Formal methods for control synthesis in partially observed environments : application to autonomous robotic manipulation

Modern robots are increasingly expected to function in uncertain and dynamically challenging environments, often in proximity with humans. In addition, wide scale adoption of robots requires on-the-fly adaptability of software for diverse application. These requirements strongly suggest the need to adopt formal representations of high level goals and safety specifications, especially as temporal logic formulas. This approach allows for the use of formal verification techniques for controller synthesis that can give guarantees for safety and performance. Robots operating in unstructured environments also face limited sensing capability. Correctly inferring a robot's progress toward high level goal can be challenging.

This thesis develops new algorithms for synthesizing discrete controllers in partially known environments under specifications represented as linear temporal logic (LTL) formulas. It is inspired by recent developments in finite abstraction techniques for hybrid systems and motion planning problems. The robot and its environment is assumed to have a finite abstraction as a Partially Observable Markov Decision Process (POMDP), which is a powerful model class capable of representing a wide variety of problems. However, synthesizing controllers that satisfy LTL goals over POMDPs is a challenging problem which has received only limited attention.

This thesis proposes tractable, approximate algorithms for the control synthesis problem using Finite State Controllers (FSCs). The use of FSCs to control finite POMDPs allows for the closed system to be analyzed as finite global Markov chain. The thesis explicitly shows how transient and steady state behavior of the global Markov chains can be related to two different criteria with respect to satisfaction of LTL formulas. First, the maximization of the probability of LTL satisfaction is related to an optimization problem over a parametrization of the FSC. Analytic computation of gradients are derived which allows the use of first order optimization techniques.

The second criterion encourages rapid and frequent visits to a restricted set of states over infinite executions. It is formulated as a constrained optimization problem with a discounted long term reward objective by the novel utilization of a fundamental equation for Markov chains - the Poisson equation. A new constrained policy iteration technique is proposed to solve the resulting dynamic program, which also provides a way to escape local maxima.

The algorithms proposed in the thesis are applied to the task planning and execution challenges faced during the DARPA Autonomous Robotic Manipulation - Software challenge.

Formal methods in the foundations of science

The intent of this study is to provide formal apparatus which facilitates the investigation of problems in the methodology of science. The introduction contains several examples of such problems and motivates the subsequent formalism.

A general definition of a formal language is presented, and this definition is used to characterize an individual’s view of the world around him. A notion of empirical observation is developed which is independent of language. The interplay of formal language and observation is taken as the central theme. The process of science is conceived as the finding of that formal language that best expresses the available experimental evidence.

To characterize the manner in which a formal language imposes structure on its universe of discourse, the fundamental concepts of elements and states of a formal language are introduced. Using these, the notion of a basis for a formal language is developed as a collection of minimal states distinguishable within the language. The relation of these concepts to those of model theory is discussed.

An a priori probability defined on sets of observations is postulated as a reflection of an individual’s ontology. This probability, in conjunction with a formal language and a basis for that language, induces a subjective probability describing an individual’s conceptual view of admissible configurations of the universe. As a function of this subjective probability, and consequently of language, a measure of the informativeness of empirical observations is introduced and is shown to be intuitively plausible – particularly in the case of scientific experimentation.

The developed formalism is then systematically applied to the general problems presented in the introduction. The relationship of scientific theories to empirical observations is discussed and the need for certain tacit, unstatable knowledge is shown to be necessary to fully comprehend the meaning of realistic theories. The idea that many common concepts can be specified only by drawing on knowledge obtained from an infinite number of observations is presented, and the problems of reductionism are examined in this context.

A definition of when one formal language can be considered to be more expressive than another is presented, and the change in the informativeness of an observation as language changes is investigated. In this regard it is shown that the information inherent in an observation may decrease for a more expressive language.

The general problem of induction and its relation to the scientific method are discussed. Two hypotheses concerning an individual’s selection of an optimal language for a particular domain of discourse are presented and specific examples from the introduction are examined.

