Advertisement

Journal of Intelligent and Robotic Systems

, Volume 57, Issue 1–4, pp 123–141 | Cite as

On the Generation of Trajectories for Multiple UAVs in Environments with Obstacles

  • Armando Alves Neto
  • Douglas G. Macharet
  • Mario F. M. Campos
Article

Abstract

This paper presents a methodology based on a variation of the Rapidly-exploring Random Trees (RRTs) that generates feasible trajectories for a team of autonomous aerial vehicles with holonomic constraints in environments with obstacles. Our approach uses Pythagorean Hodograph (PH) curves to connect vertices of the tree, which makes it possible to generate paths for which the main kinematic constraints of the vehicle are not violated. These paths are converted into trajectories based on feasible speed profiles of the robot. The smoothness of the acceleration profile of the vehicle is indirectly guaranteed between two vertices of the RRT tree. The proposed algorithm provides fast convergence to the final trajectory. We still utilize the properties of the RRT to avoid collisions with static, environment bound obstacles and dynamic obstacles, such as other vehicles in the multi-vehicle planning scenario. We show results for a set of small unmanned aerial vehicles in environments with different configurations.

Keywords

Multiple UAV trajectory planning Rapidly-exploring Random Trees Pythagorean Hodograph curves UAV swarm 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Siegwart, R., Nourbakhsh, I.R.: Introduction to Autonomous Mobile Robots. MIT, Cambridge (2004)Google Scholar
  2. 2.
    LaValle, S.M.: Planning Algorithms. Cambridge University Press, Cambridge (2006)MATHGoogle Scholar
  3. 3.
    Dubins, L.E.: On curves of minimal length with a constraint on average curvature, and with prescribed initial and terminal positions and tangents. Am. J. Math. 79, 497–516 (1957)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Kuwata, Y., Richards, A., Schouwenaars, T., How, J.P.: Robust constrained receding horizon control for trajectory planning. In: Proceedings of the AIAA Guidance, Navigation and Control Conference (2005)Google Scholar
  5. 5.
    Wzorek, M., Doherty, P.: Reconfigurable path planning for an autonomous unmanned aerial vehicle. Hybrid Information Technology, 2006. ICHIT ’06. International Conference on vol. 2, pp. 242–249 (2006)Google Scholar
  6. 6.
    Bortoffl, S.A.: Path planning for UAVs. In: Proceedings of the American Control Conference (2000)Google Scholar
  7. 7.
    Dogan, A.: Probabilistic path planning for UAVs. In: Proceedings of 2nd AIAA Unmanned Unlimited Systems, Technologies, and Operations (2003)Google Scholar
  8. 8.
    Cheng, P., Shen, Z., LaValle, S.: RRT-based trajectory design for autonomous automobiles and spacecraft. Arch. Control Sci. 11(3–4), 167–194 (2001)MATHMathSciNetGoogle Scholar
  9. 9.
    Griffiths, S., Saunders, J., Curtis, A., Barber, B., McLain, T., Beard, R.: Maximizing miniature aerial vehicles. Robot. Autom. Mag. IEEE 13(3), 34–43 (2006). doi: 10.1109/MRA.2006.1678137 CrossRefGoogle Scholar
  10. 10.
    Griffiths, S., Saunders, J., Curtis, A., Barber, B., McLain, T., Beard, R.: Advances in unmanned aerial vehicles: state of the art and road to autonomy, chap. Obstacle and Terrain Avoidance for Miniature Aerial Vehicles, pp. 213–244. Springer, Tampa (2007)Google Scholar
  11. 11.
    Schouwenaars, T., How, J., Feron, E.: Decentralized cooperative trajectory planning of multiple aircraft with hard safety guarantees. In: Proceedings of the AIAA Guidance, Navigation and Control Conference (2004)Google Scholar
  12. 12.
    Shanmugavel, M., Tsourdos, A., Zbikowski, R., White, B.A., Rabbath, C.A., Léchevin, N.: A solution to simultaneous arrival of multiple UAVs using Pythagorean Hodograph curves. In: Proceedings of the IEEE American Control Conference (ACC), pp. 2813–2818. Minneapolis (2006)Google Scholar
  13. 13.
    Li, T.Y., Chou, H.C.: Motion planning for a crowd of robots. Proc. IEEE Int. Conf. Robot. Autom. 3, 4215–4221 (2003)Google Scholar
  14. 14.
    Belta, C., Kumar, V.: Abstraction and control for groups of robots. IEEE Trans. Robot. 20(5), 865–875 (2004)CrossRefGoogle Scholar
  15. 15.
    Warren, C.: Multiple robot path coordination using artificial potential fields. Robotics and Automation, 1990. Proceedings, 1990 IEEE International Conference on vol. 1, pp. 500–505 (1990)Google Scholar
  16. 16.
    Marcolino, L.S., Chaimowicz, L.: No robot left behind: coordination to overcome local minima in swarm navigation. In: Proceedings of the 2008 IEEE International Conference on Robotics and Automation (2008)Google Scholar
  17. 17.
    Gayle, R., Sud, A., Lin, M., Manocha, D.: Reactive deformation roadmaps: motion planning of multiple robots in dynamic environments. IEEE/RSJ International Conference on Intelligent Robots and Systems pp. 3777–3783 (2007)Google Scholar
  18. 18.
    Leroy, S., Laumond, J.P.: Multiple path coordination for mobile robots: a geometric algorithm. In: Proc. of the International Joint Conference on Artificial Intelligence (IJCAI, pp. 1118–1123 (1999)Google Scholar
  19. 19.
    Kreyszig, E.: Differential Geometry, vol. 1. Dover, New York (1991)Google Scholar
  20. 20.
    Lavalle, S.M.: Rapidly-exploring random trees: a new tool for path planning. Tech. Rep., Computer Science Dept., Iowa State University (1998)Google Scholar
  21. 21.
    Farouki, R.T., Sakkalis, T.: Pythagorean Hodographs. IBM J. Res. Develop. 34(5), 736–752 (1990)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Farouki, R.T., Neff, C.A.: Hermite interpolation by Pythagorean Hodograph quintics. Math. Comput. 64, 1589–1609 (1995)MATHCrossRefMathSciNetGoogle Scholar
  23. 23.
    Farouki, R.T.: The elastic bending energy of Pythagorean Hodograph curves. Comput. Aided Geom. Des. 13, 227–241 (1996)MATHCrossRefMathSciNetGoogle Scholar
  24. 24.
    Shkel, A.M., Lumelsky, V.: Classification of the Dubins set. In: Robotics and Autonomous Systems, vol. 34, pp. 179–202 (2001)Google Scholar
  25. 25.
    Iscold, P.: Development of a small unmanned aerial vehicle for aerial reconaiscence. In: International Congress of Mobility Engineering. São Paulo, Brazil (2007)Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • Armando Alves Neto
    • 1
  • Douglas G. Macharet
    • 1
  • Mario F. M. Campos
    • 1
  1. 1.Computer Vision and Robotic Laboratory (VeRlab), Computer Science DepartmentUniversidade Federal de Minas GeraisBelo HorizonteBrazil

Personalised recommendations