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Controlling a Parent System Through the Abstraction of a Swarm Acting Upon It Open Access

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This dissertation discusses the control of parent-child systems in which a parent system is acted on by a set of controllable child systems (i.e. a swarm). Using swarms of robots to accomplish complex tasks has several benefits over using a single robot; for example, members of the swarm can each focus on simpler sub-problems, allowing for less complex design, and if a swarm member breaks down, it may be easier to replace than a larger single robot. Many such complex tasks can be broken into this parent-child class of system. Examples of such systems include a swarm of robots pushing an object over a surface or a swarm of aerial vehicles carrying a large load. There are also many not-so-obvious problems that can be framed this way; for example, a multi-legged robot could be viewed as a swarm of legs manipulating a body, or an array of flaps on an aircraft wing could be considered a swarm controlling the flow over the wing.The first part of this dissertation outlines a general approach for decoupling the swarm from the parent system through a low-dimensional abstract state space. The conditions that enable this approach are given along with how constraints on both systems propagate through the abstract state and impact the requirements of their controllers. Next a method using Deep Learning techniques is proposed to learn such an abstract state, rather than design it by hand. This allows for broader applications in which an abstract state may not be obvious. Lastly, a method of estimating the abstract state in a decentralized fashion is presented, allowing the methods discussed previously to be implemented without global state observers.To demonstrate the techniques presented, we consider a representative problem consisting of a tilting plane with a swarm of robots driving on top. Both homogeneous and heterogeneous swarms of varying sizes, properties, and dynamics are used to demonstrate the modularity of these methods. The controllers are shown to be locally asymptotically stable, and an estimate of the region of attraction is calculated for each controller.

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