Viability-Based Guaranteed Safe Robot Navigation

  • Mohamed Amine Bouguerra
  • Thierry Fraichard
  • Mohamed Fezari


Guaranteeing safe, i.e. collision-free, motion for robotic systems is usually tackled in the Inevitable Collision State (ICS) framework. This paper explores the use of the more general Viability theory as an alternative when safe motion involves multiple motion constraints and not just collision avoidance. Central to Viability is the so-called viability kernel, i.e. the set of states of the robotic system for which there is at least one trajectory that satisfies the motion constraints forever. The paper presents an algorithm that computes off-line an approximation of the viability kernel that is both conservative and able to handle time-varying constraints such as moving obstacles. Then it demonstrates, for different robotic scenarios involving multiple motion constraints (collision avoidance, visibility, velocity), how to use the viability kernel computed off-line within an on-line reactive navigation scheme that can drive the robotic system without ever violating the motion constraints at hand.


Provable safety Collision avoidance Autonomous navigation Viability theory 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



  1. 1.
    Aubin, J.P., Bayen, A., Saint-Pierre, P.: Viability Theory: New Directions. Springer, Berlin (2011)CrossRefGoogle Scholar
  2. 2.
    Bekris, K., Kavraki, L.: Greedy but safe replanning under kinodynamic constraints. In: IEEE International Conference on Robotics and Automation (ICRA). Roma (IT) (2007).
  3. 3.
    Blaich, M., Weber, S., Reuter, J., Hahn, A.: Motion safety for vessels: an approach based on inevitable collision states. In: IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). Hamburg (DE) (2015).
  4. 4.
    Bohórquez, N., Sherikov, A., Dimitrov, D., Wieber, P.B.: Safe navigation strategies for a biped robot walking in a crowd. In: IEEE-RAS International Conference on Humanoid Robots (Humanoids). Cancun (MX) (2016).
  5. 5.
    Bouguerra, M., Fraichard, T., Fezari, M.: Safe motion using viability kernel. In: IEEE International Conference on Robotics and Automation (ICRA). Seattle (US) (2015).
  6. 6.
    Bouraine, S., Fraichard, T., Salhi, H.: Provably safe navigation for mobile robots with limited field-of-views in dynamic environments. Auton. Robot. 32(3) (2012). CrossRefGoogle Scholar
  7. 7.
    Brias, A., Mathias, J.D., Deffuant, G.: Accelerating viability kernel computation with cuda architecture: application to bycatch fishery management. Comput. Manag. Sci. 13(3), 371–391 (2016). MathSciNetCrossRefGoogle Scholar
  8. 8.
    Chan, N., Kuffner, J., Zucker, M.: Improved motion planning speed and safety using regions of inevitable collision. In: CISM-IFToMM Symposium on Robot Design, Dynamics, and Control (2008)Google Scholar
  9. 9.
    Chitsaz, H., LaValle, S.M.: Time-optimal paths for a Dubins airplane. In: Proceedings IEEE Conference Decision and Control. New Orleans, LA (US) (2007)Google Scholar
  10. 10.
    Donald, B., Xavier, P., Canny, J., Reif, J.: Kinodynamic motion planning. J. ACM (JACM) 40(5) (1993). MathSciNetCrossRefGoogle Scholar
  11. 11.
    Fraichard, T.: Trajectory planning in a dynamic workspace: a state-time space approach. Adv. Robot. 13(1) (1998). CrossRefGoogle Scholar
  12. 12.
    Fraichard, T., Asama, H.: Inevitable collision states. a step towards safer robots? Adv. Robot. 18(10) (2004). CrossRefGoogle Scholar
  13. 13.
    Fraichard, T., Howard, T.: Iterative motion planning and safety issue. In: Eskandarian, A. (ed.) Handbook of Intelligent Vehicles. Springer (2012)Google Scholar
  14. 14.
    Frazzoli, E., Dahleh, M., Feron, E.: Real-time motion planning for agile autonomous vehicles. J. Guid. Control. Dyn. 25(1) (2002). CrossRefGoogle Scholar
  15. 15.
    Hsu, D., Kindel, R., Latombe, J.C., Rock, S.: Randomized kinodynamic motion planning with moving obstacles. Int. J. Robot. Res. (IJRR) 21(3) (2002). CrossRefGoogle Scholar
  16. 16.
    Kalisiak, M., van de Panne, M.: Approximate safety enforcement using computed viability envelopes. In: IEEE International Conference on Robotics and Automation (ICRA). New Orleans (US). (2004)
  17. 17.
    Kalisiak, M., van de Panne, M.: Faster motion planning using learned local viability models. In: IEEE International Conference on Robotics and Automation (ICRA). Roma (IT). (2007)
