Biswadip Dey

Trajectory smoothing as a linear optimal control problem

In many areas of science and engineering there is a need for techniques to robustly extract velocity and its derivatives from a finite sample of observed positions. The extracted information can be used to infer related quantities such as curvature and speed, which are important for analysis of strategies and feedback laws associated with the motion. In this work a novel approach is proposed to reconstruct trajectories from a set of discrete observations. A simple linear model is used as the generative model for trajectories, and high values of the jerk (derivative of the acceleration) path integral are penalized during reconstruction. The positions, reconstructed in this way, can be represented as a linear combination of the sample data. The regularization (penalty) parameter plays a very important role in the reconstruction process, and it may be determined from data using ordinary cross validation.

Station keeping through beacon-referenced cyclic pursuit

This paper investigates a modification of cyclic CB pursuit in a multi-agent system in which each agent pays attention to a neighbor and a beacon. The problem admits shape equilibria with collective circling about the beacon, with the circling radius and angular separation of agents determined by choice of parameters in the feedback law. Stability of circling shape equilibria is shown for a 2-agent system, and the results are demonstrated on a collective of mobile robots tracked by a motion capture system.

Synchronization bound for networks of nonlinear oscillators

Investigation of synchronization phenomena in networks of coupled nonlinear oscillators plays a pivotal role in understanding the behavior of biological and mechanical systems with oscillatory properties. We derive a general sufficient condition for synchronization of a network of nonlinear oscillators using a nonsmooth Lyapunov function, and we obtain conditions under which synchronization is guaranteed for a network of Fitzhugh-Nagumo (FN) oscillators in biologically relevant model parameter regimes. We incorporate two types of heterogeneity into our study of FN oscillators: 1) the network structure is arbitrary and 2) the oscillators have non-identical external inputs. Understanding the effects of heterogeneities on synchronization of oscillators with inputs provides a promising step toward control of key aspects of networked oscillatory systems.

Biomimetic algorithms for coordinated motion: Theory and implementation

Drawing inspiration from flight behavior in biological settings (e.g. territorial battles in dragonflies, and flocking in starlings), this paper demonstrates two strategies for coverage and flocking. Using earlier theoretical studies on mutual motion camouflage, an appropriate steering control law for area coverage has been implemented in a laboratory test-bed equipped with wheeled mobile robots and a Vicon high speed motion capture system. The same test-bed is also used to demonstrate another strategy (based on local information), termed topological velocity alignment, which serves to make agents move in the same direction. The present work illustrates the applicability of biological inspiration in the design of multi-agent robotic collectives.

Investigating group behavior in dance: an evolutionary dynamics approach

We investigate group behavior in dance using an evolutionary dynamic model. Our approach is motivated by observations of nineteen dancers during a performance in which they choose a sequence of dance movements from a finite set of allowable movement modules as they perform. Results show evidence that subgroups of dancers performing the same movement module with greater representation are aware of their dominance, which in turn influences their switching rates between modules. We introduce the notion of awareness of dominance into the well-studied framework of replicator-mutator dynamics, where modules are represented as strategies. By letting awareness of dominance tune mutation strength, we demonstrate its influence in the evolution of strategies. The tuning yields a feedback controlled bifurcation in the model dynamics, which predicts persistence of dominant strategies as observed in the behavior of the dance group.

Stability and pure shape equilibria for beacon-referenced cyclic pursuit

Cyclic pursuit systems provide a means to generate useful global behaviors in a collective of autonomous agents based on dyadic pursuit interactions between neighboring agents in a cycle graph. Here we consider a modified version of the cyclic pursuit framework in which a stationary beacon provides an additional reference for the agents in the system. Building on the framework proposed in our previous work, we derive necessary conditions for stability of circling equilibria in the n-agent system. Furthermore, we employ a change of variables to reveal the existence of a family of invariant manifolds related to spiral motions which maintain the formation shape up to geometric similarity.

