My research encompasses four major areas of systems theory--- bio-inspired control, multi-agent robotic systems, social networks and computational cognitive neuroscience. My research relies on tools from linear/nonlinear dynamics and control, information theory, hybrid systems, graph theory, machine learning as well as experimental analysis.
Communication-Through-Motion in multi-agent systems:
A key direction of my past and ongoing research targets on understanding communication-through-motion in multi-agent systems. During my PhD studies, I have investigated this framework by using two distinct prototypes. First, I used a dance model, salsa, as a medium for human group behavior in which a leader is responsible to transmit signals to a follower by using his gestures and positioning. I constructed a mathematical framework that provides a way to specify control protocols for corresponding motion primitives and to measure the quality of an execution. I investigated the decision-making process and the communication strategy of the leader. I showed that the dance performance can be abstracted to a topological space and the constraints on the motion transitions can be mapped to the invariants defined in topological knot theory. The proposed model was used to solve two different problems. A forward problem was defined as generating choreographed motion sequences by humanoid robots. Whereas, an inverse problem was defined as generating an autonomous artificial intelligence that could observe, deconstruct and evaluate an execution based on information theoretic measures. I also studied communication-through-motion in the context of human-robot interactions.
Animal Collective Behavior: Understanding the Perceptual Modalities in Bat Flight:
With a team of biologists I studied bat cave emergence in order to understand the ways in which the animals communicate and use sensory perceptions of their neighbors and environments to control their motion. The work was based on data reconstructed from a large collection of 3-dimensional video records of Myotis velifer, emerging from a cave at the Bamberger Ranch Preserve near Johnson City, Texas. Our analysis of reconstructed flight data suggested that vision, echolocation, and spatial memory together with the possible exercise of an ability in using predictive navigation are mutually reinforcing aspects of a composite perceptual system that guides flight. Moreover, using an idealized geometry of bat eyes, we introduced the concept of time-to-transit and proposed several steering control laws for an idealized flight model that involves leader-follower interactions and reactions to the environmental features. We have shown that the proposed framework can be used to emulate the observed flight of a typical bat.
Social Decision-Making in Human Group Behavior:
We investigate the influence of individual or subgroup level decisions in social networks to the overall group behavior. The study examines the mechanisms of social decision-making in human collective behavior by investigating a structured improvisational dance in which a group of dancers make a sequence of compositional choices among pre-defined dance motion primitives. In the analyses, we use a nonlinear evolutionary dynamics model to investigate the group behavior in dance and this generates a bidirectional study. In one direction we benefit from the dynamical model to understand dancers' decision-making process. In the reverse direction, motivated by the observations from experimental data, we modify the dynamical model by introducing nonlinearities and the notion of feedback controlled bifurcation in this context that enriches the model's steady-state behavior.
Human Inspired Design for Neural Network Architectures:
In collaboration with colleagues from Princeton Neuroscience Institute and Intel, we investigate the role of the network structure in human cognitive processes. We are particularly interested in the notion of ``multitasking'' in neural network architectures which is defined as the ability to carry out multiple independent (rather than interrelated or interacting) processes (tasks) at the same time. We show that there is a fundamental trade-off in neural network architectures like the human brain between the learning efficiency, and concurrent multitasking that is relevant for the design of artificial systems and the study of natural ones.