Collective motion, sensor networks, and ocean sampling

This paper addresses the design of mobile sensor networks for optimal data collection. The development is strongly motivated by the application to adaptive ocean sampling for an autonomous ocean observing and prediction system. A performance metric, used to derive optimal paths for the network of mobile sensors, defines the optimal data set as one which minimizes error in a model estimate of the sampled field. Feedback control laws are presented that stably coordinate sensors on structured tracks that have been optimized over a minimal set of parameters. Optimal, closed-loop solutions are computed in a number of low-dimensional cases to illustrate the methodology. Robustness of the performance to the influence of a steady flow field on relatively slow-moving mobile sensors is also explored © 2006 IEEE.

Group coordination and cooperative control of steered particles in the plane

The paper overviews recent and ongoing efforts by the authors to develop a design methodology to stabilize isolated relative equilibria in a kinematic model of identical particles moving in the plane at unit speed. Isolated relative equilibria correspond to either parallel motion of all particles with fixed relative spacing or to circular motion of all particles about the same center with fixed relative headings. © Springer-Verlag Berlin Heidelberg 2006.

Collective motion of self-propelled particles: Stabilizing symmetric formations on closed curves

We provide feedback control laws to stabilize formations of multiple, unit speed particles on smooth, convex, and closed curves with definite curvature. As in previous work we exploit an analogy with coupled phase oscillators to provide controls which isolate symmetric particle formations that are invariant to rigid translation of all the particles. In this work, we do not require all particles to be able to communicate; rather we assume that inter-particle communication is limited and can be modeled by a fixed, connected, and undirected graph. Because of their unique spectral properties, the Laplacian matrices of circulant graphs play a key role. The methodology is demonstrated using a superellipse, which is a type of curve that includes circles, ellipses, and rounded rectangles. These results can be used in applications involving multiple autonomous vehicles that travel at constant speed around fixed beacons. ©2006 IEEE.

Oscillator models and collective motion: Splay state stabilization of self-propelled particles

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. © 2005 IEEE.

Collective motion: Bistability and trajectory tracking

This paper presents analysis and application of steering control laws for a network of self-propelled, planar particles. We explore together the two stably controlled group motions, parallel motion and circular motion, for modeling and design purposes. We show that a previously considered control law simultaneously stabilizes both parallel and circular group motion, leading to Instability and hysteresis. We also present behavior primitives that enable piecewise-linear network trajectory tracking.