Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

Combined Optimal Control and Combinatorial Optimization for Searching and Tracking Using an Unmanned Aerial Vehicle

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

Abstract

Combined searching and tracking of objects using Unmanned Aerial Vehicles (UAVs) is an important task with many applications. One way to approach this task is to formulate path-planning as a continuous optimal control problem. However, such formulations will, in general, be complex and difficult to solve with global optimality. Therefore, we propose a two-layer framework, in which the first layer uses a Traveling-Salesman-type formulation implemented using combinatorial optimization to find a near-globally-optimal path. This path is refined in the second layer using a continuous optimal control formulation that takes UAV dynamics and constraints into consideration. Searching and tracking problems usually trade-off, often in a manual or ad-hoc manner, between searching unexplored areas and keeping track of already known objects. Instead, we derive a result that enables prioritization between searching and tracking based on the probability of finding a new object weighted against the probability of losing tracked objects. Based on this result, we construct a new algorithm for searching and tracking. This algorithm is validated in simulation, where it is compared to multiple base cases as well as a case utilizing perfect knowledge of the positions of the objects. The simulations demonstrate that the algorithm performs significantly better than the base cases, with an improvement of approximately 5-15%, while it is approximately 20-25% worse than the perfect case.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Eik, K.: Review of experiences within ice and iceberg management. J. Navig. 61(4), 557–572 (2008)

    Article  Google Scholar 

  2. Lešinskis, I., Pavlovičs, A.: The aspects of implementation of unmanned aerial vehicles for ice situation awareness in maritime traffic. Transport Means - Proceedings of the International Conference, pp. 65–68 (2011)

  3. Tomic, T., Schmid, K., Lutz, P., Domel, A., Kassecker, M., Mair, E., Grixa, I.L., Ruess, F., Suppa, M., Burschka, D.: Toward a fully autonomous UAV: Research platform for indoor and outdoor urban search and rescue. IEEE Robotics & Automation Magazine 19(3), 46–56 (2012)

    Article  Google Scholar 

  4. Goodrich, M.A., Morse, B.S., Gerhardt, D., Cooper, J.L., Quigley, M., Adams, J.A., Humphrey, C.: Supporting wilderness search and rescue using a camera-equipped mini uav. Journal of Field Robotics 25(1-2), 89–110 (2008)

    Article  Google Scholar 

  5. Glade, D.: Unmanned Aerial Vehicles: Implications for military operations, DTIC Document, Tech. Rep. (2000)

  6. Eggers, J., Draper, M.H.: Multi-UAV control for tactical reconnaissance and close air support missions: operator perspectives and design challenges. In: Proceedings NATO RTO Human Factors and Medicine Symp. HFM-135. NATO TRO, Neuilly-sur-Siene. CEDEX, Biarritz (2006)

  7. DeSena, J.T., Martin, S.R., Clarke, J.C., Dutrow, D.A., Kohan, B.C., Kadar, I.: Decentralized closed-loop collaborative surveillance and tracking performance sensitivity to communications connectivity. In: Proceedings of SPIE Vol, vol. 8745, pp. 874507–1 (2013)

  8. Girard, A.R., Howell, A.S., Hedrick, J.K.: Border patrol and surveillance missions using multiple unmanned air vehicles. In: 43rd IEEE Conference on decision and control, 2004. CDC. vol. 1. IEEE, pp. 620–625 (2004)

  9. Isenor, A.W., Allardb, Y., Lapinskia, A.-L.S., Demersb, H., Radulescub, D.: Coordinating UAV information for executing national security-oriented collaboration, vol. 9248 (2014)

  10. Schrijver, A.: On the history of combinatorial optimization (till 1960). Handbooks in Operations Research and Management Science 12, 1–68 (2005)

    Article  MATH  Google Scholar 

  11. Dantzig, G., Fulkerson, R., Johnson, S.: Solution of a large-scale traveling-salesman problem. J. Oper. Res. Soc. Am. 2(4), 393–410 (1954)

    MathSciNet  MATH  Google Scholar 

  12. Applegate, D., Bixby, R., Chvátal, V., Cook, W.: The traveling salesman problem: A computational study (2011)

  13. Balas, E.: The prize collecting traveling salesman problem. Networks 19(6), 621–636 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  14. Gutin, G., Punnen, A.P.: The traveling salesman problem and its variations (2006)

