The cohesive movement of a biological population is a commonly observed natural phenomenon. With the advent of platforms of unmanned vehicles, this occurrence is attracting renewed interest from the engineering community. The purpose of this workshop is to foster advances in the modeling and analysis of biological swarms and to explore design ideas for efficient algorithms to control groups of autonomous agents. This interdisciplinary program draws from ideas in biology (experimental and theoretical), mathematics (including PDEs, dynamical systems, and numerical analysis), physics (statistical mechanics and non-equilibrium thermodynamics), computer science (distributed AI), and engineering (control theory).
Biological perspectives on formation and dissolution of groups are motivated by the fact that nearly all organisms are aggregated relative to environmental variables and to other members of their own species. Swarms, schools, flocks and herds successfully perform tasks that individual members cannot. Aggregated populations fulfill different objectives from those met by dispersed populations. The relationships between individual behaviors and resulting group characteristics are of ecological and evolutionary importance.
Biological studies of collective motion are developing rapidly, spurred by technological improvements in the observation of behavioral interactions among individuals within groups, by advances in behavioral theory and computer simulations, and by insights such as those gathered from studies of how kinship within a group affects group characteristics. In biomechanics, among other fields, collaboration between biologists and engineers has advanced biological understanding and inspired engineering concepts. The topic of biological aggregation, particularly active social aggregation behaviors such as swarming and schooling, is now ripe for this kind of cross-disciplinary collaboration.
In many areas of science and engineering, it is important to quantify the location of coherent structures, whether large scale — internal waves in the ocean — or microscopic, such as space-time chaos in CO platinum reactions. In two dimensional problems, the structures may be viewed by remote sensing and imaging. However, in many cases, direct measurement may be the only way to locate coherent structures. Direct measurements require multiple coordinated mobile sensors. The problem of coordination of collective sensing naturally leads to new mathematical explorations of pattern-forming systems. Sensors could be put on mobile vehicles, and in the future, micro- or nano-particles might be used for exploration and control– an idea that was once proposed by Richard Feynman. As machines get smaller, it is evident that new possibilities for direct sensing may be found in fluid control, materials science, and bio-engineering, among other fields. By forming systems which are not only coupled but interact with their environment we will encounter problems that require new mathematical tools to make reasonable predictions. Such tools will require areas as diverse as nonlinear analysis of PDE-ODE systems, stochastic nonlinear equations, communication theory, game theory and voting theory. The areas the conference will cover represent just a few of the new ideas for swarming dynamics. They will include areas such as:
Controlling unmanned autonomous vehicles
Building swarming targeting and acquisition systems
Embedding swarming sensors in advection-reaction systems
Swarming Levy distribution search processes
Search algorithms and their implementation on platforms
Pattern formation in biological swarms
Control of biological swarms, such as locusts
The attendees of this 5-day workshop will include junior and senior scientists from the varied fields mentioned above, who may not generally attend the same scientific conferences or publish in the same scientific journals. The diverse backgrounds of the attendees and a multi-format workshop structure will help forge new scientific relationships and collaborations. This program builds on a two-day program jointly held October 3 – 4, 2003, between IPAM and the Department of Mathematics at UCLA. The format will include both long format talks as well as a special time set aside for a poster session featuring work done by students and new post-docs working in this area. Social events will help to engage the participants in informal discussions.
Andrea Bertozzi
(UCLA)
Daniel Grunbaum
(University of Washington)
P. S. Krishnaprasad
(University of Maryland)
Ira Schwartz
(Naval Research Laboratory)
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