Learning Obstacle-Avoiding Lattice Paths using Swarm Heuristics: Exploring the Bijection to Ordered Trees

TL;DR

This paper introduces a novel method for generating collision-free lattice paths in grid maps by leveraging a bijection to ordered trees, enabling efficient navigation and planning.

Contribution

It presents a new scheme that transforms the lattice path problem into a one-dimensional search using bijection to ordered trees, tested with swarm heuristics.

Findings

Swarm heuristics effectively generate collision-free paths.

The scheme demonstrates high efficiency in obstacle-rich environments.

Potential applications in fast planning algorithms.

Abstract

Lattice paths are functional entities that model efficient navigation in discrete/grid maps. This paper presents a new scheme to generate collision-free lattice paths with utmost efficiency using the bijective property to rooted ordered trees, rendering a one-dimensional search problem. Our computational studies using ten state-of-the-art and relevant nature-inspired swarm heuristics in navigation scenarios with obstacles with convex and non-convex geometry show the practical feasibility and efficiency in rendering collision-free lattice paths. We believe our scheme may find use in devising fast algorithms for planning and combinatorial optimization in discrete maps.