Randomly Distributed Delayed Communication and Coherent Swarm Patterns

Insect visuomotor delay adjustments in group flight support swarm cohesion

Flying insects routinely demonstrate coordinated flight in crowded assemblies despite strict communication and processing constraints. This study experimentally records multiple flying insects tracking a moving visual stimulus. System identification techniques are used to robustly identify the tracking dynamics, including a visuomotor delay. The population delay distributions are quantified for solo and group behaviors. An interconnected visual swarm model incorporating heterogeneous delays is developed, and bifurcation analysis and swarm simulation are applied to assess swarm stability under the delays. The experiment recorded 450 insect trajectories and quantified visual tracking delay variation. Solitary tasks showed a 30ms average delay and standard deviation of 50ms, while group behaviors show a 15ms average and 8ms standard deviation. Analysis and simulation indicate that the delay adjustments during group flight support swarm formation and center stability, and are robust to measurement noise. These results quantify the role of visuomotor delay heterogeneity in flying insects and their role in supporting swarm cohesion through implicit communication.

Experimental identification of individual insect visual tracking delays in free flight and their effects on visual swarm patterns

Insects are model systems for swarming robotic agents, yet engineered descriptions do not fully explain the mechanisms by which they provide onboard sensing and feedback to support such motions; in particular, the exact value and population distribution of visuomotor processing delays are not yet quantified, nor the effect of such delays on a visually-interconnected swarm. This study measures untethered insects performing a solo in-flight visual tracking task and applies system identification techniques to build an experimentally-consistent model of the visual tracking behaviors, and then integrates the measured experimental delay and its variation into a visually interconnected swarm model to develop theoretical and simulated solutions and stability limits. The experimental techniques include the development of a moving visual stimulus and real-time multi camera based tracking system called VISIONS (Visual Input System Identification from Outputs of Naturalistic Swarms) providing the capability to recognize and simultaneously track both a visual stimulus (input) and an insect at a frame rate of 60-120 Hz. A frequency domain analysis of honeybee tracking trajectories is conducted via fast Fourier and Chirp Z transforms, identifying a coherent linear region and its model structure. The model output is compared in time and frequency domain simulations. The experimentally measured delays are then related to probability density functions, and both the measured delays and their distribution are incorporated as inter-agent interaction delays in a second order swarming dynamics model. Linear stability and bifurcation analysis on the long range asymptotic behavior is used to identify delay distributions leading to a family of solutions with stable and unstable swarm center of mass (barycenter) locations. Numerical simulations are used to verify these results with both continuous and measured distributions. The results of this experiment quantify a model structure and temporal lag (transport delay) in the closed loop dynamics, and show that this delay varies across 50 individuals from 5-110ms, with an average delay of 22ms and a standard deviation of 40ms. When analyzed within the swarm model, the measured delays support a diversity of solutions and indicate an unstable barycenter.

Noise Induced Pattern Switching in Randomly Distributed Delayed Swarms

We study the effects of noise on the dynamics of a system of coupled self-propelling particles in the case where the coupling is time-delayed, and the delays are discrete and randomly generated. Previous work has demonstrated that the stability of a class of emerging patterns depends upon all moments of the time delay distribution, and predicts their bifurcation parameter ranges. Near the bifurcations of these patterns, noise may induce a transition from one type of pattern to another. We study the onset of these noise-induced swarm re-organizations by numerically simulating the system over a range of noise intensities and for various distributions of the delays. Interestingly, there is a critical noise threshold above which the system is forced to transition from a less organized state to a more organized one. We explore this phenomenon by quantifying this critical noise threshold, and note that transition time between states varies as a function of both the noise intensity and delay distribution.