We introduce a new method for synthesizing kinematic relationships for a general class of continuous backbone, or continuum, robots. The resulting kinematics enable real-time task and shape control by relating workspace (Cartesian) coordinates to actuator inputs, such as tendon lengths or pneumatic pressures, via robot shape coordinates. This novel approach, which carefully considers physical manipulator constraints, avoids artifacts of simplifying assumptions associated with previous approaches, such as the need to fit the resulting solutions to the physical robot. It is applicable to a wide class of existing continuum robots and models extension, as well as bending, of individual sections. In addition, this approach produces correct results for orientation, in contrast to some previously published approaches. Results of real-time implementations on two types of spatial multisection continuum manipulators are reported.

Development methods for (sequential) programs that run in isolation have been studied elsewhere. Programs that run in parallel can interfere with each other, either via shared storage or by sending messages. Extensions to earlier development methods are proposed for the rigorous development of interfering programs. In particular, extensions to the specification method based on postconditions that are predicates of two states and the development methods of operation decomposition and data refinement are proposed.

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This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Journal of Logic and Computation following peer review. The definitive publisher-authenticated version (Coleman JW, Jones CB. A structural proof of the soundness of rely/guarantee rules.

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This paper traces the important steps in the history-up to around 1990-of research on reasoning about programs. The main focus is on sequential imperative programs but some comments are made on concurrency. Initially, researchers focussed on ways of verifying that a program satisfies its specification (or that two programs were equivalent). Over time it became clear that post facto verification is only practical for small programs and attention turned to verification methods which support the development of programs; for larger programs it is necessary to exploit a notation of compositionality. Coping with concurrent algorithms is much more challenging-this and other extensions are considered briefly. The main thesis of this paper is that the idea of reasoning about programs has been around since they were first written; the search has been to find tractable methods.

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