Continuation

Abstract: This paper is a tutorial introduction to the theory of programming language semantics developed by D. Scott and C. Strachey. The application of the theory to formal language specification is demonstrated and other applications are surveyed. The first language considered, LOOP, is very elementary and its definition merely introduces the notation and methodology of the approach. Then the semantic concepts of environments, stores, and continuations are introduced to model classes of programming language features and the underlying mathematical theory of computation due to Scott is motivated and outlined. Finally, the paper presents a formal definition of the language GEDANKEN.

Abstract: This paper presents a unique approach to the kinematic analysis of the most general six-degree-of-freedom, six-revolute-joint manipulators (Previously, the problem of computing all possible configurations of a manipulator corresponding to a given hand position was approached by reducing the problem to that of solving a high degree polynomial equation in one variable. -In-this-paper Jt is shown that the problem can be reduced to that of solving a system of eight second-degree equations in eight unknowns, it-is-fttrther-demrmstrate^-thafmis second-degree system can be routinely solved using a continuation algorithm. To complete the general analysis, a second numerical method—a continuation heuristic —is shown to generate partial solution sets quickly. Finally, in some special cases, closed form solutions wereobtained for some commonly used industrial manipulators. The results can be applied to the~analysis~of--both-six-~and-~fme'degreeuf-freedmn manipulators composed of mixed revolute and prismatic joints. The numerical stability of continuation on small second-degree systems opens the way for routine use in offline robot programming applications. \\

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