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Implicit Multiagent Coordination at Uncontrolled Intersections via Topological Braids

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Algorithmic Foundations of Robotics XV (WAFR 2022)

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Abstract

We focus on decentralized navigation among multiple non-communicating agents at uncontrolled street intersections. Avoiding collisions under such settings demands nuanced implicit coordination. This is challenging to accomplish; the high dimensionality of the space of possible behavior and the lack of explicit communication among agents complicate prediction and planning. However, the structure of these domains often collapses the space of possible collective behavior into a finite set of modes. Our key insight is that enabling agents to reason about modes may enable them to coordinate implicitly via intent signals encoded in their actions. In this paper, we represent modes as low-dimensional multiagent motion primitives in a compact and interpretable fashion using the formalism of topological braids. Based on this representation, we derive a probabilistic model that maps past behavior of multiple agents to a future mode. Using this model, we design a decentralized control algorithm that treats navigation as uncertainty minimization over the space of modes. This algorithm enables agents to collectively reject unsafe intersection crossing strategies in a distributed fashion. We demonstrate our approach in a simulated four-way uncontrolled intersection. Our model is shown to reduce the frequency of collisions by over 65% against baselines explicitly reasoning in the space of trajectories, while maintaining comparable time efficiency in challenging scenarios.

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Notes

  1. 1.

    Agents that intend to follow time-efficient and collision-free paths.

  2. 2.

    Each agent uses a distinct projection plane to define their own braid set.

References

  1. Artin, E.: Theory of braids. Ann. Math. 48(1), 101–126 (1947)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bandyopadhyay, T., Won, K.S., Frazzoli, E., Hsu, D., Lee, W.S., Rus, D.: Intention-aware motion planning. In: Proceedings of the International Workshop on the Algorithmic Foundations of Robotics (WAFR), pp. 475–491. Springer, Berlin, Heidelberg (2013)

    Google Scholar 

  3. Bhattacharya, S., Likhachev, M., Kumar., V.: Identification and representation of homotopy classes of trajectories for search-based path planning in 3d. In: Proceedings of Robotics: Science and Systems (RSS) (2011)

    Google Scholar 

  4. Birman, J.S.: Braids Links And Mapping Class Groups. Princeton University Press (1975)

    Google Scholar 

  5. Bouton, M., Cosgun, A., Kochenderfer, M.J.: Belief state planning for autonomously navigating urban intersections. In: Proceedings of the IEEE Intelligent Vehicles Symposium (IV), pp. 825–830 (2017)

    Google Scholar 

  6. Buckman, N., Pierson, A., Schwarting, W., Karaman, S., Rus, D.: Sharing is caring: socially-compliant autonomous intersection negotiation. In: Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 6136–6143 (2019)

    Google Scholar 

  7. Dosovitskiy, A., Ros, G., Codevilla, F., Lopez, A., Koltun, V.: CARLA: an open urban driving simulator. In: Proceedings of the Conference on Robot Learning (CoRL), Proceedings of Machine Learning Research, vol. 78, pp. 1–16 (2017)

    Google Scholar 

  8. Gadepally, V., Krishnamurthy, A., Özgüner, Ü.: A framework for estimating long term driver behavior. J. Adv. Transp. 1–11, 2017 (2017)

    Google Scholar 

  9. Hsu, Y.-C., Gopalswamy, S., Saripalli, S., Shell, D.A.: An MDP model of vehicle-pedestrian interaction at an unsignalized intersection. In: Proceedings of the IEEE Vehicular Technology Conference (VTC), pp. 1–6 (2018)

    Google Scholar 

  10. Hubmann, C., Becker, M., Althoff, D., Lenz, D., Stiller, C.: Decision making for autonomous driving considering interaction and uncertain prediction of surrounding vehicles. In: Proceedings of the IEEE Intelligent Vehicles Symposium (IV), pp. 1671–1678 (2017)

    Google Scholar 

  11. Isele, D., Rahimi, R., Cosgun, A., Subramanian, K., Fujimura, K.: Navigating occluded intersections with autonomous vehicles using deep reinforcement learning. In: Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), pp. 2034–2039 (2018)

