RM-Dijkstra: A surface optimal path planning algorithm based on Riemannian metric

TL;DR

RM-Dijkstra introduces a novel surface path planning algorithm based on Riemannian metrics, transforming the problem into a geometric one on a 2D plane, and demonstrates improved accuracy and smoothness over traditional methods.

Contribution

It proposes a new Riemannian metric-based approach for surface path planning, enabling more accurate and smooth paths for mobile robots on complex surfaces.

Findings

Outperforms traditional algorithms in path accuracy.

Produces smoother paths in complex scenarios.

Effectively solves surface optimal path planning problems.

Abstract

The Dijkstra algorithm is a classic path planning method, which operates in a discrete graph space to determine the shortest path from a specified source point to a target node or all other nodes based on non-negative edge weights. Numerous studies have focused on the Dijkstra algorithm due to its potential application. However, its application in surface path planning for mobile robots remains largely unexplored. In this letter, a surface optimal path planning algorithm called RM-Dijkstra is proposed, which is based on Riemannian metric model. By constructing a new Riemannian metric on the 2D projection plane, the surface optimal path planning problem is therefore transformed into a geometric problem on the 2D plane with new Riemannian metric. Induced by the standard Euclidean metric on surface, the constructed new metric reflects environmental information of the robot and ensures that the projection map is an isometric immersion. By conducting a series of simulation tests, the experimental results demonstrate that the RM-Dijkstra algorithm not only effectively solves the optimal path planning problem on surfaces, but also outperforms traditional path planning algorithms in terms of path accuracy and smoothness, particularly in complex scenarios.