  15. Pesch, H.J., Plail, M., Munich, D.: The maximum principle of optimal control: a history of ingenious ideas and missed opportunities. Control and Cybernetics 38(4A), 973–995 (2009)

    MathSciNet  MATH  Google Scholar 

  16. Betts, J.T.: Practical methods for optimal control and estimation using nonlinear programming. SIAM (2010)

  17. Biegler, L.T.: Nonlinear programming: concepts, algorithms and applications to chemical processes. SIAM (2010)

  18. Stone, L.D.: Or forum—what’s happened in search theory since the 1975 Lanchester prize? Oper. Res. 37(3), 501–506 (1989)

    Article  MathSciNet  Google Scholar 

  19. Koopman, B.O.: The theory of search. i. kinematic bases. Oper. Res. 4(3), 324–346 (1956)

    Article  MathSciNet  MATH  Google Scholar 

  20. Koopman, B.O.: The theory of search. ii. target detection. Oper. Res. 4(5), 503–531 (1956)

    Article  MathSciNet  MATH  Google Scholar 

  21. Koopman, B.O.: The theory of search: Iii. the optimum distribution of searching effort. Oper. Res. 5(5), 613–626 (1957)

    Article  MATH  Google Scholar 

  22. Walton, C.L., Gong, Q., Kaminer, I., Royset, J.O.: Optimal motion planning for searching for uncertain targets. IFAC Proceedings Volumes 47(3), 8977–8982 (2014)

    Article  Google Scholar 

  23. Stone, L.D., Royset, J.O., Washburn, A.R.: Optimal search for moving targets. Springer (2016)

  24. Golden, B.L., Raghavan, S., Wasil, E.A.: The vehicle routing problem: latest advances and new challenges. Springer Science & Business Media (2008)

  25. Oberlin, P., Rathinam, S., Darbha, S.: Today’s traveling salesman problem. IEEE Robotics & Automation Magazine 17(4), 70–77 (2010)

    Article  Google Scholar 

  26. Smith, S.L.: Task allocation and vehicle routing in dynamic environments. University of California Santa Barbara (2009)

  27. Yao, M., Zhao, M.: Unmanned aerial vehicle dynamic path planning in an uncertain environment. Robotica 33(3), 611–621 (2015)

    Article  Google Scholar 

  28. Meng, W., He, Z., Su, R., Yadav, P.K., Teo, R., Xie, L.: Decentralized multi-UAV flight autonomy for moving convoys search and track. IEEE Trans. Control Syst. Technol. 25(4), 1480–1487 (2017)

    Article  Google Scholar 

  29. Zhao, C., Zhu, M., Liang, H., Wu, Z.: The sustainable tracking strategy of moving target by UAV in an uncertain environment, Control Conference (CCC), 2016 35th Chinese, pp. 5641–5647 (2016)

  30. Furukawa, T., Bourgault, F., Lavis, B., Durrant-Whyte, H.F.: Recursive Bayesian search-and-tracking using coordinated UAVs for lost targets. IEEE International Conference on Robotics and Automation (ICRA), pp. 2521–2526 (2006)

  31. Tian, X., Bar-Shalom, Y., Pattipati, K.R.: Multi-step look-ahead policy for autonomous cooperative surveillance by UAVs in hostile environments. In: 47th IEEE Conference on decision and control, 2008. CDC 2008, pp. 2438–2443 (2008)

  32. Kassas, Z.M., Arapostathis, A., Humphreys, T.E.: Greedy motion planning for simultaneous signal landscape mapping and receiver localization. IEEE Journal of Selected Topics in Signal Processing 9(2), 247–258 (2015)

    Article  Google Scholar 

  33. Peterson, C.K., Newman, A.J., Spall, J.C.: Simulation-based examination of the limits of performance for decentralized multi-agent surveillance and tracking of undersea targets, SPIE Defense+ Security, pp. 90910F–90910F (2014)

  34. Pitre, R.R., Li, X.R., Delbalzo, R.: UAV Route planning for joint search and track missions—an information-value approach. IEEE Trans. Aerosp. Electron. Syst. 48(3), 2551–2565 (2012)

    Article  Google Scholar 

  35. Sinha, A., Kirubarajan, T., Bar-Shalom, Y.: Autonomous ground target tracking by multiple cooperative UAVs. In: 2005 IEEE Aerospace Conference, pp. 1–9 (2005)

