UAV Routing and Coordination in Stochastic, Dynamic Environments

  • John J. Enright
  • Emilio Frazzoli
  • Marco Pavone
  • Ketan Savla
Reference work entry


Recent years have witnessed great advancements in the science and technology for unmanned aerial vehicles (UAVs), for example, in terms of autonomy, sensing, and networking capabilities. This chapter surveys algorithms on task assignment and scheduling for one or multiple UAVs in a dynamic environment, in which targets arrive at random locations at random times, and remain active until one of the UAVs flies to the target’s location and performs an on-site task. The objective is to minimize some measure of the targets’ activity, for example, the average amount of time during which a target remains active. The chapter focuses on a technical approach that relies upon methods from queueing theory, combinatorial optimization, and stochastic geometry. The main advantage of this approach is its ability to provide analytical estimates of the performance of the UAV system on a given problem, thus providing insight into how performance is affected by design and environmental parameters, such as the number of UAVs and the target distribution. In addition, the approach provides provable guarantees on the system’s performance with respect to an ideal optimum. To illustrate this approach, a variety of scenarios are considered, ranging from the simplest case where one UAV moves along continuous paths and has unlimited sensing capabilities, to the case where the motion of the UAV is subject to curvature constraints, and finally to the case where the UAV has a finite sensor footprint. Finally, the problem of cooperative routing algorithms for multiple UAVs is considered, within the same queueing-theoretical framework, and with a focus on control decentralization.


