Abstract
We present a novel planning framework for navigation in dynamic, multi-agent environments with no explicit communication among agents, such as pedestrian scenes. Inspired by the collaborative nature of human navigation, our approach treats the problem as a coordination game, in which players coordinate to avoid each other as they move towards their destinations.We explicitly encode the concept of coordination into the agents’ decision making process through a novel inference mechanism about future joint strategies of avoidance. We represent joint strategies as equivalence classes of topological trajectory patterns using the formalism of braids. This topological representation naturally generalizes to any number of agents and provides the advantage of adaptability to different environments, in contrast to the majority of existing approaches. At every round, the agents simultaneously decide on their next action that contributes collisionfree progress towards their destination but also towards a global joint strategy that appears to be in compliance with all agents’ preferences, as inferred from their past behaviors. This policy leads to a smooth and rapid uncertainty decrease regarding the emerging joint strategy that is promising for real world scenarios. Simulation results highlight the importance of reasoning about joint strategies and demonstrate the efficacy of our approach.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
E. Artin. Theory of braids. \(\underline{{\rm Annals \ of \ Mathematics}}\), 48(1):pp. 101–126, 1947.
M. Bennewitz, W. Burgard, G. Cielniak, and S. Thrun. Learning motion patterns of people for compliant robot motion. \(\underline{{\rm Int. \ J. \ of \ Robotics \ Res.}}\), 24:31–48, 2005.
J. S. Birman. \(\underline{{\rm Braids \ Links \ And \ Mapping \ Class \ Groups}}\). Princeton University Press, 1975.
S. Bonneaud and W. H. Warren. An empirically-grounded emergent approach to modeling pedestrian behavior. In \(\underline{{\rm Pedestrian \ and \ Evacuation \ Dynamics \ 2012}}\), pages 625–638. Springer International Publishing, 2014.
G. Csibra and G. Gergely. The teleological origins of mentalistic action explanations: A developmental hypothesis. \(\underline{{\rm Developmental \ Science}}\), 1(2):255–259, 1998.
G. Csibra and G. Gergely. ‘Obsessed with goals’: Functions and mechanisms of teleological interpretation of actions in humans. \(\underline{{\rm Acta \ Psychologica}}\), 124(1):60–78, Jan. 2007.
Y. Diaz-Mercado and M. Egerstedt. Interactions in multi-robot systems using braids. \(\underline{{\rm Robotics, \ IEEE \ Transactions \ on}}\), 2016. Under Review.
A. D. Dragan and S. Srinivasa. Integrating human observer inferences into robot motion planning. \(\underline{{\rm Auton. \ Robots}}\), 37(4):351–368, 2014.
D. Helbing and P. Molnár. Social force model for pedestrian dynamics. \(\underline{{\rm Phys. \ Rev. \ E}}\), 51: 4282–4286, May 1995.
P. Henry, C. Vollmer, B. Ferris, and D. Fox. Learning to navigate through crowded environments. In \(\underline{{\rm IEEE \ International \ Conference \ on \ Robotics \ and \ Automation \ (ICRA)}}\), 2010.
S. Hoogendoorn and P. H. Bovy. Simulation of pedestrian flows by optimal control and differential games. \(\underline{{\rm Optimal \ Control \ Applications \ and \ Methods}}\), 24(3):153–172, 2003.
I. Karamouzas, B. Skinner, and S. J. Guy. Universal power law governing pedestrian interactions. \(\underline{{\rm Phys. \ Rev. \ Lett.}}\), 113:238701, 2014.
R. A. Knepper and D. Rus. Pedestrian-inspired sampling-based multi-robot collision avoidance. In \(\underline{{\rm RO\text{-}MAN}}\), pages 94–100. IEEE, 2012.
M. Kuderer, H. Kretzschmar, C. Sprunk, and W. Burgard. Feature-based prediction of trajectories for socially compliant navigation. In \(\underline{{\rm Proc. \ of \ Robotics: \ Science \ and \ Systems \ (RSS)}}\), Sydney, Australia, 2012.
C. I. Mavrogiannis and R. A. Knepper. Towards socially competent navigation of pedestrian environments. In \(\underline{{\rm Robotics: \ Science \ and \ Systems \ 2016 \ Workshop \ on \ Social \ Trust \ in \ Autonomous \ Robots}}\), 2016.
