Skip to main content
SpringerLink
Log in

Multi-robot Trajectory Generation for an Aerial Payload Transport System

  • Conference paper
  • First Online:
Book cover Robotics Research

Part of the book series: Springer Proceedings in Advanced Robotics ((SPAR,volume 10))

Abstract

In this work, we consider the problem of planning safe, feasible trajectories for a team of quadrotors with slung-loads operating in an obstacle-free, three-dimensional workspace. We are particularly interested in generating dynamic trajectories—trajectories where robots’ payloads are allowed to swing in accordance with the system’s natural dynamics—for fast, agile, coordinated payload transportation. This capability is applicable to tasks such as construction, where a single crane performing sequential tasks could be replaced by multiple quadrotors performing tasks in parallel for increased efficiency. We model this problem as a labeled multi-robot planning problem, where robots must navigate payloads from given start positions to fixed, non-interchangeable goal positions. Our system presents three novel challenges: (1.) Each vehicle has eight degrees-of-freedom, significantly increasing the size of the team’s joint state space. (2.) Each vehicle is a nonlinear, \(6\mathrm{th}\)-order dynamical system with four degrees of under-actuation. (3.) Each vehicle is a multi-body system. We present a safe and complete Quadratic Programming solution and validate its practicality with experiments containing up to nine quadrotors.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    http://www.asctec.de/en/.

  2. 2.

    www.gurobi.com/.

  3. 3.

    https://www.digi.com/xbee.

  4. 4.

    https://www.vicon.com/.

References

  1. Augugliaro, F., Lupashin, S., Hamer, M., Male, C., Hehn, M., Mueller, M.W., Willmann, J.S., Gramazio, F., Kohler, M., D’Andrea, R.: The flight assembled architecture installation: cooperative construction with flying machines. IEEE Control Syst. 34(4), 46–64 (2014)

    Article  MathSciNet  Google Scholar 

  2. Bennewitz, M., Burgard, W., Thrun, S.: Finding and optimizing solvable priority schemes for decoupled path planning techniques for teams of mobile robots. Robot. Auton. Syst. 41(2), 89–99 (2002)

    Article  Google Scholar 

  3. Bernard, M., Kondak, K.: Generic slung load transportation system using small size helicopters. In: IEEE International Conference on Robotics and Automation (ICRA) (2009)

    Google Scholar 

  4. Boyd, S., Vandenberghe, L.: Convex Optimization, chap. 2. Cambridge University Press, Cambridge, pp. 21–66 (2004)

    Google Scholar 

  5. Chen, J., Liu, T., Shen, S.: Online generation of collision-free trajectories for quadrotor flight in unknown cluttered environments. In: 2016 IEEE International Conference on Robotics and Automation (ICRA), 16–21 May 2016, pp. 1476–1483. Institute of Electrical and Electronics Engineers (IEEE), New York

    Google Scholar 

  6. Faust, A., Palunko, I., Cruz, P., Fierro, R., Tapia, L.: Automated aerial suspended cargo delivery through reinforcement learning. Artif. Intell. 247, 381–398 (2017). Special Issue on AI and Robotics

    Google Scholar 

  7. Flores, M.E.: Real-time trajectory generation for constrained nonlinear dynamical systems using non-uniform rational b-spline basis functions. Dissertation, California Institute of Technology (2008)

    Google Scholar 

  8. Foehn, P., Falanga, D., Kuppuswamy, N., Tedrake, R., Scaramuzza, D.: Fast trajectory optimization for agile quadrotor maneuvers with a cable-suspended payload. In: Proceedings of the Conference on Robotics: Science and Systems (RSS). Boston (2017)

    Google Scholar 

  9. Gao, F., Shen, S.: Online quadrotor trajectory generation and autonomous navigation on point clouds. In: IEEE International Symposium on Safety, Security, and Rescue Robotics (SSRR), 23–27 Oct 2016, pp. 139–146. New York (2016)

    Google Scholar 

  10. Goldenberg, M., Felner, A., Stern, R., Sharon, G., Sturtevant, N., Holte, R.C., Schaeffer, J.: Enhanced partial expansion A*. J. Artif. Intell. Res. 50(1), 141–187 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  11. Han, S.D., Rodriguez, E.J., Yu, J.: Sear: a polynomial-time expected constant-factor optimal algorithmic framework for multi-robot path planning (2017). https://arxiv.org/abs/1709.08215

  12. Alonso-Mora, J., Naegeli, T., Siegwart, R., Beardsley, P.: Collision avoidance for aerial vehicles in multi-agent scenarios. Auton. Robot. 39, 101–121 (2015)

    Google Scholar 

  13. Lee, T., Leok, M., McClamroch, N.H.: Control of complex maneuvers for a quadrotor UAV using geometric methods on SE(3). Asian J. Control 15(2), 391–408 (2011)

    Article  MATH  Google Scholar 

  14. Lindsey, Q., Mellinger, D., Kumar, V.: Construction with quadrotor teams. Auton. Robot. 33(3), 323–336 (2012)

    Article  Google Scholar 

  15. Liu, S., Watterson, M., Mohta, K., Sun, K., Bhattacharya, S., Taylor, C.J., Kumar, V.: Planning dynamically feasible trajectories for quadrotors using safe flight corridors in 3-d complex environments. IEEE Robot. Autom. Lett. (RA-L) 2(3), 1688–1695 (2017)

