FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2009, VOLUME 15, NUMBER 4, PAGES 5-28

V. A. Vinokurov

V. A. Sadovnichy

Abstract

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The paper proposes a mathematical formalism for describing artificial sense-of-touch systems. Mathematical models of obtaining, processing, and interpreting tactile information are provided. The problems of encoding and reproducing tactile information are formulated and algorithms for solving these problems are proposed. The problem of interpreting tactile information is considered, and the corresponding simple mathematical model is studied. In the framework of this simple model, an exact solution of the interpretation problem is obtained for the case of finite deformations, and the insufficiency of the linear method (Hooke's law) for describing problems of interpreting tactile data is shown. The presentation of mathematical models for the theory of artificial sense-of-touch systems in this paper is the first such detailed presentation in the Russian literature. These models are of interest for mathematicians, mechanicians, physicians, and engineers who construct or use artificial sense-of-touch systems.

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