Skip to main content
SpringerLink
Log in

GPS Denied UAV Routing with Communication Constraints

  • Published:
Journal of Intelligent & Robotic Systems Aims and scope Submit manuscript

Abstract

A novel GPS denied routing problem for UAVs is described, where the UAVs cooperatively navigate through a restricted zone deployed with noncommunicating Unattended Ground Sensors (UGS). The routing algorithm presenting in this paper ensures the UAVs maintain strict contact with at least one UGS, which allows the UGS act as beacons for relative navigation eliminating the need for dead reckoning. This problem is referred to as the Communication Constrained UAV Routing Problem (CCURP). Two architectures for cooperative navigation of two or three UAVs are considered. For the two UAV problem, a \(\frac {9}{2}\)-approximation algorithm is developed. The three UAV problem is transformed into a one-in-a-set Traveling Salesman Problem (TSP), which is solved as a regular asymmetric TSP using existing methods after applying a second transformation. Computational results corroborating the performance bounds are presented.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Applegate, D., Bixby, R., Chvatal, V., Cook, W.: Concorde tsp solver. See: http://www.tsp.gatech.edu/concorde.html (2005)

  2. Cao, Y., Muse, J., Casbeer, D., Kingston, D.: Circumnavigation of an unknown target using uavs with range and range rate measurements. In: IEEE 52nd Annual Conference on Decision and Control (CDC), 2013, pp. 3617–3622 (2013)

  3. Casbeer, D.W., Krishnamoorthy, K., Eggert, A., Chandler, P., Pachter, M.: Optimal search for a random moving intruder. In: AIAA Infotech@Aerospace Conference (2012)

  4. Christofides, N.: Worst-case analysis of a new heuristic for the travelling salesman problem. Tech. Rep. Technical Report 388, Graduate School of Industrial Administration, Carnegie-Mellon University, Pittsburgh PA (1976)

  5. Gebre-Egziabher, D., Taylor, B.: Impact and mitigation of gps-unavailability on small uav navigation, guidance and control. Tech. rep., Report 2012-2, University of Minnesota Department of Aerospace Engineering and Mechanics (2012)

  6. Hashemi, A., Cao, Y., Casbeer, D.W., Yin, G.: Unmanned aerial vehicle circumnavigation using noisy range-based measurements without global positioning system information. J. Dyn. Syst. Meas. Control. 137, 31,009–31,019 (2015)

    Article  Google Scholar 

  7. Helsgaun, K.: An effective implementation of the Lin-Kernighan traveling salesman heuristic. European Journal of Operational Research 126(1), 106–130 (2000). doi:10.1016/S0377-2217(99)00284-2. http://www.sciencedirect.com/science/article/pii/S0377221799002842

    Article  MathSciNet  MATH  Google Scholar 

  8. Oberlin, P., Rathinam, S., Darbha, S.: Today’s traveling salesman problem. IEEE Robot. Autom. Mag. 17(4), 70–77 (2010)

  9. Jonker, R., Volgenant, T.: Transforming asymmetric into symmetric traveling salesman problems. Oper. Res. Lett. 2(4), 161–163 (1983)

    Article  MATH  Google Scholar 

  10. Kerns, A.J., Shepard, D.P., Bhatti, J.A., Humphreys, T.E.: Unmanned aircraft capture and control via GPS spoofing. J. Field Rob. 31(4), 617–636 (2014)

    Article  Google Scholar 

  11. Krishnamoorthy, K., Casbeer, D.W., Chandler, P., Pachter, M., Darbha, S.: UAV Search Andamp; Capture of a Moving Ground Target under Delayed Information. In: IEEE Conference on Decision and Control (2012)

  12. Malik, W., Rathinam, S., Darbha, S.: An approximation algorithm for a symmetric generalized multiple depot, multiple travelling salesman problem. Oper. Res. Lett. 35(6), 747–753 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  13. Manyam, S., Rathinam, S., Darbha, S.: Computation of Lower Bounds for a Multiple Depot, Multiple Vehicle Routing Problem with Motion Constraints. In: IEEE 52Nd Annual Conference on Decision and Control (CDC), 2013, pp. 2378–2383 (2013)