Travel Salesman Problem Online Algorithm Voronoi Region Motion Constraint Differential Constraint 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. P.K. Agarwal, M. Sharir, Efficient algorithms for geometric optimization. ACM Comput. Surv. 30(4), 412–458 (1998)CrossRefGoogle Scholar
  2. M. Alighanbari, J.P. How, A robust approach to the UAV task assignment problem. Int. J. Robust Nonlinear Control 18(2), 118–134 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  3. D. Applegate, R. Bixby, V. Chvátal, W. Cook, On the solution of traveling salesman problems, in Proceedings of the International Congress of Mathematicians, Extra Volume ICM III,Berlin, 1998, pp. 645–656. Documenta Mathematica, Journal der Deutschen Mathematiker-Vereinigung Google Scholar
  4. S. Arora, Nearly linear time approximation scheme for Euclidean TSP and other geometric problems, in Proceedings of the 38th IEEE Annual Symposium on Foundations of Computer Science, Miami Beach, 1997, pp. 554–563Google Scholar
  5. G. Arslan, J.R. Marden, J.S. Shamma, Autonomous vehicle-target assignment: a game theoretic formulation. ASME J. Dyn. Syst. Meas. Control 129(5), 584–596 (2007)CrossRefGoogle Scholar
  6. R.W. Beard, T.W. McLain, M.A. Goodrich, E.P. Anderson, Coordinated target assignment and intercept for unmanned air vehicles. IEEE Trans. Robot. Autom. 18(6), 911–922, 2002CrossRefGoogle Scholar
  7. J. Beardwood, J. Halton, J. Hammersley, The shortest path through many points. Proc. Camb. Philos. Soc. Math. Phys. Sci. 55(4), 299–327 (1959)CrossRefzbMATHMathSciNetGoogle Scholar
  8. D.J. Bertsimas, G.J. van Ryzin, A stochastic and dynamic vehicle routing problem in the Euclidean plane. Oper. Res. 39, 601–615 (1991)CrossRefzbMATHGoogle Scholar
  9. D.J. Bertsimas, G.J. van Ryzin, Stochastic and dynamic vehicle routing in the Euclidean plane with multiple capacitated vehicles. Oper. Res. 41(1), 60–76 (1993a)CrossRefzbMATHMathSciNetGoogle Scholar
  10. D.J. Bertsimas, G.J. van Ryzin, Stochastic and dynamic vehicle routing with general interarrival and service time distributions. Adv. Appl. Probab. 25, 947–978 (1993b)CrossRefzbMATHGoogle Scholar
  11. F. Bullo, E. Frazzoli, M. Pavone, K. Savla, S.L. Smith, Dynamic vehicle routing for robotic systems. Proc. IEEE 99(9), 1482–1504 (2011)CrossRefGoogle Scholar
  12. G. Cannata, A. Sgorbissa, A minimalist algorithm for multirobot continuous coverage. IEEE Trans. Robot. 27(2), 297–312 (2011)CrossRefGoogle Scholar
  13. P. Chandler, S. Rasmussen, M. Pachter, UAV cooperative path planning, in AIAA Conference on Guidance, Navigation, and Control, Denver (2000)Google Scholar
  14. N. Christofides, Bounds for the travelling-salesman problem. Oper. Res. 20, 1044–1056 (1972)CrossRefzbMATHMathSciNetGoogle Scholar
  15. Z. Drezner (ed.), Facility Location: A Survey of Applications and Methods. Series in Operations Research (Springer, New York, 1995). ISBN:0-387-94545-8Google Scholar
  16. L.E. Dubins, 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)CrossRefzbMATHMathSciNetGoogle Scholar
  17. J.J. Enright, K. Savla, E. Frazzoli, F. Bullo, Stochastic and dynamic routing problems for multiple UAVs. AIAA J. Guid. Control Dyn. 32(4), 1152–1166 (2009)CrossRefGoogle Scholar
  18. B. Golden, S. Raghavan, E. Wasil, The Vehicle Routing Problem: Latest Advances and New Challenges. Operations Research/Computer Science Interfaces, vol. 43 (Springer, New York/London, 2008). ISBN:0387777776CrossRefGoogle Scholar
  19. S. Irani, X. Lu, A. Regan, On-line algorithms for the dynamic traveling repair problem. J. Sched. 7(3), 243–258 (2004)CrossRefzbMATHMathSciNetGoogle Scholar
  20. P. Jaillet, M.R. Wagner, Online routing problems: value of advanced information and improved competitive ratios. Transp. Sci. 40(2), 200–210 (2006)CrossRefGoogle Scholar
  21. D.S. Johnson, L.A. McGeoch, E.E. Rothberg, Asymptotic experimental analysis for the held-karp traveling salesman bound, in Proceedings of the 7th Annual ACM-SIAM Symposium on Discrete Algorithms, Atlanta, 1996, pp. 341–350Google Scholar
  22. S.O. Krumke, W.E. de Paepe, D. Poensgen, L. Stougie, News from the online traveling repairman. Theor. Comput. Sci. 295(1–3), 279–294 (2003)CrossRefzbMATHGoogle Scholar
  23. R. Larson, A. Odoni, Urban Operations Research (Prentice Hall, Englewood Cliffs, 1981)Google Scholar
  24. S. Lin, B.W. Kernighan, An effective heuristic algorithm for the traveling-salesman problem. Oper. Res. 21, 498–516 (1973)CrossRefzbMATHMathSciNetGoogle Scholar
  25. J.D.C. Little, A proof for the queuing formula: L = λW. Oper. Res. 9(3), 383–387 (1961). ISSN:0030364X.
  26. G. Mathew, I. Mezic, Spectral multiscale coverage: a uniform coverage algorithm for mobile sensor networks, in Proceedings of the 48th IEEE Control and Decision Conference, Shanghai, 2009, pp. 7872–7877Google Scholar
  27. N. Megiddo, K.J. Supowit, On the complexity of some common geometric location problems. SIAM J. Comput. 13(1), 182–196 (1984). ISSN:0097–5397CrossRefzbMATHMathSciNetGoogle Scholar
  28. A. R. Mesquita, Exploiting Stochasticity in Multi-agent Systems. PhD thesis, University of California at Santa Barbara, Santa Barbara, 2010Google Scholar
  29. B.J. Moore, K.M. Passino, Distributed task assignment for mobile agents. IEEE Trans. Autom. Control 52(4), 749–753 (2007)CrossRefMathSciNetGoogle Scholar
  30. C. H. Papadimitriou, Worst-case and probabilistic analysis of a geometric location problem. SIAM J. Comput. 10(3), 542–557 (1981)CrossRefzbMATHMathSciNetGoogle Scholar
  31. M. Pavone, Dynamic vehicle routing for Robotic networks. PhD thesis, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, 2010Google Scholar
  32. M. Pavone, K. Savla, E. Frazzoli, Sharing the load. IEEE Robot. Autom. Mag. 16(2), 52–61 (2009)CrossRefGoogle Scholar
  33. M. Pavone, A. Arsie, E. Frazzoli, F. Bullo, Distributed algorithms for environment partitioning in mobile robotic networks. IEEE Trans. Autom. Control 56(8), 1834–1848 (2011)CrossRefMathSciNetGoogle Scholar
  34. G. Percus, O.C. Martin, Finite size and dimensional dependence of the Euclidean traveling salesman problem. Phys. Rev. Lett. 76(8), 1188–1191 (1996)CrossRefzbMATHMathSciNetGoogle Scholar
  35. H.N. Psaraftis, Dynamic programming solution to the single vehicle many-to-many immediate request dial-a-ride problem. Transp. Sci. 14(2), 130–154 (1980)CrossRefGoogle Scholar
  36. D.D. Sleator, R.E. Tarjan, Amortized efficiency of list update and paging rules. Commun. ACM 28(2), 202–208 (1985)CrossRefMathSciNetGoogle Scholar
  37. S.L. Smith, F. Bullo, Monotonic target assignment for robotic networks. IEEE Trans. Autom. Control 54(9), 2042–2057 (2009)CrossRefMathSciNetGoogle Scholar
  38. D. Song, C.Y. Kim, J. Yi, Stochastic modeling of the expected time to search for an intermittent signal source under a limited sensing range, in Proceedings of Robotics: Science and Systems,Zaragoza, 2010Google Scholar
  39. J.M. Steele, Probabilistic and worst case analyses of classical problems of combinatorial optimization in Euclidean space. Math. Oper. Res. 15(4), 749 (1990)CrossRefzbMATHMathSciNetGoogle Scholar
  40. L.D. Stone, Theory of Optimal Search (Academic, New York, 1975)zbMATHGoogle Scholar
  41. P. Toth, D. Vigo (eds.), The Vehicle Routing Problem. Monographs on Discrete Mathematics and Applications (SIAM, Philadelphia, 2001). ISBN:0898715792Google Scholar
  42. P. Van Hentenryck, R. Bent, E. Upfal, Online stochastic optimization under time constraints. Ann. Oper. Res. 177(1), 151–183 (2009)CrossRefGoogle Scholar
  43. E. Zemel, Probabilistic analysis of geometric location problems. Ann. Oper. Res. 1(3), 215–238 (1984)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Kiva SystemsNorth ReadingUSA
  2. 2.Department of Aeronautics and AstronauticsMassachusetts Institute of TechnologyCambridgeUSA
  3. 3.Aeronautics and Astronautics DepartmentStanford UniversityStanfordUSA
  4. 4.Sonny Astani Department of Civil and Environmental EngineeringUniversity of Southern CaliforniaLos AngelesUSA

Personalised recommendations