Mechanics and Control of Coupled Interactions in Ambient Media

Abstract

Many multi-agent systems in nature comprise agents that interact with, and respond to, the dynamics of their environment. For example, fish school based on the fundamental fluid phenomena of vortex shedding, birds shed leading-edge vortices in formation for flocking, and emph{E. coli} bacteria secrete and push against a surrounding medium to meander in swarms. In this thesis, we investigate the mechanics and control of three different systems having agents that interact with a surrounding medium to affect motion. We make use of the textit{Chaplygin beanie}, a planar underactuated nonholonomic mechanical system outfitted with a rotor atop its body and a single wheel at its rear constraining its dynamics to the plane about which it moves. We first consider a single passively compliant Chaplygin beanie atop a platform having translational compliance, introduce the reduced equations for the system using the notion of symmetry and nonholonomic momentum, and provide proof for a particular stable behavior under arbitrary deformations of the elastic element modeling its compliance. We then direct our focus to results concerning the frequency response and control of passive Chaplygin beanies under actuation of the platform, discuss rich dynamical features arising from periodic actuation, and develop rules by which control can be exerted to collect and disperse multiple such passive vehicles. We then discuss how the latter of these results clarifies the extent to which stable behavior can be excited in the system through exogenous control.

We then leverage our understanding of the single Chaplygin beanie model to inform a geometric treatment of two such agents atop a compliant platform, again invoking symmetry and nonholonomic reduction for analysis. We discuss stability, control, and an entrainment phenomena within this multi-agent dynamical system, present results in the form of simulation, and draw analogies between its behavior and related behaviors within biological systems.

Finally, we introduce the dynamic model for a novel fluid-propulsive aquatic vehicle in an ideal fluid that exerts control over its motion using impulsive fluid-ejection events to move in its environment. We present an analysis concerning the entrainment of a cylindrical-shaped aquatic agent in flows induced by neighboring agents, present preliminary results of an agent position-stabilizing at a desired setpoint using impulsive fluid-ejection events, and discuss the next steps necessary to model multiple such agents in an inviscid fluid.