Robotic Swarms: Assembly and Complexity

This thesis focuses on the assembly of robotic swarms that move according to some global signal in a model called the “tilt” model. The model consists of a 2D board that contain open and blocked spaces, along with tiles or polyominoes that move toward a signaled cardinal direction. We look at two variations of this model called the single-step and full-tilt model, where the elements move single distances or maximally, respectively, when a signal is send. We show different methods of shape construction, defining board configurations that are universal for a set of shapes. Afterwards, we analyze different computational problems that arise from the tilt model in the latter chapters of this thesis. This thesis consists of published work in algorithmic and computational complexity conferences, along with new material that improve upon old contributions

A Multiple Radar Approach for Automatic Target Recognition of Aircraft using Inverse Synthetic Aperture Radar

Along with the improvement of radar technologies, Automatic Target Recognition (ATR) using Synthetic Aperture Radar (SAR) and Inverse SAR (ISAR) has come to be an active research area. SAR/ISAR are radar techniques to generate a two-dimensional high-resolution image of a target. Unlike other similar experiments using Convolutional Neural Networks (CNN) to solve this problem, we utilize an unusual approach that leads to better performance and faster training times. Our CNN uses complex values generated by a simulation to train the network; additionally, we utilize a multi-radar approach to increase the accuracy of the training and testing processes, thus resulting in higher accuracies than the other papers working on SAR/ISAR ATR. We generated our dataset with 7 different aircraft models with a radar simulator we developed called RadarPixel; it is a Windows GUI program implemented using Matlab and Java programming, the simulator is capable of accurately replicating a real SAR/ISAR configurations. Our objective is to utilize our multi-radar technique and determine the optimal number of radars needed to detect and classify targets.Comment: 8 pages, 9 figures, International Conference for Data Intelligence and Security (ICDIS

Covert Computation in Self-Assembled Circuits

Traditionally, computation within self-assembly models is hard to conceal because the self-assembly process generates a crystalline assembly whose computational history is inherently part of the structure itself. With no way to remove information from the computation, this computational model offers a unique problem: how can computational input and computation be hidden while still computing and reporting the final output? Designing such systems is inherently motivated by privacy concerns in biomedical computing and applications in cryptography. In this paper we propose the problem of performing "covert computation" within tile self-assembly that seeks to design self-assembly systems that "conceal" both the input and computational history of performed computations. We achieve these results within the growth-only restricted abstract tile assembly model (aTAM) with positive and negative interactions. We show that general-case covert computation is possible by implementing a set of basic covert logic gates capable of simulating any circuit (functionally complete). To further motivate the study of covert computation, we apply our new framework to resolve an outstanding complexity question; we use our covert circuitry to show that the unique assembly verification problem within the growth-only aTAM with negative interactions is coNP-complete

Signal Passing Self-Assembly Simulates Tile Automata

The natural process of self-assembly has been studied through various abstract models due to the abundant applications that benefit from self-assembly. Many of these different models emerged in an effort to capture and understand the fundamental properties of different physical systems and the mechanisms by which assembly may occur. A newly proposed model, known as Tile Automata, offers an abstract toolkit to analyze and compare the algorithmic properties of different self-assembly systems. In this paper, we show that for every Tile Automata system, there exists a Signal-passing Tile Assembly system that can simulate it. Finally, we connect our result with a recent discovery showing that Tile Automata can simulate Amoebot programmable matter systems, thus showing that the Signal-passing Tile Assembly can simulate any Amoebot system

Hardness of Reconfiguring Robot Swarms with Uniform External Control in Limited Directions

Motivated by advances is nanoscale applications and simplistic robot agents, we look at problems based on using a global signal to move all agents when given a limited number of directional signals and immovable geometry. We study a model where unit square particles move within a 2D grid based on uniform external forces. Movement is based on a sequence of uniform commands which cause all particles to move 1 step in a specific direction. The 2D grid board additionally contains \blocked spaces which prevent particles from entry. Within this model, we investigate the complexity of deciding 1) whether a target location on the board can be occupied (by any) particle (occupancy problem), 2) whether a specific particle can be relocated to another specific position in the board (relocation problem), and 3) whether a board configuration can be transformed into another configuration (reconfiguration problem). We prove that while occupancy is solvable in polynomial time, the relocation and reconfiguration problems are both NP-Complete even when restricted to only 2 or 3 movement directions. We further define a hierarchy of board geometries and show that this hardness holds for even very restricted classes of board geometry