  14. Manyam, S., Rathinam, S., Darbha, S., Casbeer, D., Chandler, P.: Routing of Two Unmanned Aerial Vehicles with Communication Constraints. In: International Conference on Unmanned Aircraft Systems (ICUAS), 2014, pp. 140–148 (2014)

  15. Manyam, S.G., Rathinam, S., Darbha, S.: Computation of lower bounds for multiple depot, multiple vehicle routing problem with motion constraints. ASME J. Dyn. Syst. Meas. Control. 137(9), 094,501–094,501-5 (2015)

    Article  Google Scholar 

  16. Noon, C.E., Bean, J.C.: An efficient transformation of the generalized traveling salesman problem. INFOR 31(1), 39–44 (1993)

    MATH  Google Scholar 

  17. Potyagaylo, S., Rand, O., Kanza, Y.: Motion Planning for an Autonomous Helicopter in a Gps-Denied Environment. In: Proceedings of the American Helicopter Society 66Th Annual Forum, Phoenix, AZ, USA (2010)

  18. Rathinam, S., Sengupta, R., Darbha, S.: Resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Trans. Autom. Sci. Eng. 4(1), 98–104 (2007)

    Article  Google Scholar 

  19. Reinelt, G.: Tsplib—a traveling salesman problem library. ORSA J. Comput. 3(4), 376–384 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  20. Shames, I., Dasgupta, S., Fidan, B., Anderson, B.: Circumnavigation using distance measurements under slow drift. IEEE Trans. Autom. Control 57(4), 889–903 (2012)

    Article  MathSciNet  Google Scholar 

  21. Steiglitz, K., Papadimitriou, C.H.: Combinatorial Optimization: Algorithms and Complexity. Prentice Hall, New Jersey (1982)

    MATH  Google Scholar 

  22. Summers, T.H., Akella, M.R., Mears, M.J.: Coordinated standoff tracking of moving targets: control laws and information architectures. J. Guid. Control. Dyn. 32(1), 56–69 (2009)

    Article  Google Scholar 

  23. Sundar, K., Rathinam, S.: Algorithms for routing an unmanned aerial vehicle in the presence of refueling depots. IEEE Trans. Autom. Sci. Eng. 11(1), 287–194 (2014)

    Article  Google Scholar 

  24. Sundar, K., Rathinam, S.: Generalized multiple depot traveling salesman problem - polyhedral study and exact algorithm. Journal of Computers and Operations Research (2015). doi:10.1016/j.cor.2015.12.014

  25. Warwick, G.: Lightsquared tests confirm GPS jamming. Aviation Week (2011)

  26. Wu, A.D., Johnson, E.N., Kaess, M., Dellaert, F., Chowdhary, G.: Autonomous flight in gps-denied environments using monocular vision and inertial sensors. Journal of Aerospace Information Systems 10(4), 172–186 (2013)

    Article  Google Scholar 

  27. Yadlapalli, S., Malik, W., Darbha, S., Pachter, M.: A lagrangian based algorithm for a multiple depot, multiple traveling salesman problem. Nonlinear Anal. Real World Appl. 10(4), 1990–1999 (2009)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Control Science Center of Excellence, Air Force Research Laboratory, WPAFB, Dayton, OH, USA

    Satyanarayana G. Manyam, David Casbeer, Yongcan Cao & Phil Chandler

  2. Department of Mechanical Engineering, Texas A & M University, College Station, TX, USA

    Sivakumar Rathinam & Swaroop Darbha

Authors
  1. Satyanarayana G. Manyam
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sivakumar Rathinam
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Swaroop Darbha
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. David Casbeer
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Yongcan Cao
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Phil Chandler
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sivakumar Rathinam.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Manyam, S.G., Rathinam, S., Darbha, S. et al. GPS Denied UAV Routing with Communication Constraints. J Intell Robot Syst 84, 691–703 (2016). https://doi.org/10.1007/s10846-016-0343-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10846-016-0343-2

Keywords

Search

Navigation