1. KOVAN Research Lab ECAL ‘09, Hande Çelikkanat, 16.09.2009 A Critical Review of Flocking Models Erol Şahin and Hande Çelikkanat KOVAN Research Lab Department of Computer Engineering Middle East Technical University Ankara, Turkey ECAL '09, Budapest, Hungary September 2009

2. KOVAN Research Lab ECAL ‘09, Hande Çelikkanat, 16.09.2009 2/17 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

3. KOVAN Research Lab ECAL ‘09, Hande Çelikkanat, 16.09.2009 3/17 Reynold's Flocking Algorithm (1987) Assumption: sense of heading, bearing and range of neighbors SeparationAlignmentCohesion 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

4. KOVAN Research Lab ECAL ‘09, Hande Çelikkanat, 16.09.2009 4/17 Statistical Physics: Trying to understand the evident order Statistical physics tools to study the emergence of collective behavior AgentsSensingNoiseNeighborhoodEnvironment Mobile / stationary particles No inertia Range, bearing and heading of neighbors Agent-based sensing Sensing/actuationLocalPeriodic boundaries / Open space Model

5. KOVAN Research Lab ECAL ‘09, Hande Çelikkanat, 16.09.2009 5/17 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

6. KOVAN Research Lab ECAL ‘09, Hande Çelikkanat, 16.09.2009 6/17 Self-Driven Particles Model (Vicsek et al., 1995) AgentsSensingNoiseNeighborhoodEnvironment Mobile, massless particles Constant speed No inertia Headings of neighbors Actuation noiseLocal (in range) Periodic boundaries Collisions allowed Model Heading set to the average of neighbors Instantaneous, synchronous update of headings Update Rule increasing noiseincreasing density local groupsrandom motionaligned 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

7. KOVAN Research Lab ECAL ‘09, Hande Çelikkanat, 16.09.2009 7/17 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, 2006 The particles are not stationary, but mobile within the flock The 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, 1998 A. Czirok and T. Vicsek, “ Collective behavior of interacting self-propelled particles,” Physica A, vol. 373, pp. 445–454, 2007

8. KOVAN Research Lab ECAL ‘09, Hande Çelikkanat, 16.09.2009 8/17 Vectorial Network Model (Aldana and Huepe, 2003) AgentsSensingNoiseNeighborhoodEnvironment Stationary particles No inertia Headings of neighbors Actuation noiseEither 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

9. KOVAN Research Lab ECAL ‘09, Hande Çelikkanat, 16.09.2009 9/17 Gregoire et al., 2003 AgentsSensingNoiseNeighborhoodEnvironment 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 motion Behavior 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.

10. KOVAN Research Lab ECAL ‘09, Hande Çelikkanat, 16.09.2009 10/17 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

11. KOVAN Research Lab ECAL ‘09, Hande Çelikkanat, 16.09.2009 11/17 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 AgentsSensingNoise Mobile particles No inertia Perfect Agent-based Heading / range / bearing sensing of neighbors No noise Model Differs from physicists’ view

12. KOVAN Research Lab ECAL ‘09, Hande Çelikkanat, 16.09.2009 12/17 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 [t i, t i+1 ), st. across each interval, the n agents are connected to each other Relaxed condition the neighboring graphs are not connected to each other, but their union is connected +=

13. KOVAN Research Lab ECAL ‘09, Hande Çelikkanat, 16.09.2009 13/17 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 AgentsSensingNoiseNeighborhoodEnvironment 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 IEEE Conference on Decision and Control, vol. 2. pp. 2010–2015, 2003

14. KOVAN Research Lab ECAL ‘09, Hande Çelikkanat, 16.09.2009 14/17 Olfati-Saber, 2006 AgentsSensingNoiseNeighborhoodEnvironment Mobile mass-particles No inertia ALG 1Range, bearing and heading of neighbors No noise LocalOpen space ALG 2Range, bearing and heading of neighbors Common goal position ALG 3Range, 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

15. KOVAN Research Lab ECAL ‘09, Hande Çelikkanat, 16.09.2009 15/17 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)

16. KOVAN Research Lab ECAL ‘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

17. KOVAN Research Lab ECAL ‘09, Hande Çelikkanat, 16.09.2009 17/17 Thank you ?