Explicit Analytical Derivation of LSL and RSR Dubins' Paths for Intercepting a Uniformly Moving Target
Titouan BELIER, lionel Lapierre, christophe viel, Loick Degorre, Damien Massé
AI summary
Problem
Autonomous vehicles need to reliably intercept moving platforms like motherships, but existing path-planning methods rely on slow numerical solvers that hinder real-time deployment on low-power hardware.
Approach
The authors derive closed-form mathematical expressions for Circle-Straight-Circle Dubins paths to compute the fastest interception trajectory with matching final heading, bypassing iterative optimization.
Key results
- Explicit analytical solution for LSL and RSR path interception geometry and time
- Implicit analytical formulation derived for LSR and RSL paths
- Up to 100× faster computation for explicit paths compared to numerical solvers
- Real-world USV experiment successfully validates moving-target interception
Why it matters
Provides a computationally lightweight, real-time motion planning tool critical for autonomous surface and underwater vehicles docking with moving platforms.
Abstract
Autonomous underwater robotics faces significant challenges, particularly in the reliable recovery of Autonomous Underwater Vehicles (AUVs) after mission completion. To address this, small AUVs can dock onto a moving mother- ship for safe transport to recovery sites, reducing operational risks. This paper presents an explicit analytical derivation of the LSL (Left-Straight-Left) and RSR (Right-Straight-Right) Dubins’ Paths for intercepting an uniformly moving target, a critical problem for robust rendezvous in dynamic marine and underwater environments. The proposed approach leverages the classical Dubins’ Path model to generate time optimal, real-time, curvature-constrained paths suitable for 2D AUVs. Experimental validation on an Unmanned Surface Vehicle (USV) demonstrates the effectiveness of the developed motion planning strategy.