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Performance and storage requirements of topology-conserving maps for robot manipulator control
(1989)
A new programming paradigm for the control of a robot manipulator by learning the mapping between the Cartesian space and the joint space (inverse Kinematic) is discussed. It is based on a Neural Network model of optimal mapping between two high-dimensional spaces by Kohonen. This paper describes the approach and presents the optimal mapping, based on the principle of maximal information gain. It is shown that Kohonens mapping in the 2-dimensional case is optimal in this sense. Furthermore, the principal control error made by the learned mapping is evaluated for the example of the commonly used PUMA robot, the trade-off between storage resources and positional error is discussed and an optimal position encoding resolution is proposed.
The human mind may produce prototypization within virtually any realm of cognition and behavior. A "comparative prototype-typology" might prove to be an interesting field of study – perhaps a new subfield of semiotics. This, however, would presuppose a clear view on the samenesses and differences of prototypization in these various fields. It seems realistic for the time being that the linguist first confine himself to describing prototypization within the realm of language proper. The literature on prototypes has steadily grown in the past ten years or so. I confine myself to mentioning the volume on Noun Classes and Categorization, edited by C. Craig (1986), which contains a wealth of factual information on the subject, along with some theoretical vistas. By and large, however, linguistic prototype research is still basically in a taxonomic stage - which, of course, represents the precondition for moving beyond. The procedure is largely per ostensionem, and by accumulating examples of prototypes. We still lack a comprehensive prototype theory. The following pages are intended, not to provide such, a theory, but to do the first steps in this direction. Section 2 will feature some elements of a functional theory of prototypes. They have been developed by this author within the frame of the UNITYP model of research on language universals and typology. Section 3 will bring a discussion of prototypization with regard to selected phenomena of a wide range of levels of analysis: Phonology, morphosyntax, speech acts, and the lexicon. Prototypization will finally be studied within one of the universal dimensions, that of APPREHENSION - the linguistic representation of the concepts of objects – as proposed by Seiler (1986).
The Stanford Project on Language Universals began its activities in October 1967 and brought them to an end in August 1976. Its directors were Joseph H. Greenberg and Charles A. Ferguson. The Cologne Project on Language Universals and Typology [with particular reference to functional aspects], abbreviated UNITYP, had its early beginnings in 1972, but deployed its full activities from 1976 onwards and is still operating. This writer, who is the principal investigator, had the privilege of collaborating with the Stanford Project during spring of 1976. […] One of the leading Greenbergian ideas is that of implicational generalizations, has been integrated as a fundamental principle in the construction of continua and of universal dimensions as proposed by UNITYP. It is hoped that the following considerations on numeral systems will be apt to bear witness to this situation. They would be unthinkable without Greenberg’s pioneering work on "Generalizations about numeral systems" (Greenberg 1978: 249 ff., henceforth referred to as Greenberg, NS). Further work on this domain and on other comparable domains almost inevitably leads one to the view that generalizations of the Greenberg type have a functional significance and that a dimensional framework is apt to bring this to the fore. This is the view on linguistic behaviour as being purposeful, and on language as a problem- solving device. The problem consists in the linguistic representation of cognitive-conceptual ideas. The solution is represented by the corresponding linguistic structures in their diversity and the task of the linguist consists in reconstructing the program and subprograms underlying the process of problem-solving. It is claimed that the construct of continua and of universal dimensions makes these programs intelligible.