The Journal of the Astronautical Sciences

, Volume 66, Issue 4, pp 554–581 | Cite as

Path Planning to a Reachable State Using Minimum Control Effort Based Navigation Functions

  • Paul Quillen
  • Josué Muñoz
  • Kamesh SubbaraoEmail author


The purpose of this paper is to present a new path-planning algorithm for planetary exploration rovers that will guide the vehicle safely to a reachable state. In particular, this work will make use of a special class of artificial potential functions called navigation functions which are guaranteed to be free of local minimum. The construction of the navigation functions in this work is motivated by the grid-based wavefront expansion method but differs in that the contour levels are defined in terms of the control effort of the system. Two new methods will be introduced in this paper for defining the navigation function. The first method will generate a minimum control effort path plan and the second method will be based on an inverse dynamics approach. Each of the control effort based methods will generate a path plan that will guide the rover’s approach towards an objective reachable state. Finally, a stable backstepping-like controller is implemented to track a trajectory defined along the path plan to the rover’s objective.


Navigation function Path planning Unmanned rovers Backstepping 



The authors acknowledge support for this project provided by AFRL through award # FA9453-16-1-0058


  1. 1.
    Huntsberger, T., Aghazarian, H., Cheng, Y., Baumgartner, E.T., Tunstel, E., Leger, C., Trebi-Ollennu, A., Schenker, P.S.: Rover autonomy for long range navigation and science data acquisition on planetary surfaces. In: IEEE International Conference on Robotics and Automation, 2002, ICRA’02, vol. 3, pp. 3161–3168. IEEE (2002)Google Scholar
  2. 2.
    Quadrelli, M.B., Wood, L.J., Riedel, J.E., McHenry, M.C., Aung, M.M., Cangahuala, L.A., Volpe, R.A., Beauchamp, P.M., Cutts, J.A.: Guidance, navigation, and control technology assessment for future planetary science missions. J. Guid. Control. Dyn. 38(7), 1165–1186 (2015)CrossRefGoogle Scholar
  3. 3.
    Ono, M., Fuchs, T.J., Steffy, A., Maimone, M., Yen, J.: Risk-aware planetary rover operation: Autonomous terrain classification and path planning. In: Aerospace Conference, 2015 IEEE, pp. 1–10. IEEE (2015)Google Scholar
  4. 4.
    Lavin, A.: Optimized mission planning for planetary exploration rovers. arXiv:1511.00195 (2015)
  5. 5.
    Lavalle, S.M.: Rapidly-exploring random trees: A new tool for path planning. Iowa State University, Technical report (1998)Google Scholar
  6. 6.
    LaValle, S.M., Kuffner, J.J. Jr: Randomized kinodynamic planning. Int. J. Robot. Res. 20(5), 378–400 (2001)CrossRefGoogle Scholar
  7. 7.
    Karaman, S., Frazzoli, E.: Incremental sampling-based algorithms for optimal motion planning. Robotics Science and Systems VI, 104 (2010)Google Scholar
  8. 8.
    Hsu, D., Kindel, R., Latombe, J.-C., Rock, S.: Randomized kinodynamic motion planning with moving obstacles. Int. J. Robot. Res. 21(3), 233–255 (2002)CrossRefGoogle Scholar
  9. 9.
    Khatib, O.: Realt-time obstacle avoidance for manipulators and mobile robots. Int. J. Robot. Res. 5(1), 90–98 (1986)CrossRefGoogle Scholar
  10. 10.
    Latombe, J.-C.: Robot Motion Planning, vol. 124. Springer Science & Business Media, Boston (2012)Google Scholar
  11. 11.
    Barraquand, J., Langlois, B., Latombe, J.-C.: Numerical potential field techniques for robot path planning. IEEE Trans. Syst. Man Cybern. 22(2), 224–241 (1992)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Rimon, E., Koditschek, D.E.: Exact robot navigation using artificial potential functions. IEEE Trans. Robot. Autom. 8(5), 501–517 (1992)CrossRefGoogle Scholar
  13. 13.
    Filippidis, I., Kyriakopoulos, K.J.: Adjustable navigation functions for unknown sphere worlds. In: 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC), pp. 4276–4281. IEEE (2011)Google Scholar
  14. 14.
    Horowitz, M.B., Burdick, J.W.: Optimal navigation functions for nonlinear stochastic systems. In: IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2014), pp. 224–231. IEEE (2014)Google Scholar
  15. 15.
    Connolly, C.I., Burns, J.B., Weiss, R.: Path planning using laplace’s equation. In: IEEE International Conference on Robotics and Automation, pp. 2102–2106. IEEE (1990)Google Scholar
  16. 16.
    Masoud, A.A., Bayoumi, M.M.: Robot navigation using the vector potential approach. In: IEEE International Conference on Robotics and Automation, 1993. Proceedings, pp. 805–811. IEEE (1993)Google Scholar
  17. 17.
    Garrido, S., Moreno, L., Blanco, D., Martin, F.: Smooth path planning for non-holonomic robots using fast marching. In: IEEE International Conference on Mechatronics, ICM 2009, pp. 1–6. IEEE (2009)Google Scholar
  18. 18.
    Ralli, E., Hirzinger, G.: Fast path planning for robot manipulators using numerical potential fields in the configuration space. In: Proceedings of the IEEE/RSJ/GI International Conference on Intelligent Robots and Systems’ 94.’Advanced Robotic Systems and the Real World’, IROS’94, vol. 3, pp. 1922–1929. IEEE (1994)Google Scholar
  19. 19.
    Wang, Y., Cao, W.: A global path planning method for mobile robot based on a three-dimensional-like map. Robotica 32(4), 611–624 (2014)CrossRefGoogle Scholar
  20. 20.
    Brock, O.: Generating Robot Motion: The integration of planning and execution. PhD thesis. Stanford University, Stanford (2000). AAI9961867Google Scholar
  21. 21.
    Lewis, F.L., Vrabie, D., Syrmos, V.L.: Optimal Control. Wiley (2012)Google Scholar
  22. 22.
    Slotine, J.-J.E., Li, W.: Applied Nonlinear Control, vol. 199. Prentice Hall, Englewood Cliffs (1991)Google Scholar
  23. 23.
    Krstic, M., Kokotovic, P.V., Kanellakopoulos, I.: Nonlinear and Adaptive Control Design, 1st edn. Wiley, New York (1995)zbMATHGoogle Scholar

Copyright information

© American Astronautical Society 2019

Authors and Affiliations

  1. 1.The University of Texas at ArlingtonArlingtonUSA
  2. 2.Flight Dynamics and Control GroupAir Force Research Laboratory/RVESAlbuquerqueUSA

Personalised recommendations