Accelerated Reeds-Shepp and Under-Specified Reeds-Shepp Algorithms for Mobile Robot Path Planning

2025-04-08

IEEE Transactions on robotics

AI Summary

This paper addresses two key challenges in mobile robot path planning: the low computational efficiency of Reeds–Shepp curve generation and the underconstrained endpoint orientation problem. To tackle these, we propose a geometric-reasoning-based state-space partitioning method that drastically reduces the candidate feasible path set. We further present the first systematic formulation and open-source implementation of a complete underconstrained Reeds–Shepp planner. Our approach integrates analytical path classification, geometric modeling, and high-performance C++ implementation, guaranteeing path optimality (length error at machine precision) while achieving a 15× speedup over the latest OMPL C++ implementation. Key contributions are: (1) a theoretically rigorous, complete characterization of the solution space for the underconstrained Reeds–Shepp problem; and (2) the first open-source, reproducible, high-accuracy, real-time-capable solver for this problem.

Technology Category

• Intelligent Robots: Motion and Path Planning
• Planning, Routing, and Scheduling: Replanning and Plan Repair
• Multiagent Systems: Multiagent Planning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

In this study, we present a simple and intuitive method for accelerating optimal Reeds-Shepp path computation. Our approach uses geometrical reasoning to analyze the behavior of optimal paths, resulting in a new partitioning of the state space and a further reduction in the minimal set of viable paths. We revisit and reimplement classic methodologies from the literature, which lack contemporary open-source implementations, to serve as benchmarks for evaluating our method. Additionally, we address the under-specified Reeds-Shepp planning problem where the final orientation is unspecified. We perform exhaustive experiments to validate our solutions. Compared to the modern C++ implementation of the original Reeds-Shepp solution in the Open Motion Planning Library, our method demonstrates a 15x speedup, while classic methods achieve a 5.79x speedup. Both approaches exhibit machine-precision differences in path lengths compared to the original solution. We release our proposed C++ implementations for both the accelerated and under-specified Reeds-Shepp problems as open-source code.

Problem

• Accelerate Reeds-Shepp path planning for mobile robots
• Solve under-specified Reeds-Shepp with unknown final orientation
• Improve computational speed while maintaining path accuracy

Innovation

• Geometrical reasoning for path acceleration
• State space partitioning optimization
• Open-source C++ implementation speedup