coordinated control of multi-agent systems lessons from … · 3 n.e. leonard – ifac world...
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Coordinated Control of Multi-agent Systems
Lessons from Collective Animal Behavior
Naomi Ehrich Leonard Mechanical & Aerospace Engineering
Princeton University [email protected]
www.princeton.edu/~naomi
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Multi-Agent Systems
Photo credit: Fish & Wildlife Service
Photo credit: NOAA
Photo credit: D. Rubenstein
NASA
WHOI
Parrish, Hamner, Animal Groups in Three Dimensions, 1997 Krause, Ruxton, Living in Groups, 2002 Sumpter, Collective Animal Behavior, 2010
Antsaklis, Baillieul, Networked Control Systems, IEEE TAC, 2004 Bullo, Cortes, Martinez, Distributed Control of Robotic Networks, 2009 Mesbahi, Egerstedt, Graph Theoretic Methods in Multiagent Networks, 2010
Midlands Power Network
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Animal Group Dynamics: Robust and Adaptive
1. Grunbaum, Schooling as a strategy for taxis in a noisy environment, Evol. Ecology, 1998 2. Couzin, et al., Collective memory and spatial sorting in animal groups, J.Theor. Biol., 2002
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Field Demonstrations of Bio-Inspired Control Algorithms Monterey Bay, CA, August 2003
Bachmayer, Leonard, IEEE Conf. Decision & Cont., 2002 Ogren, Fiorelli, Leonard, IEEE Trans Aut Control, 2004 Fiorelli et al., IEEE J. Oceanic Engineering, 2006
Monterey Bay, CA, August 2006
Sepulchre et al, IEEE Trans. Aut. Control, 2007, 2008 Leonard et al, Proc. IEEE, 2007 Leonard et al, J. Field Robotics, 2010
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Collective Decision-Making
How to enable a network of distributed agents to decide as a group?
Which alternative is true? Which action to take?
Which direction to follow? Has a change been detected?
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Role of the Interaction Network Structure in Collective Decision-Making Dynamics
1. Speed of convergence and algebraic connectivity 2. Accuracy and effective resistance 3. Speed-accuracy tradeoff and information centrality 4. Optimal selection of leaders and joint centrality 5. Controllability and graph symmetry
Jadbabaie, Lin, Morse, 2003 Olfati- Saber and Murray, 2004 Moreau, 2005
Barooah and Hespanha, 2006, 2008 Ghosh, Boyd, Saberi, 2008 Young, Scardovi, Leonard, 2010, 2013
Srivastava and Leonard, 2014
Patterson and Bamieh, 2010 Clark and Poovendran, 2011 Fardad, Lin, and Jovanovic, 2011 Fitch and Leonard, 2013
Rahmani, Ji, Mesbahi, and Egerstedt, 2009 Liu, Slotine, and Barabasi, 2011 Olshevsky, 2014 Summers, Cortesi, and Lygeros, 2014 Pasqualetti, Zampieri, and Bullo, 2014
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Animal Groups Rely on Consensus Decision-Making
www.pestipm.org
Beneficial to attack? Nathan Stone
Which way to go? Good time to migrate? Alaska-in-Pictures.com
Stroeymeyt, Guerrieri, van Zweden, d’Ettorre, PLoS One, 2010
Couzin, Krause, Franks, Levin, Nature, 2005 Eikenaar, Klinner, Szostek, Bairlein, Biol. Lett. 2014
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Towards a Realization Theory of Collective Decision Making
Animals groups adapt decision making to environment
Case study: House hunting honey bees Singularities organize group behaviors
Singularity theory: Robust bifurcation theory Proposed model provides realization Equivalence: connects collective decision making in nature and design
Wild About Britain
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House Hunting Honey Bees
“One of the most spectacular examples of an animal group functioning as an adaptive unit is a swarm of honey bees choosing its future home.” Seeley and Buhrman, 1999
T. Seeley
Karl von Frisch, Bees: their vision, chemical senses, and language, Cornell University Press, 1956. Martin Landauer, Communication among social bees, Harvard University Press, 1961 Thomas Seeley and Susannah Buhrman, Group decision making in swarms of honey bees, Behav Ecol Sociobiol, 1999 Mary Myerscough, Dancing for a decision: a matrix model for nest-site choice by honeybees, Proc. Roy. Soc. B, 2003
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Communication: the “Waggle Dance”
K. von Frisch, Nobel Lecture, Dec. 12, 1973 Seeley, Visscher, Passino, Am. Scientist, 2006 Scott Camazine
Scout communicates: direction, distance, and quality of visited site
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Decision-Making: Deliberations at the Swarm
Scout, commit, recruit Scout, commit, recruit, lose interest Signal decision when quorum reached
Seeley et al., Am. Scientist, 2006
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Cross-Inhibition: Stop Signal
Seeley, Visscher, Schlegel, Hogan, Franks, Marshall, Stop signals provide cross inhibition in collective decision-making by honeybee swarms, Science, 2012.