    Google Scholar 

  12. Javdani, S., Admoni, H., Pellegrinelli, S., Srinivasa, S.S., Bagnell, J.A.: Shared autonomy via hindsight optimization for teleoperation and teaming. Int. J. Robot. Res. 37(7), 717–742 (2018)

    Article  Google Scholar 

  13. Lazar, D.A., Pedarsani, R., Chandrasekher, K., Sadigh, D.: Maximizing road capacity using cars that influence people. In: Proceedings of the IEEE Conference on Decision and Control (CDC), pp. 1801–1808 (2018)

    Google Scholar 

  14. Liebenwein, L., Schwarting, W.,  Vasile, C.-I., DeCastro, J., Alonso-Mora, J., Karaman, S., Rus, D.: Compositional and contract-based verification for autonomous driving on road networks. In: Robotics Research, pp. 163–181. Springer International Publishing, Cham (2020)

    Google Scholar 

  15. Mavrogiannis, C., Knepper, R.A.: Hamiltonian coordination primitives for decentralized multiagent navigation. Int. J. Robot. Res. 40(10–11), 1234–1254 (2021)

    Article  Google Scholar 

  16. Mavrogiannis, C., DeCastro, J., Srinivasa, S.S.: Analyzing multiagent interactions in traffic scenes via topological braids. In: Proceedings of the IEEE International Conference on Robotics and Automation (ICRA) (2022)

    Google Scholar 

  17. Mavrogiannis, C.I., Knepper, R.A.: Multi-agent path topology in support of socially competent navigation planning. Int. J. Robot. Res. 38(2–3), 338–356 (2019)

    Article  Google Scholar 

  18. Mavrogiannis, C.I., Blukis, V., Knepper, R.A.: Socially competent navigation planning by deep learning of multi-agent path topologies. In: Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 6817–6824 (2017)

    Google Scholar 

  19. McGill, S.G., Rosman, G., Ort, T., Pierson, A., Gilitschenski, I., Araki, B., Fletcher, L., Karaman, S., Rus, D., Leonard, J.J.: Probabilistic risk metrics for navigating occluded intersections. IEEE Robot. Autom. Lett. 4(4), 4322–4329 (2019)

    Article  Google Scholar 

  20. Miculescu, D., Karaman, S.: Polling-systems-based autonomous vehicle coordination in traffic intersections with no traffic signals. IEEE Trans. Autom. Control 65(2), 680–694 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  21. Murasugi, K., Kurpita, B.I.: A Study of Braids. Mathematics and Its Applications. Springer, Netherlands (1999)

    Book  MATH  Google Scholar 

  22. Najm, W.G., Smith, J.D., Yanagisawa, M.: Pre-crash scenario typology for crash avoidance research. Technical Report DOT-HS-810 767, National Highway Transportation Safety Administration (2007)

    Google Scholar 

  23. National Highway Traffic Safety Administration, US Department of Transportation. Fatality analysis reporting system (FARS) encyclopedia (2018). https://www-fars.nhtsa.dot.gov. Retrieved: [01/24/2020]

  24. Orthey, A., Toussaint, M.: Section patterns: efficiently solving narrow passage problems in multilevel motion planning. IEEE Trans. Rob. 37(6), 1891–1905 (2021)

    Article  Google Scholar 

  25. Patil, G.R., Pawar, D.S.: Microscopic analysis of traffic behavior at unsignalized intersections in developing world. Transp. Lett. 8(3), 158–166 (2016)

    Article  Google Scholar 

  26. Pierson, A.,  Schwarting, W., Karaman, S., Rus, D.: Navigating congested environments with risk level sets. In: Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), pp. 5712–5719 (2018)

    Google Scholar 

  27. Pokorny, F.T., Goldberg, K., Kragic, D.: Topological trajectory clustering with relative persistent homology. In: Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), pp. 16–23 (2016)

    Google Scholar 

  28. Roh, J., Mavrogiannis, C., Madan, R., Fox, D., Srinivasa, S.S.: Multimodal trajectory prediction via topological invariance for navigation at uncontrolled intersections. In: Proceedings of the Conference on Robot Learning, vol. 155, pp. 2216–2227 (2021)

