kovan research lab ecal ‘09, hande Çelikkanat, 16.09.2009 a critical review of flocking models...
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KOVAN Research LabECAL ‘09, Hande Çelikkanat, 16.09.2009
A Critical Review of Flocking Models
Erol Şahin and Hande Çelikkanat
KOVAN Research LabDepartment of Computer Engineering
Middle East Technical UniversityAnkara, Turkey
ECAL '09, Budapest, HungarySeptember 2009
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KOVAN Research LabECAL ‘09, Hande Çelikkanat, 16.09.2009
Flocking in Nature
• Rapid, directed movement
• No dedicated leader• No collisions• Robust and scalable• Protection against
predators• Energy efficiency• Migration over long
distances
Flocking is one of the miracles of nature in which a group of animals such as birds and fishes move and maneuver as if they were a
single creature
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KOVAN Research LabECAL ‘09, Hande Çelikkanat, 16.09.2009
Reynold's Flocking Algorithm (1987)
Assumption: sense of heading, bearing and range of neighbors
SeparationAlignment Cohesion
Individuals avoid
collisions
with their neighbors
Individuals match their heading to the average heading of their neighbors
Individuals move to the geometric center of
their neighbors
• Realistic-looking simulations of flock of birds
• Depends only on local interactions
synthesis of flocking for the first time
C. Reynolds, “Flocks, herds and schools: A distributed behavioral model,” in SIGGRAPH ’87: Proc. of the 14th annual conference on computer graphics and interactive techniques, pp. 25–34, ACM Press, July 1987
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KOVAN Research LabECAL ‘09, Hande Çelikkanat, 16.09.2009
Statistical Physics: Trying to understand the evident order
• Statistical physics tools to study the emergence of collective behavior
Agents Sensing Noise Neighborhood Environment
Mobile / stationary particles
No inertia
Range, bearing and heading of neighbors
Agent-based sensing
Sensing/actuation Local Periodic boundaries / Open space
Model
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KOVAN Research LabECAL ‘09, Hande Çelikkanat, 16.09.2009
The Mermin-Wagner Theorem: The limits of theory
A theory of equilibrium ferromagnets
Ordered phase (= global alignment of headings)
cannot emerge
in 1- or 2-D systems with no external field (= goal)
having only local interactions
at non-zero temperatures (=non-zero noise)
Short-range interactions cannot produce
long-range order
N. D. Mermin and H. Wagner, “ Absence of ferromagnetism or antiferromagnetism in one- or two-dimensional isotropic Heisenberg models ,” Physical Review Letters, vol. 17, no. 22, pp. 1133–1136, 1966
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KOVAN Research LabECAL ‘09, Hande Çelikkanat, 16.09.2009
Self-Driven Particles Model (Vicsek et al., 1995)
Agents Sensing Noise Neighborhood Environment
Mobile, massless particles
Constant speed
No inertia
Headings of neighbors
Actuation noise Local (in range) Periodic boundaries
Collisions allowed
Model
Heading set to the average of neighbors
Instantaneous, synchronous update of headings
Update Rule
increasing noise increasing density
local groupsrandom motion aligned motion
Phase transition from unaligned to aligned motion(disordered to ordered state)
T. Vicsek, A. Czirok, E. Ben-Jacob, I. Cohen, and O. Shochet, “Novel type of phase transition in a system of self-driven particles,” Physical Review Letters, vol. 75, no. 6, 1995
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KOVAN Research LabECAL ‘09, Hande Çelikkanat, 16.09.2009
A contradiction?
Toner and Tu, 1998• Flocks are non-equilibrium dynamical systems• Hence not constrained by Mermin-Wagner theorem• Flocking is spontaneous symmetry breaking towards an arbitrary direction• d < 4: Fluctuations in local velocity of the flock so large, that motion in one part of the flock relative to the rest beats diffusion, and it becomes the principle means of information transfer
Czirok and Vicsek, 2006The particles are not stationary, but mobile within the flockThe local neighbors of a particle change in time
→ long-range interactions→ long-range order
J. Toner and Y. Tu, “Flocks, herds, and schools: A quantitative theory of flocking,” Physical Review E, vol. 58, no. 4, pp. 4828–4858, 1998A. Czirok and T. Vicsek, “Collective behavior of interacting self-propelled particles,” Physica A, vol. 373, pp. 445–454, 2007
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KOVAN Research LabECAL ‘09, Hande Çelikkanat, 16.09.2009
Vectorial Network Model (Aldana and Huepe, 2003)
Agents Sensing Noise Neighborhood Environment
Stationary particles
No inertia
Headings of neighbors
Actuation noise Either local or
random (long-range)
Static
Model
Heading set to the average of neighbors
Instantaneous, synchronous update of headings
Update Rule
Phase transition from unaligned to aligned motion... if :
1. there exists random connections (even few)
2. noise below critical level
If totally local, Mermin-Wagner Theorem applies
M. Aldana and C. Huepe, “Phase transitions in self-driven many-particle systems and related non-equilibrium models: A network approach,” Journal of Statistical Physics, vol. 112, no. 1-2, pp. 135–153, 2003
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KOVAN Research LabECAL ‘09, Hande Çelikkanat, 16.09.2009
Gregoire et al., 2003
Agents Sensing Noise Neighborhood Environment
Mobile, massless particles
No inertia
Headings and ranges of neighbors
Actuation noise
Local (Voronoi neighbors) Open space
Model
Heading averaging (α) + attraction / repulsion (β)
Instantaneous, synchronous update of headings
Update Rule
Results in coherent motionBehavior defined by α vs. β
β
α
moving droplet
immobile solid
fluid droplet
flying crystal
G. Gregoire, H. Chate, and Y. Tu, “Moving and staying together without a leader,” Physica D, vol. 181, pp. 157–170, 2003.
