Stabilization of symmetric formations to motion around convex loops

We provide a cooperative control algorithm to stabilize symmetric formations to motion around closed curves suitable for mobile sensor networks. This work extends previous results for stabilization of symmetric circular formations. We study a planar particle model with decentralized steering control subject to limited communication. Because of their unique spectral properties, the Laplacian matrices of circulant graphs play a key role. We illustrate the result for a skewed superellipse, which is a type of curve that includes circles, ellipses, and rounded parallelograms. © 2007 Elsevier B.V. All rights reserved.

Alternating spatial patterns for coordinated group motion

Motivated by recent observations of fish schools, we study coordinated group motion for individuals with oscillatory speed. Neighbors that have speed oscillations with common frequency, amplitude and average but different phases, move together in alternating spatial patterns, taking turns being towards the front, sides and back of the group. We propose a model and control laws to investigate the connections between these spatial dynamics, communication when sensing is range or direction limited, and convergence of coordinated group motions. ©2007 IEEE.

Stabilization of collective motion in three dimensions: A consensus approach

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. We first 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. © 2007 IEEE.

Oscillator models and collective motion

A description of the so called "particles with coupled oscillator dynamics" (PCOD) is presented which is used to model, analyze and synthesize collective motion. An oscillator model with spatial dynamics is presented to help describe how to design steering control laws while it is being used to study biological collectives. Lastly, both engineering and biological analysis were described.

Stabilization of planar collective motion: All-to-all communication

This paper proposes a design methodology to stabilize isolated relative equilibria in a model of all-to-all coupled 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 with fixed relative phases. The stabilizing feedbacks derive from Lyapunov functions that prove exponential stability and suggest almost global convergence properties. The results of the paper provide a low-order parametric family of stabilizable collectives that offer a set of primitives for the design of higher-level tasks at the group level. © 2007 IEEE.

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.

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.

Plane-strain discrete dislocation plasticity with climb-assisted glide motion of dislocations

A small-strain two-dimensional discrete dislocation plasticity (DDP) framework is developed wherein dislocation motion is caused by climb-assisted glide. The climb motion of the dislocations is assumed to be governed by a drag-type relation similar to the glide-only motion of dislocations: such a relation is valid when vacancy kinetics is either diffusion limited or sink limited. The DDP framework is employed to predict the effect of dislocation climb on the uniaxial tensile and pure bending response of single crystals. Under uniaxial tensile loading conditions, the ability of dislocations to bypass obstacles by climb results in a reduced dislocation density over a wide range of specimen sizes in the climb-assisted glide case compared to when dislocation motion is only by glide. A consequence is that, at least in a single slip situation, size effects due to dislocation starvation are reduced. By contrast, under pure bending loading conditions, the dislocation density is unaffected by dislocation climb as geometrically necessary dislocations (GNDs) dominate. However, climb enables the dislocations to arrange themselves into lower energy configurations which significantly reduces the predicted bending size effect as well as the amount of reverse plasticity observed during unloading. The results indicate that the intrinsic plasticity material length scale associated with GNDs is strongly affected by thermally activated processes and will be a function of temperature. © 2013 IOP Publishing Ltd.

Warping trajectories for video synchronization

Temporal synchronization of multiple video recordings of the same dynamic event is a critical task in many computer vision applications e.g. novel view synthesis and 3D reconstruction. Typically this information is implied, since recordings are made using the same timebase, or time-stamp information is embedded in the video streams. Recordings using consumer grade equipment do not contain this information; hence, there is a need to temporally synchronize signals using the visual information itself. Previous work in this area has either assumed good quality data with relatively simple dynamic content or the availability of precise camera geometry. In this paper, we propose a technique which exploits feature trajectories across views in a novel way, and specifically targets the kind of complex content found in consumer generated sports recordings, without assuming precise knowledge of fundamental matrices or homographies. Our method automatically selects the moving feature points in the two unsynchronized videos whose 2D trajectories can be best related, thereby helping to infer the synchronization index. We evaluate performance using a number of real recordings and show that synchronization can be achieved to within 1 sec, which is better than previous approaches. Copyright 2013 ACM.

Decadal persistence of cycles in lava lake motion at Erebus volcano, Antarctica

Studies of Erebus volcano's active lava lake have shown that many of its observable properties (gas composition, surface motion and radiant heat output) exhibit cyclic behaviour with a period of ~10 min. We investigate the multi-year progression of the cycles in surface motion of the lake using an extended (but intermittent) dataset of thermal infrared images collected by the Mount Erebus Volcano Observatory between 2004 and 2011. Cycles with a period of ~5-18 min are found to be a persistent feature of the lake's behaviour and no obvious long-term change is observed despite variations in lake level and surface area. The times at which gas bubbles arrive at the lake's surface are found to be random with respect to the phase of the motion cycles, suggesting that the remarkable behaviour of the lake is governed by magma exchange rather than an intermittent flux of gases from the underlying magma reservoir. © 2014 The Authors.