Building Patterned Shapes in Robot Swarms with Uniform Control Signals

This paper investigates a restricted version of robot motion planning, in which particles on a board uniformly respond to global signals that cause them to move one unit distance in a particular direction. We look at the problem of assembling patterns within this model. We first derive upper and lower bounds on the worst-case number of steps needed to reconfigure a general purpose board into a target pattern. We then show that the construction of k-colored patterns of size-n requires Ω(n log k) steps in general, and Ω(n log k + √ k) steps if the constructed shape must always be placed in a designated output location. We then design algorithms to approach these lower bounds: We show how to construct k-colored 1 × n lines in O(n log k + k) steps with unique output locations. For general colored shapes within a w×h bounding box, we achieve O(wh log k+hk) steps

Relocating Units in Robot Swarms with Uniform Control Signals is PSPACE-Complete

This paper investigates a restricted version of robot motion planning, in which particles on a board uniformly respond to global signals that cause them to move one unit distance in a particular direction on a 2D grid board with geometric obstacles. We show that the problem of deciding if a particular particle can be relocated to a specified location on the board is PSPACE-complete when only allowing 1x1 particles. This shows a separation between this problem, called the relocation problem, and the occupancy problem in which we ask whether a particular location can be occupied by any particle on the board, which is known to be in P with only 1x1 particles. We then consider both the occupancy and relocation problems for the case of extremely simple rectangular geometry, but slightly more complicated pieces consisting of 1x2 and 2x1 domino particles, and show that in both cases the problems are PSPACE-complete

Real-Time Road Hazard Information System

Infrastructure is a significant factor in economic growth for systems of government. In order to increase economic productivity, maintaining infrastructure quality is essential. One of the elements of infrastructure is roads. Roads are means which help local and national economies be more productive. Furthermore, road damage such as potholes, debris, or cracks is the cause of many on-road accidents that have cost the lives of many drivers. In this paper, we propose a system that uses Convolutional Neural Networks to detect road degradations without data pre-processing. We utilize the state-of-the-art object detection algorithm, YOLO detector for the system. First, we developed a basic system working on data collecting, pre-processing, and classification. Secondly, we improved the classification performance achieving 97.98% in the overall model testing, and then we utilized pixel-level classification and detection with a method called semantic segmentation. We were able to achieve decent results using this method to detect and classify four different classes (Manhole, Pothole, Blurred Crosswalk, Blurred Street Line). We trained a segmentation model that recognizes the four classes mentioned above and achieved great results with this model allowing the machine to effectively and correctly identify and classify our four classes in an image. Although we obtained excellent accuracy from the detectors, these do not perform particularly well on embedded systems due to their network size. Therefore, we opted for a smaller, less accurate detector that will run in real time on a cheap embedded system, like the Google Coral Dev Board, without needing a powerful and expensive GPU

Full Tilt: Universal Constructors for General Shapes with Uniform External Forces

We investigate the problem of assembling general shapes and patterns in a model in which particles move based on uniform external forces until they encounter an obstacle. In this model, corresponding particles may bond when adjacent with one another. Succinctly, this model considers a 2D grid of “open” and “blocked” spaces, along with a set of slidable polyominoes placed at open locations on the board. The board may be tilted in any of the 4 cardinal directions, causing all slidable polyominoes to move maximally in the specified direction until blocked. By successively applying a sequence of such tilts, along with allowing different polyominoes to stick when adjacent, tilt sequences provide a method to reconfigure an initial board configuration so as to assemble a collection of previous separate polyominoes into a larger shape. While previous work within this model of assembly has focused on designing a specific board configuration for the assembly of a specific given shape, we propose the problem of designing universal configurations that are capable of constructing a large class of shapes and patterns. For these constructions, we present the notions of weak and strong universality which indicate the presence of “excess” polyominoes after the shape is constructed. In particular, for given integers h, w, we show that there exists a weakly universal configuration with O(hw) 1 × 1 slidable particles that can be reconfigured to build any h × w patterned rectangle. We then expand this result to show that there exists a weakly universal configuration that can build any h × w-bounded size connected shape. Following these results, which require an admittedly relaxed assembly definition, we go on to show the existence of a strongly universal configuration (no excess particles) which can assemble any shape within a previously studied “drop” class, while using quadratically less space than previous results. Finally, we include a study of the complexity of deciding if a particle within a configuration may be relocated to another position, and deciding if a given configuration may be transformed into a second given configuration. We show both problems to be PSPACE-complete even when no particles stick to one another and movable particles are restricted to 1 × 1 tiles and a single 2 × 2 polyomino