C. I. Mavrogiannis and R. A. Knepper. Interpretation and communication of pedestrian intentions using braid groups. In \(\underline{{\rm Workshop \ on \ Intention \ Recognition \ in \ Human\text{- }Robot \ Interaction, \ 11th \ ACM/IEEE \ International \ Conference \ on \ Human \ Robot \ Interaction HRI)}}\), 2016.
M. Moussaïd, D. Helbing, and G. Theraulaz. How simple rules determine pedestrian behavior and crowd disasters. \(\underline{{\rm Proceedings \ of \ the \ National \ Academy \ of \ Sciences}}\), 108(17): 6884–6888, Apr. 2011.
J. J. Park, C. Johnson, and B. Kuipers. Robot navigation with model predictive equilibrium point control. In \(\underline{{\rm Intelligent \ Robots \ and \ Systems \ (IROS), \ 2012 \ IEEE/RSJ \ International \ Conference \ on}}\), pages 4945–4952. IEEE, 2012.
S. Pellegrini, A. Ess, K. Schindler, and L. J. V. Gool. You’ll never walk alone: Modeling social behavior for multi-target tracking. In \(\underline{{\rm ICCV}}\), pages 261–268. IEEE Computer Society, 2009.
E. A. Sisbot, L. F. Marin-Urias, R. Alami, and T. Siméon. A human aware mobile robot motion planner. \(\underline{{\rm IEEE \ Transactions \ on \ Robotics}}\), 23(5):874–883, 2007.
J.-L. Thiffeault. Braids of entangled particle trajectories. \(\underline{{\rm Chaos}}\), 20(1), 2010.
J.-L. Thiffeault and M. Budišić. Braidlab: A software package for braids and loops, 2013–2016. URL http://arXiv.org/abs/1410.0849. Version 3.2.1.
P. Trautman, J. Ma, R. M. Murray, and A. Krause. Robot navigation in dense human crowds: Statistical models and experimental studies of human-robot cooperation. \(\underline{{\rm Int. \ J. \ of \ Robotics \ Res.}}\), 34(3):335–356, 2015.
A. Treuille, S. Cooper, and Z. Popović. Continuum crowds. \(\underline{{\rm ACM \ Transactions \ on \ Graphics}}\), 25(3):1160–1168, July 2006.
J. van den Berg, S. J. Guy, M. C. Lin, and D. Manocha. Reciprocal \(\underline{{\rm n}}\)-body collision avoidance. In \(\underline{{\rm Robotics \ Research \ \text{- } \ The \ 14th \ International \ Symposium, \ ISRR \ 2009, \ August \ 31 \ \text{- } \ September \ 3, \ 2009, \ Lucerne, \ Switzerland}}\), pages 3–19, 2009.
N. H. Wolfinger. Passing Moments: Some Social Dynamics of Pedestrian Interaction. \(\underline{{\rm Journal \ of \ Contemporary \ Ethnography}}\), 24(3):323–340, 1995.
J. Yen. Finding the k shortest loopless paths in a network. \(\underline{{\rm management \ Science}}\), pages 712–716, 1971.
B. Zhou, X. Tang, and X. Wang. Learning collective crowd behaviors with dynamic pedestrian-agents. \(\underline{{\rm International \ Journal \ of \ Computer \ Vision}}\), 111(1):50–68, 2015.
B. D. Ziebart, N. Ratliff, G. Gallagher, C. Mertz, K. Peterson, J. A. Bagnell, M. Hebert, A. K. Dey, and S. Srinivasa. Planning-based prediction for pedestrians. In \(\underline{{\rm Proc. \ of \ the \ International \ Conference \ on \ Intelligent \ Robots \ and \ Systems}}\), 2009.
G. M. Ziegler. \(\underline{{\rm Lectures \ on \ polytopes}}\). Springer-Verlag, New York, 1995.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Mavrogiannis, C.I., Knepper, R.A. (2020). Decentralized Multi-Agent Navigation Planning with Braids. In: Goldberg, K., Abbeel, P., Bekris, K., Miller, L. (eds) Algorithmic Foundations of Robotics XII. Springer Proceedings in Advanced Robotics, vol 13. Springer, Cham. https://doi.org/10.1007/978-3-030-43089-4_56
Download citation
DOI: https://doi.org/10.1007/978-3-030-43089-4_56
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-43088-7
Online ISBN: 978-3-030-43089-4
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)