Geometric algebra as a framework for the perception—action cycle
In this paper we will present a mathematical framework for embedding the realization of technical systems which are designed on principles of the perception—action cycle (PAC). The use of PAC as a design principle of `systems which should have both capabilities of perception and action is motivated by ethology and has its theoretical roots in the theory of non—linear dynamic systems. PAC is the frame of autonomous behavior. It relates perception and action in a purposive manner. The global competence of such systems results from cooperation and competition of a set of behaviors, each as an observable manifestation of a certain kind of competence. If both acquired skill and experience are the sources to yield competence, there is hope also to gain such attractive system properties like robustness and adaptivity. The essence behind this extension of the active vision paradigm is a certain kind of equivalence between visual perception and action. That means both perceptual categories and those of actions are mutually supported and have to be mutually verified. Perception and action constitute the afferent and efferent interfaces of the agent to its environment. Using them in a mature stage the active agent stabilizes its relation to the environment by equalizing categories of perception with those of action. The first ones are defined by the experience that similar patterns cause similar actions (or reactions) and the second ones correspond to the skill that similar actions cause similar patterns. Following that line it should be possible to design both technical visual systems with support of active components of movement and seeing robots. This necessitates the fusion of computer vision (as active vision), robotics, signal processing, and neural computation. It becomes obvious that representations will take on central importance. They have to relate the agent with the environment in Euclidean space—time. Evaluating the actual situation with respect to the representation problem we have to state both serious shortcomings within the disciplines and gaps between them.
KeywordsClifford Algebra Projective Geometry Geometric Algebra Outer Product Geometric Product
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