  36. Sinha, A.: Autonomous surveillance by multiple cooperative UAVs. In: Proceedings of SPIE Vol, vol. 5913, pp. 59131V–1 (2005)

  37. Mavrommati, A., Tzorakoleftherakis, E., Abraham, I., Murphey, T.D.: Real-time area coverage and target localization using receding-horizon ergodic exploration, arXiv:1708.08416 (2017)

  38. Oispuu, M., Sciotti, M., Charlish, A.: Air route selection for improved air-to-ground situation assessment. SPIE Defense, Security, and Sensing, pp. 87420M–87420M (2013)

  39. Vanegas Alvarez, F.: Uncertainty based online planning for UAV missions in GPS-denied and cluttered environments, Ph.D. dissertation Queensland University of Technology (2017)

  40. Tichavsky, P., Muravchik, C.H., Nehorai, A.: Posterior cramér-Rao bounds for discrete-time nonlinear filtering. IEEE Trans. Signal Process. 46(5), 1386–1396 (1998)

    Article  Google Scholar 

  41. Hernandez, M.: Performance bounds for target tracking: computationally efficient formulations and associated applications. Integrated Tracking, Classification, and Sensor Management: Theory and Applications, pp. 255–310 (2012)

  42. Esmailifar, S.M., Saghafi, F.: Cooperative localization of marine targets by UAVs. Mech. Syst. Signal Process. 87, 23–42 (2017)

    Article  Google Scholar 

  43. Koohifar, F., Kumbhar, A., Guvenc, I.: Receding horizon multi-UAV cooperative tracking of moving rf source. IEEE Commun. Lett. 21(6), 1433–1436 (2017)

    Article  Google Scholar 

  44. Albert, A., Imsland, L.: Performance bounds for tracking multiple objects using a single UAV, pp. 1539–1546 (2017)

  45. Gelb, A.: Applied optimal estimation. MIT press (1974)

  46. Leira, F., Johansen, T.A., Fossen, T.I.: Automatic detection classification and tracking of objects in the ocean surface from uavs using a thermal camera (2015)

  47. Sinopoli, B., Schenato, L., Franceschetti, M., Poolla, K., Jordan, M.I., Sastry, S.S.: Kalman filtering with intermittent observations. IEEE Trans. Autom. Control 49(9), 1453–1464 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  48. Irving, R.S.: Integers, polynomials and rings: A course in algebra. Springer Science & Business Media (2003)

  49. Chen, D.-S., Batson, R.G., Dang, Y.: Applied integer programming: Modeling and solution. Wiley (2010)

  50. Dormand, J.R., Prince, P.J.: A family of embedded runge-Kutta formulae. J. Comput. Appl. Math. 6(1), 19–26 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  51. Löfberg, J.: YALMIP: A Toolbox for modeling and optimization in MATLAB. In: Proceedings of the CACSD Conference (2004)

  52. IBM Ilog CPLEX optimization studio CPLEX user’s manual, http://www.ibm.com, 2015, accessed: 2015-09-12

  53. Shampine, L.F., Reichelt, M.W.: The matlab ODE suite. SIAM J. Sci. Comput. 18(1), 1–22 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  54. Andersson, J.: A General-Purpose Software Framework for Dynamic Optimization, PhD Thesis, Arenberg Doctoral School, KU Leuven, Department of Electrical Engineering (ESAT/SCD) and Optimization in Engineering Center, Kasteelpark Arenberg 10, 3001-Heverlee, Belgium (2013)

  55. Wächter, A., Biegler, L.T.: On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Math. Program. 106(1), 25–57 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  56. Punyawee, A., Panumate, C., Iida, H.: Finding comfortable settings of snake game using game refinement measurement. In: International Conference on Computer Science and its Applications, pp. 66–73 (2016)

  57. Fossen, T.I.: Handbook of marine craft hydrodynamics and motion control. Wiley (2011)

Download references

Author information

Authors and Affiliations

  1. Department of Engineering Cybernetics Norwegian University of Science Technology, Trondheim, Norway

    Anders Albert & Lars Imsland

Authors
  1. Anders Albert
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lars Imsland
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Anders Albert.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Albert, A., Imsland, L. Combined Optimal Control and Combinatorial Optimization for Searching and Tracking Using an Unmanned Aerial Vehicle. J Intell Robot Syst 95, 691–706 (2019). https://doi.org/10.1007/s10846-018-0915-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10846-018-0915-4

Keywords

Search

Navigation