Cross inhibitory stop signal aids deadlock breaking among near-equal quality sites
Scouts apply a vibrational “stop signal” with a head butt to scouts dancing for alternative sites.
James Nieh
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Dynamic Model Seeley et al, Science, 2012.
Decay Commitment Recruitment Stop signal inhibition
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Equal Alternatives
D. Pais, P.M. Hogan, T. Schlegel, N.R. Franks, N.E. Leonard, J.A.R. Marshall, A mechanism for value-sensitive decision-making, PLoS One, 2013.
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Equal Alternatives
Pitchfork singularity at 70% quorum threshold
Pais et al, PLoS One, 2013.
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Sensitivity to Value
Pitchfork bifurcation
Pais et al, PLoS One, 2013.
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Stop Signal as an Adaptive Control Gain
Pais et al, PLoS One, 2013.
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Near-equal Alternatives
Asymmetric model lives in the universal unfolding of pitchfork singularity
Pais et al, PLoS One, 2013.
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Hysteresis in Value Difference
Pais et al, PLoS One, 2013.
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Singularities in Bifurcation Theory Golubitsky and Schaeffer, Springer, 1985
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Pitchfork Singularity and Its Unfolding
Golubitsky and Schaeffer, Springer, 1985
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Honey Bee Model: Organized by Pitchfork
Solutions satisfy:
Recognition of pitchfork singularity:
A. Franci, V. Srivastava, N.E. Leonard, In prep.
Unfolding:
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Honey Bee Model: Organized by Pitchfork
Local analysis: Pitchfork singularity
Global analysis: Monotone systems with bounded trajectories
A. Franci, V. Srivastava, N.E. Leonard, In prep.
(M.W. Hirsch, 1988, H.L. Smith, 1995, D. Angeli and E.D. Sontag, 2004)
(Golubitsky and Schaeffer, 1985)
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for all pitchfork singularities
Couzin, Ioannou, Demirel, Gross, Torney, Hartnett, Conradt, Levin, Leonard, Uninformed individuals promote democratic consensus in animal groups, Science, 2011
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for all pitchfork singularities
Abstract collective decision-making model organized by pitchfork
Motivating work: A. Franci and R. Sepulchre, Realization of nonlinear behaviors from organizing centers, IEEE CDC, 2014
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Abstract Model
Agent state:
Fully committed to alternative A Uncommitted Fully committed to alternative B
A. Franci, V. Srivastava, N.E. Leonard, In prep.
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Abstract Model
A. Franci, V. Srivastava, N.E. Leonard, In prep.
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Analysis of Abstract Model
(by Lyapunov-Schmidt)
Pitchfork singularity:
by recognition on
A. Franci, V. Srivastava, N.E. Leonard, In prep.
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Refinement of Abstract Model
A. Franci, V. Srivastava, N.E. Leonard, In prep.
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Summary and Further Generalization
Realization of collective decision making organized by pitchfork rigorously connects performance analysis of animal groups with multi-agent control design Singularity theory provides a systematic approach organized by singularity Generalize realization to other singularities: Example: Decision-making among n > 2 alternatives
D. Pais, C. Caicedo, N.E. Leonard, Hopf bifurcations and limit cycles in evolutionary network dynamics, SIAM J. Dynamical Systems, 2012
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Further Connections
Young, Scardovi, Cavagna, Giardina, Leonard, PLoS Comp. Bio, 2013
Robustness of starling flocks
Flock Logic: emergent leadership
Leonard et al, In Controls and Art, Springer, 2014
Pursuit and evasion of herds
Photo: zebras by Will Scott, Mpala, Kenya, July 2014 Scott and Leonard, IEEE CDC, 2014
Human coordinated decision making
R. Groten, D. Feth
Shen, Schwemmer, Groten, Feth, Ludvig, Leonard, In prep.
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Thank you!
Colleagues: Iain Couzin, Simon Levin
Support: U.S. Office of Naval Research, Army Research Office, National Science Foundation
Tian Shen, Paul Reverdy, Vaibhav Srivastava, Brendan Andrade, George Young, Katie Fitch, Will Scott
Lily, Tim, and Amara Leonard
Darren Pais
Patrick Hogan
James Marshall
Vaibhav Srivastava
Alessio Franci