    Google Scholar 

  16. Luna, R., Bekris, K.E.: Push and swap: fast cooperative path-finding with completeness guarantees. In: International Joint Conference on Artificial Intelligence (IJCAI). Barcelona, Spain (2011)

    Google Scholar 

  17. Mellinger, D., Kumar, V.: Minimum snap trajectory generation and control for quadrotors. In: 2011 IEEE International Conference on Robotics and Automation (ICRA), 9–13 May 2011, pp. 2520–2525. New York (2011)

    Google Scholar 

  18. Murray, R.M., Rathinam M., Sluis W.: Differential flatness of mechanical control systems: a catalog of prototype systems. In: ASME International Congress and Exposition (1995)

    Google Scholar 

  19. Peng, J., Akella, S.: Coordinating multiple robots with kinodynamic constraints along specified paths. Int. J. Robot. Res. (IJRR) 24(4), 295–310 (2005)

    Article  Google Scholar 

  20. Preiss J.A., Hönig W., Ayanian N., Sukhatme G.S.: Downwash-aware trajectory planning for large quadrotor teams. In: IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) (2017)

    Google Scholar 

  21. Richter, C., Bry, A., Roy, N.: Polynomial trajectory planning for aggressive quadrotor flight in dense indoor environments. In: Inaba, M., Corke, P. (eds.) Robotics Research: The 16th International Symposium ISRR, vol. 1, pp. 649–666. Springer International Publishing, Cham (2016)

    Google Scholar 

  22. Solovey, K., Salzman, O., Halperin, D.: Finding a needle in an exponential haystack: discrete RRT for exploration of implicit roadmaps in multi-robot motion planning. Int. J. Robot. Res. (IJRR) 35(5), 501–513 (2016)

    Article  Google Scholar 

  23. Spirakis, P., Yap, C.K.: Strong NP-hardness of moving many discs. Inf. Process. Lett. 19(1), 55–59 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  24. Sreenath, K., Kumar, V.: Dynamics, control and planning for cooperative manipulation of payloads suspended by cables from multiple quadrotor robots. In: Robotics: Science and Systems (RSS) (2013)

    Google Scholar 

  25. Sreenath, K., Lee, T., Kumar, V.: Geometric control and differential flatness of a quadrotor UAV with a cable-suspended load. In: IEEE Conference on Decision and Control (CDC) (2013)

    Google Scholar 

  26. Standley, T.: Finding optimal solutions to cooperative pathfinding problems. In: AAAI Conference on Artificial Intelligence. Atlanta (2010)

    Google Scholar 

  27. Tang, S., Kumar, V.: Mixed integer quadratic program trajectory generation for a quadrotor with a cable-suspended payload. In: IEEE International Conference on Robotics and Automation (ICRA), May 26–30 2015, pp. 2215–2222. New York

    Google Scholar 

  28. Tang, S., Kumar, V.: A complete algorithm for generating safe trajectories for multi-robot teams. In: Bicchi, A., Burgard, W., (eds.) Robotics Research: Volume 2, pp. 599–616. Springer International Publishing, Cham (2018)

    Google Scholar 

  29. Tang, S., Thomas, J., Kumar, V.: Hold or take optimal plan (hoop): a quadratic programming approach to multi-robot trajectory generation. Int. J. Robot. Res. (IJRR) (2018), in press

    Google Scholar 

  30. Yu, J., Rus, D.: An Effective Algorithmic Framework for Near Optimal Multi-robot Path Planning, pp. 495–511. Springer International Publishing, Cham (2018)

    Google Scholar 

Download references

Acknowledgements

We gratefully acknowledge the support of ONR grants N00014-09-1-1051 and N00014-09-1-103, NSF grant IIS-1426840, ARL grant W911NF-08-2-0004. Sarah Tang is supported by NSF Research Fellowship Grant No. DGE-1321851. The authors thank Jeremy Wang for the fabrication of the payload suspension attachments.

Author information

Authors and Affiliations

  1. GRASP Lab, University of Pennsylvania, Philadelphia, PA, USA

    Sarah Tang & Vijay Kumar

  2. University of California, Berkeley, CA, USA

    Koushil Sreenath

Authors
  1. Sarah Tang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Koushil Sreenath
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Vijay Kumar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sarah Tang .

Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Illinois at Urbana-Champaign, Urbana, IL, USA

    Nancy M. Amato

  2. Department of Computer Science, Johns Hopkins University, Baltimore, MD, USA

    Greg Hager

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

    Shawna Thomas

  4. Department of Electrical Engineering, Pontificia Universidad Católica de Chile, Santiago, Chile

    Miguel Torres-Torriti

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Tang, S., Sreenath, K., Kumar, V. (2020). Multi-robot Trajectory Generation for an Aerial Payload Transport System. In: Amato, N., Hager, G., Thomas, S., Torres-Torriti, M. (eds) Robotics Research. Springer Proceedings in Advanced Robotics, vol 10. Springer, Cham. https://doi.org/10.1007/978-3-030-28619-4_70

Download citation

Publish with us

Policies and ethics

Search

Navigation