RM-Dijkstra：リーマン計量に基づく曲面上の最適経路計画アルゴリズム
RM-Dijkstra: A surface optimal path planning algorithm based on Riemannian metric
曲面上の経路計画を2次元平面のリーマン計量問題に変換し、Dijkstra法を拡張して滑らかで高精度な最適経路を求める手法を提案した。
詳しい要約
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2. 先行研究と比べてどこがすごい？
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著者: Yu Zhang, Xiao-Song Yang
分類: cs.RO, math.OC
原文アブストラクト
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.
