Keeping speed and distance for aligned motion

Spatial flocking: Control by speed, distance, noise and delay

Fish, birds, insects and robots frequently swim or fly in groups. During their three dimensional collective motion, these agents do not stop, they avoid collisions by strong short-range repulsion, and achieve group cohesion by weak long-range attraction. In a minimal model that is isotropic, and continuous in both space and time, we demonstrate that (i) adjusting speed to a preferred value, combined with (ii) radial repulsion and an (iii) effective long-range attraction are sufficient for the stable ordering of autonomously moving agents in space. Our results imply that beyond these three rules ordering in space requires no further rules, for example, explicit velocity alignment, anisotropy of the interactions or the frequent reversal of the direction of motion, friction, elastic interactions, sticky surfaces, a viscous medium, or vertical separation that prefers interactions within horizontal layers. Noise and delays are inherent to the communication and decisions of all moving agents. Thus, next we investigate their effects on ordering in the model. First, we find that the amount of noise necessary for preventing the ordering of agents is not sufficient for destroying order. In other words, for realistic noise amplitudes the transition between order and disorder is rapid. Second, we demonstrate that ordering is more sensitive to displacements caused by delayed interactions than to uncorrelated noise (random errors). Third, we find that with changing interaction delays the ordered state disappears at roughly the same rate, whereas it emerges with different rates. In summary, we find that the model discussed here is simple enough to allow a fair understanding of the modeled phenomena, yet sufficiently detailed for the description and management of large flocks with noisy and delayed interactions. Our code is available at http://github.com/fij/floc.

Automated Planar Tracking the Waving Bodies of Multiple Zebrafish Swimming in Shallow Water

Zebrafish (Danio rerio) is one of the most widely used model organisms in collective behavior research. Multi-object tracking with high speed camera is currently the most feasible way to accurately measure their motion states for quantitative study of their collective behavior. However, due to difficulties such as their similar appearance, complex body deformation and frequent occlusions, it is a big challenge for an automated system to be able to reliably track the body geometry of each individual fish. To accomplish this task, we propose a novel fish body model that uses a chain of rectangles to represent fish body. Then in detection stage, the point of maximum curvature along fish boundary is detected and set as fish nose point. Afterwards, in tracking stage, we firstly apply Kalman filter to track fish head, then use rectangle chain fitting to fit fish body, which at the same time further judge the head tracking results and remove the incorrect ones. At last, a tracklets relinking stage further solves trajectory fragmentation due to occlusion. Experiment results show that the proposed tracking system can track a group of zebrafish with their body geometry accurately even when occlusion occurs from time to time.