Degree

Doctor of Philosophy (PhD)

Department

The Division of Electrical and Computer Engineering

Document Type

Dissertation

Abstract

In recent years, the study of autonomous entities such as unmanned vehicles has begun to revolutionize both military and civilian devices. One important research focus of autonomous entities has been coordination problems for autonomous robot swarms. Traditionally, robot models are used for algorithms that account for the minimum specifications needed to operate the swarm. However, these theoretical models also gloss over important practical details. Some of these details, such as time, have been considered before (as epochs of execution). In this dissertation, we examine these details in the context of several problems and introduce new performance measures to capture practical details. Specifically, we introduce three new metrics: (1) the distance complexity (reflecting power usage and wear-and-tear of robots), (2) the spatial complexity (reflecting the space needed for the algorithm to work), and (3) local computational complexity (reflecting the computational requirements for each robot in the swarm).

We apply these metrics in the study of some well-known and important problems, such as Complete Visibility and Arbitrary Pattern Formation. We also introduce and study a new problem, Doorway Egress, that captures the essence of a swarm’s navigation through restricted spaces. First, we examine the distance and spatial complexity used across a class of Complete Visibility algorithms. Second, we provide algorithms for Complete Visibility on an integer plane, including some that are asymptotically optimal in terms of time, distance complexity, and spatial complexity. Third, we introduce the problem of Doorway Egress and provide algorithms for a variety of robot swarm models with various optimalities. Finally, we provide an optimal algorithm for Arbitrary Pattern Formation on the grid.

Date

4-11-2022

Committee Chair

Vaidyanathan, Ramachandran

DOI

10.31390/gradschool_dissertations.5809

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