dubins

Overview

This software finds the shortest paths between configurations for the Dubins' car [Dubins57], the forward only car-like vehicle with a constrained turning radius. A good description of the equations and basic strategies for doing this are described in section 15.3.1 "Dubins Curves" of the book "Planning Algorithms" [LaValle06].

The approach used to find paths is based on the algebraic solutions published in [Shkel01]. However, rather than using angular symmetries to improve performance, the simpler approach to test all possible solutions is used here.

This code is primarily a Cython wrapper of https://github.com/AndrewWalker/Dubins-Curves

Installing

You can install the latest stable version from PyPI

$ pip install dubins

Or, you can install the latest development version from GitHub

$ pip install git+git://github.com/AndrewWalker/pydubins.git

Example

Discrete Sampling of a Dubin's path at finite step sizes

import dubins

q0 = (x0, y0, theta0)
q1 = (x1, y1, theta1)
turning_radius = 1.0
step_size = 0.5

path = dubins.shortest_path(q0, q1, turning_radius)
configurations, _ = path.sample_many(step_size)

Acknowledgements

This work was completed as part of [Walker11].

• Francis Valentinis
• Royce Smart - who tested early versions of this code while completing his PhD thesis [Smart08].

References

[Dubins57]

Dubins, L. E. (July 1957). "On Curves of Minimal Length with a Constraint on Average Curvature, and with Prescribed Initial and Terminal Positions and Tangents". American Journal of Mathematics 79 (3): 497–516

[LaValle06]

LaValle, S. M. (2006). "Planning Algorithms". Cambridge University Press

[Shkel01]

Shkel, A. M. and Lumelsky, V. (2001). "Classification of the Dubins set". Robotics and Autonomous Systems 34 (2001) 179–202

[Walker11]

Walker, A. (2011). "Hard Real-Time Motion Planning for Autonomous Vehicles", PhD thesis, Swinburne University.

[Smart08]

Royce, S. (2008). "Evolutionary Control of Autonomous Underwater Vehicles". PhD thesis, RMIT