Piecewise linear regressions for approximating distance metrics

TL;DR

This paper introduces a binary space partition-based data structure for fast, locally linear approximation of distance metrics in robot configuration spaces, enhancing multi-robot planning and remote analysis.

Contribution

It presents a novel data structure that efficiently summarizes configuration space distances, enabling rapid queries and potential applications in multi-robot and remote motion planning.

Findings

Query speed surpasses graph search methods

Memory usage is promising for large spaces

Applicable to multi-robot and remote computation scenarios

Abstract

This paper presents a data structure that summarizes distances between configurations across a robot configuration space, using a binary space partition whose cells contain parameters used for a locally linear approximation of the distance function. Querying the data structure is extremely fast, particularly when compared to the graph search required for querying Probabilistic Roadmaps, and memory requirements are promising. The paper explores the use of the data structure constructed for a single robot to provide a heuristic for challenging multi-robot motion planning problems. Potential applications also include the use of remote computation to analyze the space of robot motions, which then might be transmitted on-demand to robots with fewer computational resources.