Control-theoretic data smoothing

The problem of recovering continuous time signals from a set of discrete measurements is ill-posed in a classical sense (non-uniqueness of solution). Our approach introduces generative models with inputs, states and outputs, and regularizes this problem by trading total fit-error against suitable penalty functionals of input and state. This enables us to apply techniques from optimal control and obtain solutions in a semi-analytical way. Using a modified version of Pontryagins maximum principle, this paper treats data smoothing as an optimal control problem. In addition to addressing data smoothing problems in Euclidean settings, our results are also applicable to problems arising in finite dimensional matrix Lie group settings. In particular, this paper discusses an example problem on SE(2), and exploits symmetry and reduction to an integrable Hamiltonian system as means to data smoothing.

BeeNestABM: An open-source agent-based model of spatiotemporal distribution of bumblebees in nests

This software features the MATLAB source code for an interactive computational model that can be used to study the localized responses of bumblebees to sublethal exposures to a prevalent class of pesticides called neonicotinoids. The code involves an agent-based stochastic model for the interactions between and movements of individual bees within a nest and the nest-related disruptions that occur due to pesticide exposure. The dynamic states of the bees are stored in a matrix, the default data structure of MATLAB. Agent-based modeling allows for building understanding of the colony scale impacts of multiple interacting factors that affect numerous individuals in close proximity and how those change upon pesticide exposure. The scientific significance is that the model solved in the software focuses on the effects of pesticides that occur in bumblebees over short time scales (hours to days) inside a single nest, which includes a much smaller spatial region with finer resolution than that considered in the state-of-the-art (Thorbek, Campbell, and Thompson 2017). These temporal and spatial scales are appropriate for modeling the effects of neonicotinoid pesticides that account for colony size and interactions between exposed and unexposed individuals. The short and local scales allow the model to explicitly consider neighbor interactions and individual bee interactions with structures inside an isolated environment without confounding external factors. The BeeNestABM model tracks bumblebee activity and motility using empirically estimated probabilities for transitions between active (mobile) and inactive states (Figure 1A). The location of a bee in relation to the structures such as brood and food pots within the nest influence the transition probabilities and the orientation of bee movement through a combination of random walk and attraction toward the nest structures (Figure 1B), and the transition probabilities contain a component that considers whether the transition is occuring spontaneously or due to social modulation upon collison with a neighboring bee (Figure 1C).

Cluster Synchronization of Diffusively Coupled Nonlinear Systems: A Contraction-Based Approach

Finding the conditions that foster synchronization in networked nonlinear systems is critical to understanding a wide range of biological and mechanical systems. However, the conditions proved in the literature for synchronization in nonlinear systems with linear coupling, such as has been used to model neuronal networks, are in general not strict enough to accurately determine the system behavior. We leverage contraction theory to derive new sufficient conditions for cluster synchronization in terms of the network structure, for a network where the intrinsic nonlinear dynamics of each node may differ. Our result requires that network connections satisfy a cluster-input-equivalence condition, and we explore the influence of this requirement on network dynamics. For application to networks of nodes with FitzHugh–Nagumo dynamics, we show that our new sufficient condition is tighter than those found in previous analyses that used smooth or nonsmooth Lyapunov functions. Improving the analytical conditions for when cluster synchronization will occur based on network configuration is a significant step toward facilitating understanding and control of complex networked systems.

Collective motion under beacon-referenced cyclic pursuit

Abstract Cyclic pursuit frameworks, which are built upon pursuit interactions between neighboring agents in a cycle graph, provide an efficient way to create useful global behaviors in a collective of autonomous robots. Previous work had considered cyclic pursuit with a constant bearing (CB) pursuit law, and demonstrated the existence of circling equilibria for the corresponding dynamics. In this work, we propose a beacon-referenced version of the CB pursuit law, wherein a stationary beacon provides an additional reference for the individual agents in a collective. When implemented in a cyclic framework, we show that the resulting dynamics admit relative equilibria corresponding to a circling orbit around the beacon, with the circling radius and the distribution of agents along the orbit determined by parameters of the proposed pursuit law. We also derive necessary conditions for stability of the circling equilibria, which provides a guide for parameter selection. Finally, by introducing a change of variables, we demonstrate the existence of a family of invariant manifolds related to spiraling motions around the beacon which preserve the “pure shape” of the collective, and study the reduced dynamics on a representative manifold.