An Analytic Solution to the 3D CSC Dubins Path Problem

TL;DR

This paper derives an analytic solution for the 3D Dubins path problem involving CSC paths, modeling start and goal configurations as manipulator frames, and reveals multiple solutions exist in non-singular regions.

Contribution

It introduces an analytic method for solving the 3D Dubins path problem with CSC paths, incorporating manipulator kinematics and solution multiplicity.

Findings

Up to seven valid CSC solutions can exist in non-singular regions.

The approach models start and goal as manipulator frames, linking path planning with inverse kinematics.

An implementation is provided at https://github.com/aabecker/dubins3D.

Abstract

We present an analytic solution to the 3D Dubins path problem for paths composed of an initial circular arc, a straight component, and a final circular arc. These are commonly called CSC paths. By modeling the start and goal configurations of the path as the base frame and final frame of an RRPRR manipulator, we treat this as an inverse kinematics problem. The kinematic features of the 3D Dubins path are built into the constraints of our manipulator model. Furthermore, we show that the number of solutions is not constant, with up to seven valid CSC path solutions even in non-singular regions. An implementation of solution is available at https://github.com/aabecker/dubins3D.