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Multi-agent Trajectory Prediction and Generation with Topological Invariants Enforced by Hamiltonian Dynamics

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Algorithmic Foundations of Robotics XIII (WAFR 2018)

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Abstract

We present a planning framework for decentralized navigation in dynamic multi-agent environments where no explicit communication takes place among agents. Our framework is based on a novel technique for computationally efficient multi-agent trajectory generation from symbolic topological specifications. At planning time, this technique allows an agent to generate a diverse set of potential future scene evolutions in the form of Cartesian, multi-agent trajectory representations. The planning agent selects and executes the next action assigned to it from the evolution of minimum cost. The proposed strategy enables an agent to maintain a smooth and consistent navigation behavior that is robust to behaviors generated by heterogeneous agents and to unexpected events such as agents with changing intentions. Simulation results demonstrate the efficacy of our approach in responding to such situations and its potential for real-world applications in crowded environments.

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Notes

  1. 1.

    A vortex is a region in a fluid in which the flow revolves around an axis line.

References

  1. Aref, H.: Point vortex dynamics: a classical mathematics playground. J. Math. Phys. 48(6), 065401 (2007)

    Article  MathSciNet  Google Scholar 

  2. Berger, M.A.: Hamiltonian dynamics generated by Vassiliev invariants. J. Phys. A: Math. Gen. 34(7), 1363 (2001)

    Article  MathSciNet  Google Scholar 

  3. Berger, M.A.: Topological invariants in braid theory. Lett. Math. Phys. 55(3), 181–192 (2001)

    Article  MathSciNet  Google Scholar 

  4. Chen, Y.F., Everett, M., Liu, M., How, J.P.: Socially aware motion planning with deep reinforcement learning. In: Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 1343–1350 (2017)

    Google Scholar 

  5. Helbing, D., Molnár, P.: Social force model for pedestrian dynamics. Phys. Rev. E 51, 4282–4286 (1995)

    Article  Google Scholar 

  6. Karamouzas, I., Skinner, B., Guy, S.J.: Universal power law governing pedestrian interactions. Phys. Rev. Lett. 113, 238701 (2014)

    Article  Google Scholar 

  7. Kim, B., Pineau, J.: Socially adaptive path planning in human environments using inverse reinforcement learning. Int. J. Soc. Robot. 8(1), 51–66 (2016)

    Article  Google Scholar 

  8. Knepper, R.A., Rus, D.: Pedestrian-inspired sampling-based multi-robot collision avoidance. In: Proceedings of the 2012 IEEE International Symposium on Robot and Human Interactive Communication, pp. 94–100 (2012)

    Google Scholar 

  9. Kretzschmar, H., Spies, M., Sprunk, C., Burgard, W.: Socially compliant mobile robot navigation via inverse reinforcement learning. Int. J. Robot. Res. 35(11), 1289–1307 (2016)

    Article  Google Scholar 

  10. Ma, W.C., Huang, D.A., Lee, N., Kitani, K.M.: Forecasting interactive dynamics of pedestrians with fictitious play. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 4636–4644 (2017)

    Google Scholar 

  11. Mavrogiannis, C., Knepper, R.A.: Decentralized navigation planning using multi-agent trajectory prediction governed by Hamiltonian dynamics. In: Workshop on Multi-robot Perception-Driven Control and Planning, IEEE/RSJ International Conference on Intelligent Robots and Systems (2018)

    Google Scholar 

  12. 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, pp. 6817–6824 (2017)

    Google Scholar 

  13. Mavrogiannis, C.I., Knepper, R.A.: Decentralized multi-agent navigation planning with braids. In: Proceedings of the International Workshop on the Algorithmic Foundations of Robotics (2016)

    Google Scholar 

  14. Mavrogiannis, C.I., Knepper, R.A.: Multi-agent path topology in support of socially competent navigation planning. Int. J. Robot. Res. 38, 338–356 (2018)

    Article  Google Scholar 

  15. Mavrogiannis, C.I., Thomason, W.B., Knepper, R.A.: Social momentum: a framework for legible navigation in dynamic multi-agent environments. In: Proceedings of the ACM/IEEE International Conference on Human-Robot Interaction, pp. 361–369 (2018)

    Google Scholar 

  16. Moussaïd, M., Helbing, D., Theraulaz, G.: How simple rules determine pedestrian behavior and crowd disasters. Proc. Nat. Acad. Sci. 108(17), 6884–6888 (2011)

    Article  Google Scholar 

  17. Rösmann, C., Hoffmann, F., Bertram, T.: Integrated online trajectory planning and optimization in distinctive topologies. Robot. Auton. Syst. 88, 142–153 (2017)

    Article  Google Scholar 

  18. Sisbot, E.A., Marin-Urias, L.F., Alami, R., Siméon, T.: A human aware mobile robot motion planner. IEEE Trans. Robot. 23(5), 874–883 (2007)

    Article  Google Scholar 

  19. Trautman, P., Ma, J., Murray, R.M., Krause, A.: Robot navigation in dense human crowds: statistical models and experimental studies of human-robot cooperation. Int. J. Robot. Res. 34(3), 335–356 (2015)

    Article  Google Scholar 

  20. van den Berg, J., Guy, S.J., Lin, M.C., Manocha, D.: Reciprocal n-body collision avoidance. In: Proceedings of the International Symposium on Robotics Research, pp. 3–19 (2009)

    Google Scholar 

  21. Zucker, M., Ratliff, N., Dragan, A., Pivtoraiko, M., Klingensmith, M., Dellin, C., Bagnell, J.A.D., Srinivasa, S.: CHOMP: covariant Hamiltonian optimization for motion planning. Int. J. Robot. Res. 32(9–10), 1164–1193 (2013)

    Article  Google Scholar 

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Acknowledgment

This material is based upon work supported by the National Science Foundation under Grants IIS-1526035 and IIS-1563705. We are grateful for this support.

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Correspondence to Christoforos I. Mavrogiannis .

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Mavrogiannis, C.I., Knepper, R.A. (2020). Multi-agent Trajectory Prediction and Generation with Topological Invariants Enforced by Hamiltonian Dynamics. In: Morales, M., Tapia, L., Sánchez-Ante, G., Hutchinson, S. (eds) Algorithmic Foundations of Robotics XIII. WAFR 2018. Springer Proceedings in Advanced Robotics, vol 14. Springer, Cham. https://doi.org/10.1007/978-3-030-44051-0_43

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