Reconstruction, Analysis and Synthesis of Collective Motion

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As collective motion plays a crucial role in modern day robotics and engineering, it seems appealing to seek inspiration from nature, which abounds with examples of collective motion (starling flocks, fish schools etc.). This approach towards understanding and reverse-engineering a particular aspect of nature forms the foundation of this dissertation, and its main contribution is threefold.

First we identify the importance of appropriate algorithms to extract parameters of motion from sampled observations of the trajectory, and then by assuming an appropriate generative model we turn this into a regularized inversion problem with the regularization term imposing smoothness of the reconstructed trajectory. First we assume a linear triple-integrator model, and by penalizing high values of the jerk path integral we reconstruct the trajectory through an analytical approach. Alternatively, the evolution of a trajectory can be governed by natural Frenet frame equations. Inadequacy of integrability theory for nonlinear systems poses the utmost challenge in having an analytic solution, and forces us to adopt a numerical optimization approach. However, by noting the fact that the underlying dynamics defines a left invariant vector field on a Lie group, we develop a framework based on Pontryagin's maximum principle. This approach toward data smoothing yields a semi-analytic solution.

Equipped with appropriate algorithms for trajectory reconstruction we analyze flight data for biological motions, and this marks the second contribution of this dissertation. By analyzing the flight data of big brown bats in two different settings (chasing a free-flying praying mantis and competing with a conspecific to catch a tethered mealworm), we provide evidence to show the presence of a context specific switch in flight strategy. Moreover, our approach provides a way to estimate the behavioral latency associated with these foraging behaviors. On the other hand, we have also analyzed the flight data of European starling flocks, and it can be concluded from our analysis that the flock-averaged coherence (the average cosine of the angle between the velocities of a focal bird and its neighborhood center of mass, averaged over the entire flock) gets maximized by considering 5-7 nearest neighbors. The analysis also sheds some light into the underlying feedback mechanism for steering control.

The third and final contribution of this dissertation lies in the domain of control law synthesis. Drawing inspiration from coherent movement of starling flocks, we introduce a strategy (Topological Velocity Alignment) for collective motion, wherein each agent aligns its velocity along the direction of motion of its neighborhood center of mass. A feedback law has also been proposed for achieving this strategy, and we have analyzed two special cases (two-body system; and an N-body system with cyclic interaction) to show effectiveness of our proposed feedback law. It has been observed through numerical simulation and robotic implementation that this approach towards collective motion can give rise to a splitting behavior.