Discrete optimization methods to determine trajectories for Dubins' vehicles

doi:10.1016/j.endm.2010.05.003

Electronic Notes in Discrete Mathematics

Volume 36, 1 August 2010, Pages 17-24

https://doi.org/10.1016/j.endm.2010.05.003 Get rights and content

Abstract

Dubins' vehicles describe a twice differentiable curve of bounded curvature. In this work we present an algorithm for the Traveling Salesman Problem for Dubins' vehicles. In our approach, we propose using a version of the Traveling Salesman Problem that minimizes both distance and direction change angles to determine the tour specifying the order in which the points should be visited. In order to calculate the point-to-point Dubins' path we rely on a result by Dubins, and apply a shortest path algorithm on a discretized search space. Results indicate that the new algorithm obtains better solutions than the ones found in the literature in similar computation times.

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(1957)

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¹: This work was partially supported by FAPEMIG (Edital Universal).

²: This author was partially supported by CNPq grant 302560/2007-6.

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Discrete optimization methods to determine trajectories for Dubins' vehicles

Abstract

Robotics and Autonomous Systems

On curves of minimal length with a constraint on average curvature, and with prescribed initial and terminal positions and tangents

American Journal of Mathematics