An RRT* algorithm based on Riemannian metric model for optimal path planning

TL;DR

This paper introduces a Riemannian metric-based RRT* algorithm for optimal path planning in high-dimensional spaces, improving path smoothness and environmental adaptability by transforming the problem into a geometric one on a 2D plane.

Contribution

It proposes a novel Riemannian metric model and an RRT*-R algorithm that effectively handle environmental variations and enhance path quality in high-dimensional path planning.

Findings

The RRT*-R algorithm outperforms the original RRT* in smoothness and optimization.

Paths generated are close to the theoretical minimum geodesic distance.

The method effectively avoids environmental hazards like height and resistance changes.

Abstract

This paper presents a Riemannian metric-based model to solve the optimal path planning problem on two-dimensional smooth submanifolds in high-dimensional space. Our model is based on constructing a new Riemannian metric on a two-dimensional projection plane, which is induced by the high-dimensional Euclidean metric on two-dimensional smooth submanifold and reflects the environmental information of the robot. The optimal path planning problem in high-dimensional space is therefore transformed into a geometric problem on the two-dimensional plane with new Riemannian metric. Based on the new Riemannian metric, we proposed an incremental algorithm RRT*-R on the projection plane. The experimental results show that the proposed algorithm is suitable for scenarios with uneven fields in multiple dimensions. The proposed algorithm can help the robot to effectively avoid areas with drastic changes in height, ground resistance and other environmental factors. More importantly, the RRT*-R algorithm shows better smoothness and optimization properties compared with the original RRT* algorithm using Euclidean distance in high-dimensional workspace. The length of the entire path by RRT*-R is a good approximation of the theoretical minimum geodesic distance on projection plane.