О направленном перемещении графоходного автомата без компаса на бесконечной цепи

Решена задача организации направленного перемещения графоходного автомата без компаса на бесконечной цепи (т. е. бесконечном связном 2-регулярном графе). Получены необходимые и достаточные условия в виде ограничений на свойства автомата и разметку цепи, при которых автомат сохраняет направление перемещения на цепи. Предложены два типа вершинной разметки цепи, допускающие направленное перемещение автомата: так называемые детерминированная и слабо детерминированная разметки. Разработаны методы и алгоритмы обхода автоматом конечных и бесконечных помеченных цепей. Для обоих типов разметки разработаны алгоритмы разметки цепей, все вершины которых не помечены или помечены одной и той же меткой. Полученные результаты закладывают основы для изучения навигации автоматов без компаса и их коллективов в стационарных однородных дискретных средах.Розв’язано задачу органiзацiї спрямованого перемiщення графохiдного автомату без компаса на нескiнченному ланцюзi (тобто нескiнченному зв’язному 2-регулярному графi). Отриманi необхiднi та достатнi умови у виглядi обмежень на властивостi автомата i розмiтку ланцюга, за яких автомат зберiгає напрямок перемiщення на ланцюзi. Запропоновано два типи вершинної розмiтки ланцюгу, що допускають спрямоване перемiщення автомата: так званi детермiнована i слабо детермiнована розмiтки. Розроблено методи та алгоритми обходу автоматом скiнченних i нескiнченних помiчених ланцюгiв. Для обох типiв розмiтки розроблено алгоритми розмiтки ланцюгiв, усi вершини яких не позначенi або позначенi однiєю i тiєю ж позначкою. Отриманi результати закладають основи для вивчення навiгацiї автоматiв без компасу та їх колективiв у стацiонарних однорiдних дискретних середовищах.This paper deals with the problem of organizing a directional movement of a graph-walking automaton on infinite path graph (i.e. infinite connected two-regular graph)

Directional movement of a collective of compassless automata on square lattice of width 2

We study the following problem: Can a collective of finite automata maintain directed movement on a two-dimensional integer lattice of width 2, where the elements (vertices) are anonymous? The automata do not distinguish between vertices based on their coordinates of direction (that means each automaton has no compass). We considered collectives consisting of an automaton and some pebbles, which are automata of the simplest form, whose positions are entirely determined by the automaton. We demonstrate that a collective of one automaton and a maximum of three pebbles cannot maintain a direction of movement on the lattice. However, a collective of one automaton and four pebbles can do so

A general class of combinatorial filters that can be minimized efficiently

State minimization of combinatorial filters is a fundamental problem that arises, for example, in building cheap, resource-efficient robots. But exact minimization is known to be NP-hard. This paper conducts a more nuanced analysis of this hardness than up till now, and uncovers two factors which contribute to this complexity. We show each factor is a distinct source of the problem's hardness and are able, thereby, to shed some light on the role played by (1) structure of the graph that encodes compatibility relationships, and (2) determinism-enforcing constraints. Just as a line of prior work has sought to introduce additional assumptions and identify sub-classes that lead to practical state reduction, we next use this new, sharper understanding to explore special cases for which exact minimization is efficient. We introduce a new algorithm for constraint repair that applies to a large sub-class of filters, subsuming three distinct special cases for which the possibility of optimal minimization in polynomial time was known earlier. While the efficiency in each of these three cases previously appeared to stem from seemingly dissimilar properties, when seen through the lens of the present work, their commonality now becomes clear. We also provide entirely new families of filters that are efficiently reducible.Comment: 9 pages, 3 figure

Sensing and Infrastructure Design for Robots: A Plan-Based Perspective

Currently there do not exist general-purpose robots, and the procedures by which robots are designed are often ad hoc. Additionally, designers must deal with considerations including budget, energy requirements, and the availability of parts, all of which complicate the problem. Abstract formal theories have, among other benefits, the potential to assist designers in developing and understanding the capabilities of novel robotic systems. Of particular interest is the concept of action-based sensors, which focus on the idea that a robot need only know enough to know what action to perform next. As a mathematical abstraction, action-based sensors prescribe actions to the agent; details of the sensor itself are irrelevant. From this information-oriented perspective, this concept also links planning directly to the design problem: the definition of what action “should” be taken depends upon the plan a robot is executing, serving to specify its desired behavior. While the theoretical abstractions of sensors are technology-neutral, we present ways to connect action-based sensors to the considerations and constraints faced by real robot designers. Action-based sensors have been formalized in terms of specific plans (informally those that take the fewest actions to achieve a goal), but there exist cases in which it is useful to consider other plans. In extending this formalization to include all plans, we find that certain plans have obstructions that prevent their expression as action-based sensors. We have developed an algorithm to remove these obstructions, which result from the interactions between a robot and its environment. After this, we move from the question of what a robot must sense about the environment to the question of how an environment should provide information. The use of infrastructure for spaces shared by multiple agents is another way in which designers can simplify tasks for agents. The complexity of this design problem arises from infrastructure’s ability to modify both what an agent observes and the outcome of actions. We present a method for modeling the impact of infrastructure to determine its utility to a given agent, and also consider how the utility of the infrastructure can vary depending on the differing needs of agents and how they make use of the environment. The present work, in addition to extending Erdmann’s original theory, focuses on the way in which information that must be retained by the agent can be contained within a plan’s structure. Use of a graph-based framework allows for us to identify if that structure is necessary for successful execution of the plan. This dissertation then shifts to a complementary design problem, examining the ability of infrastructure to externalize information and actuation requirements. It also presents a model for predicting the impact of introducing new infrastructure. Finally, it will explore the ways in which information can be used to estimate sensor failures in robots and bound the space of possible configurations. Transitioning from the design of robots and their environments to their operation, this dissertation also presents a method for estimating sensor failures. Through knowledge of the world structure and expected observations, inconsistencies can be tracked to form hypotheses on potential sensor failures. We introduce a lattice-based method of expressing these failures, as well as an algorithm for tracking inconsistencies. The algorithm allows for an often concise representation of a potentially exponential set of hypotheses, enabling use during a robot’s execution. This basis also allows for the robot to determine if a failure interferes with its ability to complete a task. We also present a method through which the sensors that are required for task completion can be determined at any point. The primary means to validate the theoretical results in this dissertation are a range of case studies. For action-based sensors, we consider several varieties of design problems including sensor selection and navigation problems. Moving beyond the sets of action-based sensors considered in these design problems, we also examine concise combinatorial representations for sets of sensors more generally, and apply these to settings involving robot self-diagnosis. For infrastructure, we provide a taxonomy as a guide by which to examine several different cases in which infrastructure is introduced to an environment. These case studies focus both on changes in agent behavior after being introduced, as well as ways in which the value of the introduced infrastructure can be deter-mined. For the identification of sensor failures, an example is also presented that demonstrates the concise nature of the model, particularly when compared to naïve methods