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KOVAN Research LabECAL ‘09, Hande Çelikkanat, 16.09.2009
Huepe et al., 2008
• Compared original SDP model (Vicsek et al., 1995) extended SDP model with attraction/repulsion
(Gregoire et al., 2003)
Unrealistically high local density values in original SDP
[No repulsive term]
Not suitable for modeling natural or robotic swarms with typically low densities (Ballerini et al., 2008)
C. Huepe and M. Aldana, “New tools for characterizing swarming systems: A comparison of minimal models,” Physica A, vol. 387, pp. 2809–2822, 2008
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KOVAN Research LabECAL ‘09, Hande Çelikkanat, 16.09.2009
Control Theory:Stability through perfect sensing
• Devise flocking algorithms with a set of control laws
• Analytically prove stability
• “Flocking” may refer to:• motion with leader
• movement towards a goal
• formation control with perfect position information
Agents Sensing Noise
Mobile particles
No inertia
Perfect
Agent-based
Heading / range / bearing sensing of neighbors
No noise
Model
Differs from physicists’ view
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KOVAN Research LabECAL ‘09, Hande Çelikkanat, 16.09.2009
A. Jadbabaie, J. Lin, and A. Morse, “Coordination of groups of mobile autonomous agents using nearest neighbor rules,” IEEE Transactions on Automatic Control, vol. 48, no. 6, pp. 988–1001, 2003.
• A theoretical explanation for emergent alignment in SDP model
• Investigated its stability by considering the changing nearest neighbor sets (neighboring graphs)
• Neglected noise
Jadbabaie et al., 2003
Stable when there exists an infinite sequence of contiguous, non-empty,
bounded time-intervals [ti, ti+1), st. across each interval, the n agents are connected to each other
Relaxed conditionthe neighboring graphs are not connected to each other, but
their union is connected
+ =
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KOVAN Research LabECAL ‘09, Hande Çelikkanat, 16.09.2009
Tanner et al., 2003• Stable control law for flocking in free space
• In fixed/dynamic topology cases
• Stability (heading convergence and collision avoidance) proved by Graph Theory and Lyapunov's theorem
Agents Sensing Noise Neighborhood Environment
Mobile mass-particles
No inertia
Range, bearing and velocity of neighbors
No noise 1. Fixed
2. Varying with time
Open space
Model
Control Law
heading alignmentattraction/repulsion
H. G. Tanner, A. Jadbabaie, and G. J. Pappas, “Stable flocking of mobile agents part i: fixed topology,” in Proceedings of the 42nd IEEEConference on Decision and Control, vol. 2. pp. 2010–2015, 2003
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KOVAN Research LabECAL ‘09, Hande Çelikkanat, 16.09.2009
Olfati-Saber, 2006
Agents Sensing Noise Neighborhood Environment
Mobile mass-particles
No inertia
ALG 1 Range, bearing and heading of neighbors
No noise Local Open space
ALG 2 Range, bearing and heading of neighbors
Common goal position
ALG 3 Range, bearing and heading of neighbors
Virtual agents on obstacle peripheries
Model
ALG1 equivalent to Reynolds’ algorithm
Leads to fragmentation for large groups (>10)
ALG 2 and ALG 3 generate stable flocking
(at the cost of more unrealistic sensing assumptions)
R. Olfati-Saber, “Flocking for multi-agent dynamic systems: Algorithms and theory,” IEEE Transactions on Automatic Control, vol. 51, no. 3, pp. 401–420, 2006
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KOVAN Research LabECAL ‘09, Hande Çelikkanat, 16.09.2009
What about robots?
Imperfect sensing and actuation
(very high noise)
Asynchronous decision making of agents
Inertial effects
(heading updates not instantaneous)
Not agent-based, but raw sensory readings (Typical of IR and sonar sensors)
Not continuous, but highly discrete sensing
(Typical of IR and sonar sensors)
Systematic and stochastic delays in sensing
Effects of physical volume
(Quasi-static particles which cannot move within the flock easily)
KOVAN Research LabECAL ‘09, Hande Çelikkanat, 16.09.2009
• A good option to unify the theories in a physical environment• We have implemented self-organized flocking on the Kobot robot
platform• and studied
– Leaderless and goal-free flocking– An unacknowledged, informed minority of the group steering the flock– Migration over long distances
H. Celikkanat, A. E. Turgut, and E. Sahin, Guiding a robot flock via informed robots, DARS 2008
H. Celikkanat, Control of a mobile robot swarm via informed robots, M.Sc. Thesis, Middle East Technical University, Ankara, Turkey, 2008
F. Gokce and E. Sahin,To flock or not to flock: The pros and cons of flocking in long-range “migration” of mobile robot swarms, AAMAS 2008
A. E. Turgut, C. Huepe, H. Celikkanat, F. Gokce, and E. Sahin,Modeling phase transition in self-organized mobile robot flocks, ANTS 2008
A. E. Turgut, H. Celikkanat, F. Gokce, and E. Sahin,Self-organized flocking in mobile robot swarms, Swarm Intelligence, vol. 2, no. 2-4, 2008
A. E. Turgut, H. Celikkanat, F. Gokce, and E. Sahin, Self-organized flocking with a mobile robot swarm, AAMAS 2008
Robots in the big picture