  18. 18.
    Korda, M., Henrion, D., Jones, C.: Convex computation of the maximum controlled invariant set for polynomial control systems. SIAM J. Control. Optim. 52(5) (2014). MathSciNetCrossRefGoogle Scholar
  19. 19.
    Liniger, A., Lygeros, J.: Real-time control for autonomous racing based on viability theory. arXiv:1701.08735 (2017)
  20. 20.
    Lygeros, J.: On reachability and minimum cost optimal control. Automatica 40(6) (2004). MathSciNetCrossRefGoogle Scholar
  21. 21.
    Macek, K., Vasquez, D., Fraichard, T., Siegwart, R.: Towards safe vehicle navigation in dynamic urban scenarios. Automatika 50(3–4) (2009).
  22. 22.
    Maidens, J., Kaynama, S., Mitchell, I., Oishi, M., Dumont, G.: Lagrangian methods for approximating the viability kernel in high-dimensional systems. Automatica 49(7) (2013). MathSciNetCrossRefGoogle Scholar
  23. 23.
    Martinez-Gomez, L., Fraichard, T.: An efficient and generic 2d inevitable collision state-checker. In: IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). Nice (FR) (2008).
  24. 24.
    McNaughton, M., Urmson, C., Dolan, J., Lee, J.W.: Motion planning for autonomous driving with a conformal spatiotemporal lattice. In: IEEE International Conference on Robotics and Automation (ICRA) (2011)Google Scholar
  25. 25.
    Mitchell, I., Bayen, A., Tomlin, C.: A time-dependent hamilton-jacobi formulation of reachable sets for continuous dynamic games. IEEE Trans. Autom. Control 50(7) (2005). MathSciNetCrossRefGoogle Scholar
  26. 26.
    Mitsch, S., Ghorbal, K., Platzer, A.: On provably safe obstacle avoidance for autonomous robotic ground vehicles. In: Robotics: Science and Systems (RSS). (2013)
  27. 27.
    Monnet, D., Ninin, J., Jaulin, L.: Computing an inner and an outer approximation of the viability kernel. Reliab. Comput. 22 (2016).
  28. 28.
    Owen, M., Beard, R., McLain, T.: Implementing dubins airplane paths on fixed-wing uavs. In: Handbook of Unmanned Aerial Vehicles. Springer, Berlin (2014)Google Scholar
  29. 29.
    Pancanti, S., Pallottino, L., Salvadorini, D., Bicchi, A.: Motion planning through symbols and lattices. In: IEEE International Conference on Robotics and Automation (ICRA). New Orleans (US) (2004)Google Scholar
  30. 30.
    Pivtoraiko, M., Knepper, R., Kelly, A.: Differentially constrained mobile robot motion planning in state lattices. J. Field Rob. 26(3) (2009). CrossRefGoogle Scholar
  31. 31.
    Rufli, M., Siegwart, R.: On the design of deformable input-/state- lattice graphs. In: IEEE International Conference on Robotics and Automation (ICRA) (2010)Google Scholar
  32. 32.
    Saint-Pierre, P.: Approximation of the viability kernel. Appl. Math. Optim. 29(2) (1994). MathSciNetCrossRefGoogle Scholar
  33. 33.
    Savino, G., Giovannini, F., Fitzharris, M., Pierini, M.: Inevitable collision states for motorcycle-to-car collision scenarios. IEEE Trans. Intell. Transp. Syst. 17(9) (2016). CrossRefGoogle Scholar
  34. 34.
    Schouwenaars, T., How, J., Feron, E.: Receding horizon path planning with implicit safety guarantees. In: American Control Conference. Boston (US) (2004)Google Scholar
  35. 35.
    Seder, M., Petrovic, I.: Dynamic window based approach to mobile robot motion control in the presence of moving obstacles. In: IEEE International Conference on Robotics and Automation (ICRA) (2007)Google Scholar
  36. 36.
    She, Z., Xue, B.: Computing an invariance kernel with target by computing lyapunov-like functions. IET Control Theory Appl. 7(15) (2013). MathSciNetCrossRefGoogle Scholar
  37. 37.
    Shiller, Z., Gal, O., Raz, A.: Adaptive time horizon for on-line avoidance in dynamic environments. In: IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). San Francisco (US). (2011)
  38. 38.
    Ziegler, J., Stiller, C.: Spatiotemporal state lattices for fast trajectory planning in dynamic on-road driving scenarios. In: IEEE/RSJ International Conference on Intelligent Robots and Systems (2009)Google Scholar

Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Automatic and Signals Laboratory Annaba (LASA)Department of Electronics, Badji Mokhtar University AnnabaAnnabaAlgeria
  2. 2.Université Grenoble Alpes, Inria, CNRS, Grenoble INP, LIGGrenobleFrance

Personalised recommendations