE) algorithm for planning of shortest collision-free path in 2-D environments has shown significant promise in improvement of its performance over several seminal algorithms from existing literature. Recognizing that a suitable directional sampling feature could potentially enhance the performance of the GSE algorithm further, this letter proposes two sampling schemes - basic and augmented directional sampling - and presents GSE-D and GSE-AD algorithms, respectively, as expansion over the GSE. These algorithms, by default, enjoy the advantages of the GSE. Both the directional sampling schemes enable drawing random sample points with more preference towards the direction of the Goal leading to lower cost of computed shortest path on an average. While the basic directional sampling strategy faces a drawback in computational time when obstacle density in the direction towards the Goal is high, the augmented directional sampling scheme is free of this limitation. Probabilistic analysis and extensive numerical simulation studies show the effectiveness of the GSE-D and GSE-AD in performance in terms of computational time efficiency and shortest path cost when compared with the GSE, other seminal and existing directional algorithms.