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Algebraic aspects of designing behavior based systems

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Algebraic Frames for the Perception-Action Cycle (AFPAC 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1315))

Abstract

We address in this paper the design of behavior based systems from a bottom-up viewpoint. Although behavior is an observable property of a system, and therefore immediately causes a topdown model, the approach has to be inverted to support the learning of equivalence classes of the perception-action cycle. After introducing the paradigm in the frame of a socio-ecological theory of biological systems, we discuss the natural science problems to be solved for successful design of behavior based systems by a bootstrap of perception-action cycles. The necessary fusion of robotics with computer vision, neural computation, and signal theory needs a common theoretical framework. This framework consists of a global algebraic frame for embedding the perceptual and motor categories, a local algebraic framework for bottom up construction of the necessary information, and a framework for learning and self-control, based on the equivalence of perception and action. Geometric algebra will be identified as the adequate global algebraic frame, and the Lie theory will be introduced as the local algebraic frame. We will demonstrate several applications of the frames in early visual processing. Finally, we will finish our discussion with the fusion of local approaches and the global algebraic frame with respect to both the formulation of an adequate multidimensional signal theory and the design of algebraic embedded neural processing. In both cases we will discuss the relation to the non-linear Volterra series approach, which, in our framework, will be reduced to a linear one.

This work was supported by DFG grant So 320-2-1.

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  1. Cognitive Systems Group, Institute of Computer Science, Christian-Albrechts-University, Kiel, Germany

    Gerald Sommer

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  1. Gerald Sommer
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Gerald Sommer Jan J. Koenderink

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Sommer, G. (1997). Algebraic aspects of designing behavior based systems. In: Sommer, G., Koenderink, J.J. (eds) Algebraic Frames for the Perception-Action Cycle. AFPAC 1997. Lecture Notes in Computer Science, vol 1315. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0017858

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  • DOI: https://doi.org/10.1007/BFb0017858

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  • Print ISBN: 978-3-540-63517-8

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