IEEE CDC 2014 Workshop - Geometry of Collective Behavior: Control, Dynamics and Reconstruction

Workshop Description

The goal of this full-day workshop is to provide a self-contained and structured perspective of advances in the study of collective dynamic behavior in nature (bird flocks, fish schools) and technology (such as autonomous air-land-sea vehicles). To this end, the workshop will introduce the participant to a class of models and interaction strategies, associated control laws, and principles and algorithms for the discovery and synthesis of control laws that achieve collective behavior with a purpose. In addition to the stated examples, the study of collective behavior has a distinguished role in the foundations of physical science, as in work on the problem of stability of the solar system (by Lagrange, Laplace and their illustrious descendants), and James Clerk Maxwell’s investigation of the character and stability of Saturn’s rings (1859). Technical linkages to this scientific heritage will be pointed out.

As a distinctive feature of this workshop, geometric ideas will occupy a central place in the conceptual framework of the presentations. Geometry enters the investigation of collective behavior from multiple vantage points: the structure of configuration space; the synthesis of control strategies; the role of symmetries and reduction in closed loop dynamics; the analysis of empirical data from biology; and the realization of control strategies in autonomous systems. In this workshop we will present an exposition of developments in these directions, including some low dimensional examples. We will also examine methods to assimilate sampled observations of collectives of continuous time dynamical systems, e.g. predator-prey encounters and bird (starlings) flocking events, into generative models with continuous time inputs and outputs. Results of such assimilation (reconstruction) will then be used to evaluate hypotheses of interest, based on correlations, delays, and possible mechanisms of interaction between elementary units of the observed population. We will discuss models via moving frames and methods from nonlinear smoothing, to solve the problem of numerically reconstructing collectives. We will also discuss optimal control methods for computational schemes, and questions of integrability of extremals.

The lectures will rely on basic tools from the theory of Lie groups and Lie algebras, and differential geometry. These tools will be presented in an accessible and just-in-time manner during course of the workshop. Software tools developed by the lecturers will be demonstrated on real datasets (from biology to underwater robotics). Laboratory implementations of control laws on robotic platforms (in a test-bed at the University of Maryland) will provide illustrations of the strengths and broad applicability of the theoretical framework of the workshop.

Target Audience

The intended audience would include graduate students and post-doctoral researchers, industry participants with a focus on distributed sensing and control in multi-agent robotics. Only pre-requisites assumed would be knowledge of differential equations, matrix algebra, basic mechanics, and interest and curiosity about the biological basis of collective behavior with applications to robotics. Senior researchers and control software designers interested in the broad area of collaborative autonomous systems and seeking to explore geometric methods may also find this workshop useful.

List of Speakers in Alphabetical Order and their Biographies

Biswadip Dey is a PhD student at the University of Maryland, College Park expecting to graduate in 2015. He holds a Bachelor’s degree from Jadavpur University in India, and a Master’s Degree from Indian Institute of Technology, Bombay. His current research focus is on collective behavior in biology, and reconstruction algorithms.

Kevin Galloway is an Assistant Professor in the Department of Electrical and Computer Engineering at the US Naval Academy in Annapolis, Maryland. He received his PhD from the University of Maryland College Park in 2011, and held a post-doctoral research fellowship at the University of Michigan, Ann Arbor, between 2011 and 2013. His current focus is on strategies for collective behavior, and bipedal locomotion.

Eric Justh (see old website) is an Electronics Engineer at the Naval Research Laboratory (NRL) in Washington, D.C. He received the PhD degree from the University of Maryland, College Park in 1998. He has held post-doctoral positions at the University of Maryland and the Army Research Laboratory prior to joining NRL. His research interests include theory and implementation of collective behavior in unmanned systems.

P. S. Krishnaprasad is a Professor in the Department of Electrical and Computer Engineering at the University of Maryland, College Park, since 1980. He also holds a joint appointment with the Institute for Systems Research. He received his PhD degree in 1977 from Harvard University. His current research interests include robotics and collective behavior, and physics of nonequilibrium states.

Matteo Mischiati is a Post-doctoral Research Associate at the Janelia Farm Research Campus of HHMI, in Ashburn, Virginia. He received his PhD from the University of Maryland, College Park, in 2011. His current research focus includes all aspects of prey capture behavior in dragonflies, and collective behavior.

Fumin Zhang is an Associate Professor at the School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta. He received his PhD from the University of Maryland, College Park in 2004, and was a Post-doctoral Research Associate at Princeton University during 2004-2007. His current research interests include the theory of collective behavior, underwater robotics and sensor systems.

Workshop Goals

The workshop is aimed at providing a unified and panoramic view of the subject of collective behavior as developed from a geometric viewpoint over a decade at the University of Maryland and other institutions. It will focus on examining problems of collective behavior from a bottom-up approach using building-blocks originating in the mathematics of pursuit-evasion, as well as from a top-down approach with roots in many-body theory in physics and chemistry. It will also bring to light some numerical methods for reconstructing empirical data from studies of biological collectives (birds primarily), and use the results to examine hypotheses about the sensorimotor feedback laws that enable collective behavior in nature. It will include discussions of applications to sensor-driven path tracking by robots (specifically underwater robots) using the models developed by the speakers. It will also provide some exposure to numerical computations and software implementations in a test-bed of robots tracked by a motion-capture system at the University of Maryland

Synopsis of Workshop Content and Major Topics

The workshop presentations will be made in the following sequence allowing 45 minutes for each lecture (interspersed with dedicated periods for discussions):

