Spatial Models of Bistability in Biological Collectives

in Proceedings of the 46th IEEE Conference on Decision and Control (2007, December)

We explore collective behavior in biological systems using a cooperative control framework. In particular, we study a hysteresis phenomenon in which a collective switches from circular to parallel motion ... [more ▼]

We explore collective behavior in biological systems using a cooperative control framework. In particular, we study a hysteresis phenomenon in which a collective switches from circular to parallel motion under slow variation of the neighborhood size in which individuals tend to align with one another. In the case that the neighborhood radius is less than the circular motion radius, both circular and parallel motion can occur. We provide Lyapunov-based analysis of bistability of circular and parallel motion in a closed-loop system of selfpropelled particles with coupled-oscillator dynamics. [less ▲]

Stabilization of Collective Motion in Three Dimensions : A Consensus Approach

in Proceedings of 46th IEEE Conference on Decision and Control (2007, December)

This paper proposes a methodology to stabilize relative equilibria in a model of identical, steered particles moving in three- dimensional Euclidean space. Exploiting the Lie group structure of the ... [more ▼]

This paper proposes a methodology to stabilize relative equilibria in a model of identical, steered particles moving in three- dimensional Euclidean space. Exploiting the Lie group structure of the resulting dynamical system, the stabilization problem is reduced to a consensus problem on the Lie algebra. The resulting equilibria correspond to parallel, circular and helical formations. We rst derive the stabilizing control laws in the presence of all-to-all communication. Providing each agent with a consensus estimator, we then extend the results to a general setting that allows for unidirectional and time-varying communication topologies. [less ▲]

Cooperative attitude synchronization in satellite swarms: a consensus approach

in Proceedings of the 17th IFAC Symposium on Automatic Control in Aerospace (2007, June)

The present paper considers the problem of autonomous synchronization of attitudes in a swarm of spacecraft. Building upon our recent results on consensus on manifolds, we model the spacecraft as ... [more ▼]

The present paper considers the problem of autonomous synchronization of attitudes in a swarm of spacecraft. Building upon our recent results on consensus on manifolds, we model the spacecraft as particles on SO(3) and drive these particles to a common point in SO(3). Unlike the Euler angle or quaternion descriptions, this model suffers no singularities nor double-points. Our approach is fully cooperative and autonomous: we use no leader nor external reference. We present two types of control laws, in terms of applied control torques, that globally drive the swarm towards attitude synchronization: one that requires tree-like or all-to-all inter-satellite communication (most efficient) and one that works with nearly arbitrary communication (most robust). [less ▲]

Discrete-time synchronization on the N-torus

in Proceedings of the 17th MTNS Symposium, Kyoto 2006 (2006, August)

In this paper, we study the behavior of a discrete-time network of N agents, each evolving on the circle. The global convergence analysis on the N-torus is a distinctive feature of the present work with ... [more ▼]

In this paper, we study the behavior of a discrete-time network of N agents, each evolving on the circle. The global convergence analysis on the N-torus is a distinctive feature of the present work with respect to previous synchronization results that have focused on convergence in the Euclidean space (R^n)^N. We address the question from a control perspective, but make several connections with existing models, including the Hopfield network, the Vicsek model and the (continuous-time) Kuramoto model. We propose two different distributed algorithms. The first one achieves convergence to equilibria in shape space that are the local extrema of a potential U_L built on the graph Laplacian associated to a fixed, undirected interconnection topology; it can be implemented with sensor-based interaction only, since each agent just relies on the relative position of its neighbors. The second one achieves synchronization under varying and/or directed communication topology using local estimates of a consensus variable that are communicated between interacting agents. Both algorithms are based on the notion of centroid and can be interpreted as descent algorithms. The proposed approach can be extended to other embedded compact manifolds. [less ▲]

Oscillator Models and Collective Motion: Splay State Stabilization of Self-Propelled Particles

in Proceedings of the 44th IEEE Conference on Decision and Control and European Control Conference (2005)

This paper presents a Lyapunov design for the stabilization of collective motion in a planar kinematic model of N particles moving at constant speed. We derive a control law that achieves asymptotic ... [more ▼]

This paper presents a Lyapunov design for the stabilization of collective motion in a planar kinematic model of N particles moving at constant speed. We derive a control law that achieves asymptotic stability of the splay state formation, characterized by uniform rotation of N evenly spaced particles on a circle. In designing the control law, the particle headings are treated as a system of coupled phase oscillators. The coupling function which exponentially stabilizes the splay state of particle phases is combined with a decentralized beacon control law that stabilizes circular motion of the particles in the splay state formation around the center of mass of the group. [less ▲]