Beacon-referenced Mutual Pursuit in Three Dimensions

Motivated by station-keeping applications in various unmanned settings, this paper introduces a steering control law for a pair of agents operating in the vicinity of a fixed beacon in a three-dimensional environment. This feedback law is a modification of the previously studied three-dimensional constant bearing (CB) pursuit law, in the sense that it incorporates an additional term to allocate attention to the beacon. We investigate the behavior of the closed-loop dynamics for a two agent mutual pursuit system in which each agent employs the beacon-referenced CB pursuit law with regards to the other agent and a stationary beacon. Under certain assumptions on the associated control parameters, we demonstrate that this problem admits circling equilibria wherein the agents move on circular orbits with a common radius, in planes perpendicular to a common axis passing through the beacon. As the common radius and distances from the beacon are determined by choice of parameters in the feedback law, this approach provides a means to engineer desired formations in a three-dimensional setting

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

When Hawks Attack: Animal-borne Video Studies of Goshawk Pursuit and Prey-evasion Strategies

Video filmed by a camera mounted on the head of a Northern Goshawk (Accipiter gentilis) was used to study how the raptor used visual guidance to pursue prey and land on perches. A combination of novel image analysis methods and numerical simulations of mathematical pursuit models was used to determine the goshawk's pursuit strategy. The goshawk flew to intercept targets by fixing the prey at a constant visual angle, using classical pursuit for stationary prey, lures or perches, and usually using constant absolute target direction (CATD) for moving prey. Visual fixation was better maintained along the horizontal than vertical direction. In some cases, we observed oscillations in the visual fix on the prey, suggesting that the goshawk used finite-feedback steering. Video filmed from the ground gave similar results. In most cases, it showed goshawks intercepting prey using a trajectory consistent with CATD, then turning rapidly to attack by classical pursuit; in a few cases, it showed them using curving non-CATD trajectories. Analysis of the prey's evasive tactics indicated that only sharp sideways turns caused the goshawk to lose visual fixation on the prey, supporting a sensory basis for the surprising frequency and effectiveness of this tactic found by previous studies. The dynamics of the prey's looming image also suggested that the goshawk used a tau-based interception strategy. We interpret these results in the context of a concise review of pursuit–evasion in biology, and conjecture that some prey deimatic ‘startle’ displays may exploit tau-based interception

Analysis and synthesis of collective motion: from geometry to dynamics

The subject of this dissertation is collective motion, the coordinated motion of two or more individuals, in three-dimensional space. Inspired by the problems of understanding collective motion in nature and designing artificial collectives that can produce complex behaviors, we introduce mathematical methods for the analysis of collective motion data, and biologically-inspired algorithms for generating collective motion in engineered systems. We explore two complementary approaches to the analysis and synthesis of collective motion. The first "top-down" approach consists in exploiting the geometry of n-body systems to identify certain elementary components of collective motion. A main contribution of this thesis is to reveal a new geometrical structure (fiber bundle) of the translation-reduced configuration space and a corresponding classification of collective motions alternative to the classical one based on reduction to shape space. We derive a mathematical framework for decomposing arbitrary collective motions into elementary components, which can help identify the main modes of an observed collective phenomenon. We synthesize vector fields that implement some of the most interesting elementary collective motions, and suggest, whenever feasible, decentralized implementations. The second "bottom-up" approach consists in starting from known biologically-plausible individual control laws and exploring how they can be used to generate collective behaviors. This approach is illustrated using the motion camouflage proportional guidance law as a building block. We show that rich and coordinated motion patterns can be obtained when two individuals are engaged in mutual pursuit with this control law. An extension of these dynamics yields coordinated motion for a collective of n individuals