Lightweight Formal Methods for the Development of High-Assurance Networking Systems

We survey several of the research efforts pursued by the iBench and snBench projects in the CS Department at Boston University over the last half dozen years. These activities use ideas and methodologies inspired by recent developments in other parts of computer science -- particularly in formal methods and in the foundations of programming languages -- but now specifically applied to the certification of safety-critical networking systems. This is research jointly led by Azer Bestavros and Assaf Kfoury with the participation of Adam Bradley, Andrei Lapets, and Michael Ocean.

Fuzzy concepts and formal methods

It has been recognised that formal methods are useful as a modelling tool in requirements engineering. Specification languages such as Z permit the precise and unambiguous modelling of system properties and behaviour. However some system problems, particularly those drawn from the information systems problem domain, may be difficult to model in crisp or precise terms. It may also be desirable that formal modelling should commence as early as possible, even when our understanding of parts of the problem domain is only approximate. This thesis suggests fuzzy set theory as a possible representation scheme for this imprecision or approximation. A fuzzy logic toolkit that defines the operators, measures and modifiers necessary for the manipulation of fuzzy sets and relations is developed. The toolkit contains a detailed set of laws that demonstrate the properties of the definitions when applied to partial set membership. It also provides a set of laws that establishes an isomorphism between the toolkit notation and that of conventional Z when applied to boolean sets and relations. The thesis also illustrates how the fuzzy logic toolkit can be applied in the problem domains of interest. Several examples are presented and discussed including the representation of imprecise concepts as fuzzy sets and relations, system requirements as a series of linguistically quantified propositions, the modelling of conflict and agreement in terms of fuzzy sets and the partial specification of a fuzzy expert system. The thesis concludes with a consideration of potential areas for future research arising from the work presented here.

How to Improve the Production Process for interactive TV with semi-formal Methods

The central question for this paper is how to improve the production process by closing the gap between industrial designers and software engineers of television(TV)-based User Interfaces (UI) in an industrial environment. Software engineers are highly interested whether one UI design can be converted into several fully functional UIs for TV products with different screen properties. The aim of the software engineers is to apply automatic layout and scaling in order to speed up and improve the production process. However, the question is whether a UI design lends itself for such automatic layout and scaling. This is investigated by analysing a prototype UI design done by industrial designers. In a first requirements study, industrial designers had created meta-annotations on top of their UI design in order to disclose their design rationale for discussions with software engineers. In a second study, five (out of ten) industrial designers assessed the potential of four different meta-annotation approaches. The question was which annotation method industrial designers would prefer and whether it could satisfy the technical requirements of the software engineering process. One main result is that the industrial designers preferred the method they were already familiar with, which therefore seems to be the most effective one although the main objective of automatic layout and scaling could still not be achieved.

Formal methods @ runtime

Heuristics, simulation, artificial intelligence techniques and combinations thereof have all been employed in the attempt to make computer systems adaptive, context-aware, reconfigurable and self-managing. This paper complements such efforts by exploring the possibility to achieve runtime adaptiveness using mathematically-based techniques from the area of formal methods. It is argued that formal methods @ runtime represents a feasible approach, and promising preliminary results are summarised to support this viewpoint. The survey of existing approaches to employing formal methods at runtime is accompanied by a discussion of their challenges and of the future research required to overcome them. © 2011 Springer-Verlag.

Formal methods for the development and verification of autonomic IT systems

This chapter explores ways in which rigorous mathematical techniques, termed formal methods, can be employed to improve the predictability and dependability of autonomic computing. Model checking, formal specification, and quantitative verification are presented in the contexts of conflict detection in autonomic computing policies, and of implementation of goal and utility-function policies in autonomic IT systems, respectively. Each of these techniques is illustrated using a detailed case study, and analysed to establish its merits and limitations. The analysis is then used as a basis for discussing the challenges and opportunities of this endeavour to transition the development of autonomic IT systems from the current practice of using ad-hoc methods and heuristic towards a more principled approach. © 2012, IGI Global.