    Google Scholar 

  29. Sadigh, D., Landolfi, N., Sastry, S.S., Seshia, S.A., Dragan, A.D.: Planning for cars that coordinate with people: leveraging effects on human actions for planning and active information gathering over human internal state. Auton. Robot. 42(7), 1405–1426 (2018)

    Article  Google Scholar 

  30. Salzmann, T., Ivanovic, B., Chakravarty, P., Pavone, M.: Trajectron++: dynamically-feasible trajectory forecasting with heterogeneous data. In: Proceedings of the European Conference on Computer Vision (ECCV), pp. 683–700 (2020)

    Google Scholar 

  31. Sezer, V., Bandyopadhyay, T., Rus, D., Frazzoli, E., Hsu, D.: Towards autonomous navigation of unsignalized intersections under uncertainty of human driver intent. In: Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 3578–3585 (2015)

    Google Scholar 

  32. Shalev-Shwartz, S., Shammah, S., Shashua, A.: Safe, Multi-Agent, Reinforcement Learning for Autonomous Driving (2016). arXiv:1610.03295

  33. Thiffeault, J.-L.: Braids of entangled particle trajectories. Chaos 20(1) (2010)

    Google Scholar 

  34. Thiffeault, J.-L., Budišić, M.: Braidlab: a software package for braids and loops, 2013–2019. Version 3.2.4

    Google Scholar 

  35. Tian, R., Li, N., Kolmanovsky, I., Yildiz, Y., Girard, A.: Game-theoretic modeling of traffic in unsignalized intersection network for autonomous vehicle control verification and validation. IEEE Trans. Intell. Transp. Syst. 23(3), 2211–2226 (2022)

    Article  Google Scholar 

  36. Wang, W., Zhang, W., Zhao, D.: Understanding V2V driving scenarios through traffic primitives. IEEE Trans. Intell. Transp. Syst. 23(1), 610–619 (2022)

    Article  Google Scholar 

  37. Zanardi, A., Zardini, G., Srinivasan, S., Bolognani, S., Censi, A., Dörfler, F., Frazzoli, E.: Posetal games: efficiency, existence, and refinement of equilibria in games with prioritized metrics. IEEE Robot. Autom. Lett. 7(2), 1292–1299 (2022)

    Article  Google Scholar 

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Acknowledgements

his work was partially funded by the National Institute of Health R01 (#R01EB019335), National Science Foundation CPS (#1544797), National Science Foundation NRI (#1637748), the Office of Naval Research, the RCTA, Amazon, and Honda Research Institute USA.

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Authors and Affiliations

  1. Paul G. Allen School of Computer Science & Engineering, University of Washington, Seattle, WA, 98195, USA

    Christoforos Mavrogiannis & Siddhartha Srinivasa

  2. Toyota Research Institute, Cambridge, MA, 02139, USA

    Jonathan A. DeCastro

Authors
  1. Christoforos Mavrogiannis
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  2. Jonathan A. DeCastro
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  3. Siddhartha Srinivasa
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Corresponding author

Correspondence to Christoforos Mavrogiannis .

Editor information

Editors and Affiliations

  1. Center for Ubiquitous Computing, University of Oulu, Oulu, Finland

    Steven M. LaValle

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

    Jason M. O’Kane

  3. Department of Aerospace Engineering, University of Maryland, College Park, MD, USA

    Michael Otte

  4. Gates Computer Science, Stanford University, Stanford, CA, USA

    Dorsa Sadigh

  5. Department of Computer Science, University of Maryland, College Park, MD, USA

    Pratap Tokekar

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Mavrogiannis, C., DeCastro, J.A., Srinivasa, S. (2023). Implicit Multiagent Coordination at Uncontrolled Intersections via Topological Braids. In: LaValle, S.M., O’Kane, J.M., Otte, M., Sadigh, D., Tokekar, P. (eds) Algorithmic Foundations of Robotics XV. WAFR 2022. Springer Proceedings in Advanced Robotics, vol 25. Springer, Cham. https://doi.org/10.1007/978-3-031-21090-7_22

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