Dubins-Curves

About

This software finds the shortest paths between configurations for the Dubins' car [Dubins51], 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.

Examples

The following code snippet demonstrates how to generate intermediate points along the shortest path between a pair of configuration (x, y, theta).

#include "dubins.h"
#include <stdio.h>

int printConfiguration(double q[3], double x, void* user_data) {
    printf("%f, %f, %f, %f\n", q[0], q[1], q[2], x);
    return 0;
}

int main()
{
    double q0[] = { 0,0,0 };
    double q1[] = { 4,4,3.142 };
    double turning_radius = 1.0;
    DubinsPath path;
    dubins_init( q0, q1, turning_radius, &path);
    dubins_path_sample_many( &path, printConfiguration, 0.1, NULL);
    return 0;
}

The following image shows some example paths, and the heading of the vehicle at each of the intermediate configurations.

Other Version

• There is a MATLAB Mex wrapper of this code on the MathWorks FileExchange
• There is a Python wrapper of this code available on GitHub and on PyPI

Citing

If you would like to cite this library in a paper or presentation, the following is recommended:

• Author: Andrew Walker
• Title: Dubins-Curves: an open implementation of shortest paths for the forward only car
• Year: 2008 -
• URL: https://github.com/AndrewWalker/Dubins-Curves

Here’s an example of a BibTeX entry:

@Misc{DubinsCurves,
  author = {Andrew Walker},
  title  = {Dubins-Curves: an open implementation of shortest paths for the forward only car},
  year   = {2008--},
  url    = "https://github.com/AndrewWalker/Dubins-Curves"
}

Contributions

This work was completed as part of [Walker11].

• Francis Valentinis
• Royce Smart - who tested early versions of this code while writing up [Smart08].
• Scott Teuscher - who wrote the MATLAB Mex wrapper

License

MIT License. See LICENSE.txt for details.

References

[Dubins51]

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