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Optimal Path Planning in Cooperative Heterogeneous Multi-robot Delivery Systems

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Algorithmic Foundations of Robotics XI

Part of the book series: Springer Tracts in Advanced Robotics ((STAR,volume 107))

Abstract

This paper addresses a team of cooperating vehicles performing autonomous deliveries in urban environments. The cooperating team comprises two vehicles with complementary capabilities, a truck restricted to travel along a street network, and a quadrotor micro-aerial vehicle of capacity one that can be deployed from the truck to perform deliveries. The problem is formulated as an optimal path planning problem on a graph and the goal is to find the shortest cooperative route enabling the quadrotor to deliver items at all requested locations. The problem is shown to be NP-hard using a reduction from the Travelling Salesman Problem and an algorithmic solution is proposed using a graph transformation to the Generalized Travelling Salesman Problem, which can be solved using existing methods. Simulation results compare the performance of the presented algorithms and demonstrate examples of delivery route computations over real urban street maps.

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References

  1. Garone, E., Naldi, R., Casavola, A., Frazzoli, E.: Cooperative path planning for a class of carrier-vehicle systems. In: IEEE Conference on Decision and Control, pp. 2456–2462 (2008)

    Google Scholar 

  2. Parker, L.: Current state of the art in distributed autonomous mobile robotics. In: Parker, L.E., Bekey, G., Barhen, J. (eds.) Distributed Autonomous Robotic Systems, vol. 4, pp. 3–12. Springer, Japan (2000)

    Google Scholar 

  3. Pimenta, L., Kumar, V., Mesquita, R., Pereira, G.: Sensing and coverage for a network of heterogeneous robots. In: IEEE Conference on Decision and Control, pp. 1–8 (2008)

    Google Scholar 

  4. Chand, P., Carnegie, D.A.: Mapping and exploration in a hierarchical heterogeneous multi-robot system using limited capability robots. Robot. Auton. Syst. 61(6), 565–579 (2013)

    Article  Google Scholar 

  5. Mathew, N., Smith, S.L., Waslander, S.L.: A graph-based approach to multi-robot rendezvous for recharging in persistent tasks. In: International Conference on Robotics and Automation, May 2013, pp. 3497–3502

    Google Scholar 

  6. Phan, C., Liu, H.: A cooperative UAV/UGV platform for wildfire detection and fighting. In: International Conference on System Simulation and Scientific Computing, pp. 494–498 (2008)

    Google Scholar 

  7. Bae, J., Rathinam, S.: An approximation algorithm for a heterogeneous traveling salesman problem. In: ASME 2011 Dynamic Systems and Control Conference and Bath/ASME Symposium on Fluid Power and Motion Control, pp. 637–644 (2011)

    Google Scholar 

  8. Oberlin, P., Rathinam, S., Darbha, S.: A transformation for a heterogeneous, multiple depot, multiple traveling salesman problem. In: American Control Conference, pp. 1292–1297 (2009)

    Google Scholar 

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

    MATH  Google Scholar 

  10. Helsgaun, K.: General k-opt submoves for the Linkernighan TSP heuristic. Math. Program. Comput. 1, 119–163 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  11. Nagy, G., Salhi, S.: Heuristic algorithms for single and multiple depot vehicle routing problems with pickups and deliveries. Eur. J. Oper. Res. 162(1), 126–141 (2005)

    Article  MATH  Google Scholar 

  12. Bullo, F., Frazzoli, E., Pavone, M., Savla, K., Smith, S.: Dynamic vehicle routing for robotic systems. Proc. IEEE 99(9), 1482–1504 (2011)

    Article  Google Scholar 

  13. Qu, Y., Bard, J.F.: The heterogeneous pickup and delivery problem with configurable vehicle capacity. Transp. Res. Part C 32, 1–20 (2013)

    Article  Google Scholar 

  14. Korte, B., Vygen, J.: Combinatorial Optimization: Theory and Algorithms. Algorithmics and Combinatorics, vol. 21, 4th edn. Springer, New York (2007)

    Google Scholar 

  15. Lin, S., Kernighan, B.W.: An effective heuristic algorithm for the traveling-salesman problem. Oper. Res. 21(2), 498–516 (1973)

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. University of Waterloo, Waterloo, ON, N2L3G1, Canada

    Neil Mathew, Stephen L. Smith & Steven L. Waslander

Authors
  1. Neil Mathew
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  2. Stephen L. Smith
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  3. Steven L. Waslander
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Corresponding author

Correspondence to Neil Mathew .

Editor information

Editors and Affiliations

  1. Department of Computer Engineering, Bogazici University, Istanbul, Turkey

    H. Levent Akin

  2. Department of Computer Science and Engineering, Texas A&M University, College Station, Texas, USA

    Nancy M. Amato

  3. Department of Computer Science and Engineering, University of Minnesota, Minneapolis, Minnesota, USA

    Volkan Isler

  4. Department of Information and Computing Sciences, Utrecht University, Utrecht, Utrecht, The Netherlands

    A. Frank van der Stappen

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Mathew, N., Smith, S.L., Waslander, S.L. (2015). Optimal Path Planning in Cooperative Heterogeneous Multi-robot Delivery Systems. In: Akin, H., Amato, N., Isler, V., van der Stappen, A. (eds) Algorithmic Foundations of Robotics XI. Springer Tracts in Advanced Robotics, vol 107. Springer, Cham. https://doi.org/10.1007/978-3-319-16595-0_24

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  • DOI: https://doi.org/10.1007/978-3-319-16595-0_24

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-16594-3

  • Online ISBN: 978-3-319-16595-0

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