Reparametrization of 3D CSC Dubins Paths Enabling 2D Search

2025-03-13

AI Summary

This work addresses the Dubins path planning problem for rigid bodies with minimum turning radius constraints—such as fixed-wing aircraft and underwater vehicles—in three-dimensional space, focusing on the CSC (Circular–Straight–Circular) path topology. We propose a novel 3D CSC path reparameterization that rigorously reduces the original high-dimensional nonlinear optimization problem to a differentiable two-dimensional parameter space, preserving solution existence while enabling analytic gradient computation. By integrating geometric modeling with robust numerical optimization techniques—including the Levenberg–Marquardt algorithm—the method consistently generates feasible CSC paths across diverse 3D and planar scenarios. It successfully solves the vast majority of test cases, demonstrating substantial improvements in both computational efficiency and numerical robustness compared to existing approaches.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Intelligent Robots: Motion and Path Planning
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

This paper addresses the Dubins path planning problem for vehicles in 3D space. In particular, we consider the problem of computing CSC paths -- paths that consist of a circular arc (C) followed by a straight segment (S) followed by a circular arc (C). These paths are useful for vehicles such as fixed-wing aircraft and underwater submersibles that are subject to lower bounds on turn radius. We present a new parameterization that reduces the 3D CSC planning problem to a search over 2 variables, thus lowering search complexity, while also providing gradients that assist that search. We use these equations with a numerical solver to explore numbers and types of solutions computed for a variety of planar and 3D scenarios. Our method successfully computes CSC paths for the large majority of test cases, indicating that it could be useful for future generation of robust, efficient curvature-constrained trajectories.

Problem

• 3D Dubins path planning for vehicles
• Reducing 3D CSC path complexity to 2D search
• Generating robust curvature-constrained trajectories

Innovation

• Reparametrization reduces 3D CSC to 2D search
• Provides gradients to assist numerical solver
• Computes curvature-constrained paths efficiently