Autonomous Robots

, Volume 41, Issue 2, pp 385–400 | Cite as

The speed graph method: pseudo time optimal navigation among obstacles subject to uniform braking safety constraints

Article

Abstract

This paper considers the synthesis of pseudo time optimal paths for a mobile robot navigating among obstacles subject to uniform braking safety constraints. The classical Brachistochrone problem studies the time optimal path of a particle moving in an obstacle free environment subject to a constant force field. By encoding the mobile robot’s braking safety constraint as a force field surrounding each obstacle, the paper generalizes the Brachistochrone problem into safe time optimal navigation of a mobile robot in environments populated by polygonal obstacles. Convexity of the safe travel time functional, a path dependent function, allows efficient construction of a speed graph for the environment. The speed graph consists of safe time optimal arcs computed as convex optimization problems in \(O(n^3 \log (1/\epsilon ))\) total time, where n is the number of obstacle features in the environment and \(\epsilon \) is the desired solution accuracy. Once the speed graph is constructed for a given environment, pseudo time optimal paths between any start and target robot positions can be computed along the speed graph in \(O(n^2\log n)\) time. The results are illustrated with examples and described as a readily implementable procedure.

Keywords

Mobile robot time optimal navigation High speed navigation Mobile robot safety 

References

  1. Brock, O., & Khatib, O. (1999) High-speed navigation using the global dynamic window approach. In IEEE international conference on robotics and automation (pp. 341–346).Google Scholar
  2. Choset, H., Lynch, K. M., Hutchinson, S., Kantor, G., Burgard, W., Kavraki, L. E., et al. (2005). Principles of Robot Motion. Cambridge MA: MIT Press.MATHGoogle Scholar
  3. Chung, T. H., Hollinger, G. A., & Isler, V. (2011). Search and pursuit-evasion in mobile robotics, a survey. Autonomous Robots, 31(4), 299–316.CrossRefGoogle Scholar
  4. Fiorini, P., & Shiller, Z. (1998). Motion planning in dynamic environments using velocity obstacles. International Journal of Robotics Research, 17(7), 760–772.CrossRefGoogle Scholar
  5. Fox, D., Burgard, W., & Thrun, S. (1997). The dynamic window approach to collision avoidance. IEEE Robotics Automation Magazine, 4(1), 23–33.CrossRefGoogle Scholar
  6. Fraichard, T. (2007) A short paper about motion safety. In IEEE International Conference on Robotics and Automation (pp. 1140–1145)Google Scholar
  7. Gelfand, I. M., & Formin, S. V. (1963). Calculus of variations. Englewood Cliffs: Prentice-Hall.Google Scholar
  8. Guizzo, E. (2008). Three engineers, hundreds of robots, one warehouse: Kiva systems. IEEE Spectrum Magazine, 7(45), 26–34.CrossRefGoogle Scholar
  9. Kant, K., & Zucker, S. W. (1986). Toward efficient trajectory planning: The path-velocity decomposition. The International Journal of Robotics Research, 5(3), 72–89.CrossRefGoogle Scholar
  10. Karaman, S., & Frazzoli, E. (2011). Sampling-based algorithms for optimal motion planning. International Journal of Robotics Research, 30(7), 846–894.CrossRefMATHGoogle Scholar
  11. Large, F., Vasquez, D., Fraichard, T., & Laugier, C. (2004) Avoiding cars and pedestrians using v-obstacles and motion prediction. In IEEE Intelligent Vehicle Symposium (pp. 537–543).Google Scholar
  12. Lavalle, S. M. (1998). Rapidly-exploring random trees: A new tool for pathplanning. Technical report, Department of Computer Science, Iowa State University.Google Scholar
  13. Manor, G. (2014) Autonomous Mobile Robot Navigation With Velocity Constraints. PhD thesis, Technion Israel Inst. of Technology, Haifa, Israel, http://robots.technion.ac.il/publications.
  14. Manor, G., & Rimon, E. (2013) The speed graph method: Time optimal navigation among obstacles subject to safe braking constraints. Technical report, Department of ME, Technion, http://robots.technion.ac.il/publications.
  15. Manor, G., & Rimon, E. (2013). VC-method: High-speed navigation of a uniformly braking mobile robot using position-velocity configuration space. Autonomous Robots, 34(4), 295–309.CrossRefGoogle Scholar
  16. Manor, G., & Rimon, E. (2014) The speed graph method: Time optimal navigation among obstacles subject to safe braking constraints. In IEEE International Conference on Robotics and Automation (pp. 1155–1160).Google Scholar
  17. Markoff, J. (2010) Google cars drive themselves in traffic. New York Times.Google Scholar
  18. Nesterov, Y . E., & Nemirovsky, A . S. (1992). Interior point polynomial methods in convex programming: Theory and applications. Berlin: Springer.Google Scholar
  19. Nirenberg, L. (1981). Variational and topological methods in nonlinear problems. Bulletin of the AMS, 4(3), 267–302.MathSciNetCrossRefMATHGoogle Scholar
  20. Sherr, I., Ramse, M. (2013) Toyota and Audi move closer to driverless cars. The Wall Street Journal.Google Scholar
  21. Shiller, Z., & Gwo, Y. R. (1991). Dynamic motion planning of autonomous vehicles. IEEE Transaction on Robotics and Automation, 7(2), 241–249.CrossRefGoogle Scholar
  22. Shiller, Z., Sharma, S., Stern, I., & Stern, A. (2013). Online obstacle avoidance at high speeds. International Journals of Robotics Research, 32, 1030–1047.CrossRefGoogle Scholar
  23. Snape, J., van den Berg, J., & Guy, S. J. (2011). The hybrid reciprocal velocity obstacle. IEEE Transactions on Robotics, 27(4), 696–706.CrossRefGoogle Scholar
  24. Teixeira, K. C., Becker, M., & Caurin, G. A. P. (2010). Caurin. Automatic routing offorklift robots in warehouse applications. In ABCM Symposium in Mechatronics (pp. 335–344).Google Scholar
  25. Wein, R., van den Berg, J., & Halperin, D. (2008). Planning high-quality paths and corridors amidst obstacles. International Journal of Robotics Research, 27, 1213–1231.CrossRefGoogle Scholar
  26. Wurman, P. R., D’Andrea, R., & Mountz, M. (2008). Coordinating hundreds of cooperative, autonomous vehicles in warehouses. AI Magazine, 29, 9–19.Google Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringTechnionHaifaIsrael

Personalised recommendations