Overview of Current Research

• Research Topics: My group's two main areas of research are (i) the use of analytical approaches to the study of biological systems, and (ii) bio-inspired methods for engineering solutions. The work in biology can be characterized as being in the area of "systems biology of decision making" with a general theme of mathematical modeling and analysis of robust emergent cooperation, game-theoretic approaches to the study of robust adaptive behavior, and more generally can be thought of as part of the area of "bioengineering" (as defined by NIH, "an integration of the physical, chemical, or mathematical sciences and engineering principles for the study of biology, medicine, behavior, or health"). Much of the work focuses on the impact of local agent sensing/decision making, dynamical agent interactions/communications, and resulting group-level dynamics and behavior (and hence falls under the area of "biocomplexity" and "complex systems" across multiple spatio-temporal scales). The work in engineering lies in the general areas of intelligent and multiagent systems and draws heavily from game theory (conventional and evolutionary), optimization theory, and stability analysis of complex systems. Since in many cases the focus is on distributed and networked systems, the theory of parallel and distributed computing is used. Specific focus areas include:

1. Swarms and coordinated motion of multiagent systems: The main focus is on mathematical modeling and stability analysis of how individual sensing and movement decisions create emergent group motion in three (or higher) dimensional space (e.g., group cohesion/dispersal properties characterized as an invariant set). Study the impact of agent dynamics, external objectives (e.g., simultaneous foraging or task completion activities), continuous and discrete-time formulations (ODEs, difference equations, and asynchronous distributed discrete event system models), sensing noise, and information flow constraints (e.g., delays in sensing and sensing network topology constraints). Applications studied include swarms of honey bees, Apis mellifera (including experimental work with T. Seeley, a biologist at Cornell Univ.), groups of air/ground vehicles, bacterial chemotaxis, and recently started work on coordinated motion by ants such as in the tandem running dyanamics for the ant Temnothorax albipennis (via collaboration with Nigel Franks and Tom Richardson, biologists at the Univ. of Bristol, England). Interested in relations to distributed spatial/temporal synchronization.
2. Solitary and social foraging: (i) Solitary agents: Classical prey and patch models including predation, speed, sensor imperfections, and risk-sensitive aspects. Applications to autonomous vehicle decision-making system design (foraging for tasks) and distributed temperature control (foraging for temperature error). Irrational choice and the state-predation trade-off with applications to gray jays, Persoreus Canadenis (with experimental work done by my collaborator T. Waite, a biologist at OSU). (ii) Social agents: (a) modeling and analysis of honey bee social foraging (with experimental work done by my collaborator T. Seeley at Cornell); (b) social foraging theory (e.g., via evolutionary game theory) for cooperate/no-cooperate decisions, group size design, and heterogenous agent mix design for multiagent systems.
3. Cooperative task scheduling and resource allocation: Modeling and analysis of strategies for distributed and networked agents performing scheduling, resource allocation, load balancing, and task assignment (several approaches extend methods from parallel and distributed computing), with the special challenges presented by the need to process spatially-distributed tasks. Multiagent task choice problems with mathematical analysis of emergent agent spatial distributions (e.g., "ideal free distributions") for honey bee social foraging, groups of autonomous vehicles, and multizone temperature control. Impact of delays and information flow constraints considered (e.g., via a computer network). Interested in evolution of complex networks in biology and engineering.
4. Cooperative choice: Mathematical modeling and analysis of the speed vs. accuracy trade-off in the distributed (and low information flow) decision-making process for nest site selection by honey bees (with experimental work done by my collaborator T. Seeley at Cornell Univ.). Relationships to neurobiological cognition for choice processes, especially mathematical models and analysis for such systems. Cooperative search and best-task-selection by vehicle groups in spite of sensor noise, spatial/agent dynamical constraints, and communication network delays and topology changes. Mathematical modeling and analysis of stochastic biological/technological group choice processes, with special interest in human group decision making.
5. Experimental research: (i) Experimental biomimicry projects: Biomimicry of solitary and social foraging for multizone temperature control (temperature error distribution is analogous to nutrient distribution), distributed attentional systems (electromechanical arcade), distributed sychronization (mimic fire flies); and (ii) Experimental engineering projects: Multizone temperature control over a network, distributed dynamic resource allocation (for temperature, balls in tubes), cooperative control (electromechanical arcade). See our Distributed Dynamical Systems Laboratory for more information.

• Education/Curriculum/Laboratory Development Initiatives: I also have a number of efforts in the area of curriculum/laboratory development to support the above research thrusts, and the education of graduate and undergraduate students. Click here for more information.

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