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

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

Station Keeping through Beacon-referenced Cyclic Pursuit

This paper investigates a modification of cyclic constant bearing (CB) pursuit in a multi-agent system in which each agent pays attention to a neighbor and a beacon. The problem admits shape equilibria with collective circling about the beacon, with the circling radius and angular separation of agents determined by choice of parameters in the feedback law. Stability of circling shape equilibria is shown for a 2-agent system, and the results are demonstrated on a collective of mobile robots tracked by a motion capture system

Reconstruction, Analysis and Synthesis of Collective Motion

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

Cluster synchronization of diffusively-coupled nonlinear systems: A contraction based approach

Finding the conditions that foster synchronization in networked oscillatory systems is critical to understanding a wide range of biological and mechanical systems. However, the conditions proved in the literature for synchronization in nonlinear systems with linear coupling, such as has been used to model neuronal networks, are in general not strict enough to accurately determine the system behavior. We leverage contraction theory to derive new sufficient conditions for cluster synchronization in terms of the network structure, for a network where the intrinsic nonlinear dynamics of each node may differ. Our result requires that network connections satisfy a cluster-input-equivalence condition, and we explore the influence of this requirement on network dynamics. For application to networks of nodes with neuronal spiking dynamics, we show that our new sufficient condition is tighter than those found in previous analyses which used nonsmooth Lyapunov functions. Improving the analytical conditions for when cluster synchronization will occur based on network configuration is a significant step toward facilitating understanding and control of complex oscillatory systems

Social decision-making driven by artistic explore-exploit tension

We studied social decision-making in the rule-based improvisational dance $There$ $Might$ $Be$ $Others$, where dancers make in-the-moment compositional choices. Rehearsals provided a natural test-bed with communication restricted to non-verbal cues. We observed a key artistic explore-exploit tension in which the dancers switched between exploitation of existing artistic opportunities and riskier exploration of new ones. We investigated how the rules influenced the dynamics using rehearsals together with a model generalized from evolutionary dynamics. We tuned the rules to heighten the tension and modeled nonlinear fitness and feedback dynamics for mutation rate to capture the observed temporal phasing of the dancers' exploration-versus-exploitation. Using bifurcation analysis, we identified key controls of the tension and showed how they could shape the decision-making dynamics of the model much like turning a "dial" in the instructions to the dancers could shape the dance. The investigation became an integral part of the development of the dance

Physics-informed neural networks for modeling rate- and temperature-dependent plasticity

This work presents a physics-informed neural network (PINN) based framework to model the strain-rate and temperature dependence of the deformation fields in elastic-viscoplastic solids. To avoid unbalanced back-propagated gradients during training, the proposed framework uses a simple strategy with no added computational complexity for selecting scalar weights that balance the interplay between different terms in the physics-based loss function. In addition, we highlight a fundamental challenge involving the selection of appropriate model outputs so that the mechanical problem can be faithfully solved using a PINN-based approach. We demonstrate the effectiveness of this approach by studying two test problems modeling the elastic-viscoplastic deformation in solids at different strain rates and temperatures, respectively. Our results show that the proposed PINN-based approach can accurately predict the spatio-temporal evolution of deformation in elastic-viscoplastic materials.Comment: 11 pages, 7 figures; Accepted in NeurIPS 2022, Machine Learning and the Physical Sciences worksho