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An Orientation Assignment Heuristic to the Dubins Traveling Salesman Problem

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Advances in Artificial Intelligence -- IBERAMIA 2014 (IBERAMIA 2014)

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Abstract

In this paper we deal with the DTSP, which is the optimization problem where a path that goes through a set of two-dimensional points must be calculated considering the use of robots modeled as Dubins vehicles. Assuming that the sequence of visits is initially obtained accordingly to the ETSP, we propose an heuristic to assign orientations for each point in order to achieve a path which is length minimized and respects the vehicle’s nonholonomic constraints. The heuristic takes into account the vehicle’s minimum turning radius and distance between neighbors points to proportionally adjust the orientation on each point, allowing the definition of shorter Dubins curves connecting them. The methodology was horoughly evaluated through numerous trials in different simulated scenarios, providing statistical examination of the final results.

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References

  1. Concorde TSP solver, http://www.tsp.gatech.edu/concorde/index.html (2013) (Online; accessed December 12, 2013)

  2. Applegate, D.L., Bixby, R.E., Chvatal, V., Cook, W.J.: The Traveling Salesman Problem: A Computational Study (Princeton Series in Applied Mathematics). Princeton University Press, Princeton (2007)

    Google Scholar 

  3. Cobano, J., Conde, R., Alejo, D., Ollero, A.: Path planning based on Genetic Algorithms and the Monte-Carlo method to avoid aerial vehicle collisions under uncertainties. In: Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), pp. 4429–4434 (May 2011)

    Google Scholar 

  4. Dubins, L.E.: 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 (1957)

    Article  MATH  MathSciNet  Google Scholar 

  5. Kuwata, Y., Fiore, G., Teo, J., Frazzoli, E., How, J.: Motion planning for urban driving using RRT. In: Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 1681–1686 (September 2008)

    Google Scholar 

  6. LaValle, S.M.: Planning Algorithms. Cambridge University Press, New York (2006)

    Book  MATH  Google Scholar 

  7. Le Ny, J., Feron, E.: An Approximation Algorithm for the Curvature-Constrained Traveling Salesman Problem. In: Proceedings of the 43rd Annual Allerton Conference on Communications, Control and Computing (2005)

    Google Scholar 

  8. Ma, X., Castañón, D.A.: Receding Horizon Planning for Dubins Traveling Salesman Problems. In: Proceedings of the 45th IEEE Conference on Decision and Control (CDC), pp. 5453–5458 (December 2006)

    Google Scholar 

  9. Macharet, D.G., Alves Neto, A., da Camara Neto, V.F., Campos, M.F.M.: Nonholonomic path planning optimization for Dubins’ vehicles. In: Proceedings of the IEEE International Conference on Robotics and Automation (ICRA 2011), pp. 4208–4213 (May 2011)

    Google Scholar 

  10. Macharet, D.G., Alves Neto, A., da Camara Neto, V.F., Campos, M.F.M.: Data gathering tour optimization for Dubins’ vehicles. In: IEEE Congress on Evolutionary Computation (CEC), pp. 1–8 (June 2012)

    Google Scholar 

  11. Macharet, D.G., Neto, A.A., Campos, M.F.M.: Feasible UAV path planning using genetic algorithms and Bézier curves. In: da Rocha Costa, A.C., Vicari, R.M., Tonidandel, F. (eds.) SBIA 2010. LNCS, vol. 6404, pp. 223–232. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  12. Marble, J.D., Bekris, K.: Towards small asymptotically near-optimal roadmaps. In: Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), pp. 2557–2562 (2012)

    Google Scholar 

  13. Medeiros, A., Urrutia, S.: Discrete optimization methods to determine trajectories for Dubins’ vehicles. Electronic Notes in Discrete Mathematics 36, 17–24 (2010), International Symposium on Combinatorial Optimization (ISCO)

    Google Scholar 

  14. Savla, K., Frazzoli, E., Bullo, F.: On the point-to-point and traveling salesperson problems for Dubins’ vehicle. In: Proceedings of the IEEE American Control Conference (ACC), vol. 2, pp. 786–791 (June 2005)

    Google Scholar 

  15. Savla, K., Frazzoli, E., Bullo, F.: Traveling Salesperson Problems for the Dubins Vehicle. IEEE Transactions on Automatic Control 53(6), 1378–1391 (2008)

    Article  MathSciNet  Google Scholar 

  16. Shanmugavel, M., Tsourdos, A., White, B., Żbikowski, R.: Co-operative path planning of multiple UAVs using Dubins paths with clothoid arcs. Control Engineering Practice 18(9), 1084–1092 (2010)

    Article  Google Scholar 

  17. Siegwart, R., Nourbakhsh, I.R., Scaramuzza, D.: Introduction to Autonomous Mobile Robots, 2nd edn. MIT Press, Cambridge (2011)

    Google Scholar 

  18. Tang, Z., Özgüner, Ü.: Motion planning for multitarget surveillance with mobile sensor agents. IEEE Transactions on Robotics 21(5), 898–908 (2005)

    Article  Google Scholar 

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Correspondence to Douglas G. Macharet .

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Macharet, D.G., Campos, M.F.M. (2014). An Orientation Assignment Heuristic to the Dubins Traveling Salesman Problem. In: Bazzan, A., Pichara, K. (eds) Advances in Artificial Intelligence -- IBERAMIA 2014. IBERAMIA 2014. Lecture Notes in Computer Science(), vol 8864. Springer, Cham. https://doi.org/10.1007/978-3-319-12027-0_37

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  • DOI: https://doi.org/10.1007/978-3-319-12027-0_37

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-12026-3

  • Online ISBN: 978-3-319-12027-0

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