(i) Models of Individual agents – self-steering particles, moving frames, particles in Lie groups, symmetries, relative equilibria and formations; (Eric Justh)

(ii) Dyadic Building-block Interactions – pursuit, escape, other (P. S. Krishnaprasad )

(iii) Tracking – virtual particles, boundary tracking, cooperative tracking, underwater applications (Fumin Zhang)

(iv) Models of Collectives – graphs, collective strategies, few body problems (Kevin Galloway)

(v) Configuration Space Methods – shape space, energy splitting, other fiberings, geodesics in quotient (Matteo Mischiati)

(vi) Data Assimilation – optimal data fitting, cross-validation, feedback laws for natural collectives (Biswadip Dey)

Bibliography

E. W. Justh and P. S. Krishnaprasad (2002). A simple control law for UAV formation flying, Institute for Systems Research Technical Report, TR 2002-38, 35 pages.

E. W. Justh and P. S. Krishnaprasad (2003). Steering Laws and Continuum Models for Planar Formations, Proc. 42nd IEEE Conference on Decision and Control, 3609-3614, IEEE, New York.

E. W. Justh and P. S. Krishnaprasad (2004). Equilibria and Steering Laws for Planar Formations, Systems and Control Letters, 52(1), 25-38.

E. W. Justh and P. S. Krishnaprasad (2005). Natural Frames and Interacting Particles in Three Dimensions, Proc. 44th IEEE Conference on Decision and Control, 2842-2846, IEEE, New York.

K. Ghose, T. K. Horiuchi, P. S. Krishnaprasad and C. F. Moss (2006). Echolocating Bats use a Nearly Time-optimal Strategy to Intercept Prey, PLoS Biology, 4, 865-873, e. 108.

E. W. Justh and P. S. Krishnaprasad (2006). Steering Laws for Motion Camouflage, Proceedings of the Royal Society A, 462, 3629-3643.

P. V. Reddy, E. W. Justh and P. S. Krishnaprasad (2006). Motion Camouflage in Three Dimensions, Proc. 45th IEEE Conference on Decision and Control, 3327-3332, IEEE, New York.

P. V. Reddy, E. W. Justh and P. S. Krishnaprasad (2007). Motion Camouflage with Sensorimotor Delay, Proc. 46th IEEE Conference on Decision and Control, 1660-1665, IEEE, New York.

K. S. Galloway, E. W. Justh and P. S. Krishnaprasad (2007). Motion Camouflage in a Stochastic Setting, Proc. 46th IEEE Conference on Decision and Control, 1652-1659, IEEE, New York.

E. Wei, E. W. Justh and P. S. Krishnaprasad (2009). Pursuit and an Evolutionary Game, Proceedings of the Royal Society A, 465, 1539-1559.

K. Galloway, E. W. Justh and P. S. Krishnaprasad (2009). Geometry of Cyclic Pursuit, Proc. 48th IEEE Conference on Decision and Control, 7485-7490, IEEE, New York.

M. Mischiati and P. S. Krishnaprasad (2010). Motion Camouflage for Coverage, Proc. American Control Conference, 6429-6435, American Automatic Control Council, Philadelphia.

C. Chiu, P. V. Reddy, W. Xian, P. S. Krishnaprasad, and Cynthia F. Moss (2010). Effects of competitive prey capture on flight behavior and sonar beam pattern in paired big brown bats Eptesicus fuscus, The Journal of Experimental Biology, 213(19), 3348-3356.

K. S. Galloway, E. W. Justh and P. S. Krishnaprasad (2010). Cyclic Pursuit in Three Dimensions, Proc. 49th IEEE Conference on Decision and Control, 7141-7146, IEEE, New York.

E. W. Justh and P. S. Krishnaprasad (2010). Extremal Collective Behavior, Proc. 49th IEEE Conference on Decision and Control, 5432-5437, IEEE, New York.

E. W. Justh and P. S. Krishnaprasad (2011). Optimal Natural Frames, Communications in Information and Systems, 11(1), 17-34 (published online October 2010).

M. Mischiati and P. S. Krishnaprasad (2011). Mutual Motion Camouflage in 3D, Proc. 18th World Congress of the International Federation of Automatic Control, 4483-4488.

K. S. Galloway, E. W. Justh and P. S. Krishnaprasad (2011). Portraits of Cyclic Pursuit, Proc. 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC), 2724-2731, IEEE, New York.

M. Mischiati and P. S. Krishnaprasad (2012). The Dynamics of Mutual Motion Camouflage, Systems and Control Letters, 61(9), 894-903, September 2012.

F. Zhang, E. W. Justh, and P. S. Krishnaprasad (2013). Boundary tracking and obstacle avoidance using gyroscopic control, A. Johann et al. (eds.), Recent Trends in Dynamical Systems, Springer Proceedings in Mathematics & Statistics 35, 417-446, Springer Basel 2013.

B. Dey and P. S. Krishnaprasad (2012). Trajectory Smoothing as a Linear Optimal Control Problem, Proc. 50th Allerton Conference on Communication, Control and Computing 2012, 1490-1497, online at IEEExplore since 2013.

K. Galloway, E. W. Justh and P. S. Krishnaprasad (2013). Symmetry and reduction in collectives: cyclic pursuit strategies, Proceedings of the Royal Society A, 469 (2158), 20130264, (23 pages of the print journal and 12 pages of electronic supplementary material).