Kenneth Basye

Inferring finite automata with stochastic output functions and an application to map learning

It is often useful for a robot to construct a spatial representation of its environment from experiments and observations, in other words, to learn a map of its environment by exploration. In addition, robots, like people, make occasional errors in perceiving the spatial features of their environments. We formulate map learning as the problem of inferring from noisy observations the structure of a reduced deterministic finite automaton. We assume that the automaton to be learned has a distinguishing sequence. Observation noise is modeled by treating the observed output at each state as a random variable, where each visit to the state is an independent trial and the correct output is observed with probability exceeding 1/2. We assume no errors in the state transition function.Using this framework, we provide an exploration algorithm to learn the correct structure of such an automaton with probability 1 − δ, given as inputs δ, an upper bound m on the number of states, a distinguishing sequence s, and a lower bound α > 1/2 on the probability of observing the correct output at any state. The running time and the number of basic actions executed by the learning algorithm are bounded by a polynomial in δ−l, m, |s|, and (1/2-α)−1.We discuss the assumption that a distinguishing sequence is given, and present a method of using a weaker assumption. We also present and discuss simulation results for the algorithm learning several automata derived from office environments.

Coping with Uncertainty in Map-Learning

In many applications in mobile robotics, it is important for a robot to explore its environment in order to construct a representation of space useful for guiding movement. We refer to such a representation as a map, and the process of constructing a map from a set of measurements as map learning. In this paper, we develop a framework for describing map-learning problems in which the measurements taken by the robot are subject to known errors. We investigate approaches to learning maps under such conditions based on Valiants probably approximately correct learning model. We focus on the problem of coping with accumulated error in combining local measurements to make global inferences. In one approach, the effects of accumulated error are eliminated by the use of local sensing methods that never mislead but occasionally fail to produce an answer. In another approach, the effects of accumulated error are reduced to acceptable levels by repeated exploration of the area to be learned. We also suggest some insights into why certain existing techniques for map learning perform as well as they do. The learning problems explored in this paper are quite different from most of the classification and boolean-function learning problems appearing in the literature. The methods described, while specific to map learning, suggest directions to take in tackling other learning problems.

A decision-theoretic approach to planning, perception, and control

The application of Bayesian decision theory as a framework for designing high-level robotic control systems is discussed. The approach to building planning and control systems integrates sensor fusion, prediction, and sequential decision making. The system explicitly uses the value of sensor information as well as the value of actions that facilitate further sensing. A stochastic decision model and a model for mobile-target localization used in the control system are described. A control system implemented to drive a small mobile robot equipped with eight sonar transducers with a maximum range of six meters and a visual processing system capable of identifying moving targets in its visual field and reporting their motion relative to the robot is also discussed.<<ETX>>

Learning dynamics: system identification for perceptually challenged agents

From the perspective of an agent, the input/output behavior of the environment in which it is embedded can be described as a dynamical system. Inputs correspond to the actions executable by the agent in making transitions between states of the environment. Outputs correspond to the perceptual information available to the agent in particular states of the environment. We view dynamical system identification as inference of deterministic finite-state automata from sequences of input/output pairs. The agent can influence the sequence of input/output pairs it is presented by pursuing a strategy for exploring the environment. We identify two sorts of perceptual errors: errors in perceiving the output of a state and errors in perceiving the inputs actually carried out in making a transition from one state to another. We present efficient, high-probability learning algorithms for a number of system identification problems involving such errors. We also present the results of empirical investigations applying these algorithms to learning spatial representations.

Uncertainty in Graph-Based Map Learning

For certain applications it is useful for a robot to predict the consequences of its actions. As a particular example, consider programming a robot to learn the spatial layout of its environment for navigation purposes. For this problem it is useful to represent the interaction of the robot with its environment as a deterministic finite automaton. In map learning the states correspond tolocally distinctive placesthe inputs to robot actions (navigation procedures), and the outputs to the information available through observation at a given place. In general, it is not possible to infer the exact structure of the underlying automaton(e.g.the robot’s sensors may not allow it to discriminate among distinct structures). However, even learning just thediscernible structure of its environment is not an easy problem when various types of uncertainty are considered. In this chapter we will examine the effects of only having probablistic information about transitions between states and only probablistic knowledge of the identity of the current state. Using this theoretical framework we can then determine whether it is at all possible for a given robot to learn some specific environment and, if so, how long this can be expected to take.

Map Learning with Indistinguishable Locations

Abstract Nearly all spatial reasoning problems involve uncertainty of one sort or another. Uncertainty arises due to the inaccuracies of sensors used in measuring distances and angles. We refer to this as directional uncertainty. Uncertainty also arises in combining spatial information when one location is mistakenly identified with another. We refer to this as recognition uncertainty. Most problems in constructing spatial representations ( maps ) for the purpose of navigation involve both directional and recognition uncertainty. In this paper, we show that a particular class of spatial reasoning problems involving the construction of representations of large-scale space can be solved efficiently even in the presence of directional and recognition uncertainty. We pay particular attention to the problems that arise due to recognition uncertainty.

Sensor abstractions for control of navigation

An approach to building high-level control systems for robotics that is based on Bayesian decision theory is presented. The authors show how this approach provides a natural and modular way of integrating sensing and planning. They develop a simple solution for a particular problem as an illustration. They also examine the cost of using such a model and consider the areas in which abstraction can reduce this cost. The authors focus on the area of spatial abstraction. They discuss an abstraction that has been used to solve problems involving robot navigation and give a detailed account of the mapping from raw sensor data to the abstraction.<<ETX>>

Graph-based mapping by mobile robots

We have developed a system for robotic map construction based on representing the robots environment as a finite automation. In this paper we first describe the automation model, then present an algorithm used to control exploration and construct a map. We describe the robotic systems used by the algorithm as procedures, and report on experiments performed using the system in simulation and in a real environment.

A decision-theoretic approach to robotic control systems

We present an approach to building high-level control systems for robotics based on Bayesian decision theory. We show how this approach provides a natural and modular way of integrating sensing and planning. We develop a simple solution for a particular problem as an illustration. We examine the cost of using such a model and consider the areas in which abstraction can reduce this cost. We focus on one area, spatial abstraction, and discuss the design issues that arise in choosing an abstraction that we have used to solve problems involving robot navigation, and give a detailed account of the mapping from raw sensor data to the abstraction.