Abstract
The paper proposes a mathematical formalism for describing artificial sense-of-touch systems. Mathematical models for obtaining, processing, and interpreting tactile information are provided. 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. Within 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 to mathematicians, mechanicians, physicians, and engineers who construct or use artificial sense-of-touch systems.
Similar content being viewed by others
References
ARTANN Laboratories, Inc., http://www.artannlabs.com.
J. P. Bell, Experimental Foundations of Deformable Rigid-Body Mechanics. Pt 1. Small Deformations [Russian translation], Nauka, Moscow (1984).
R. Hooke, Lectures de Potentia Restitutiva, or Of Spring, Explaining the Power of Springing Bodies, J. Martyn, London (1678); R. T. Gunther, ed., Early Science in Oxford, Vol. VIII, R. T. Gunther, Oxford (1931), pp. 331–356.
G. W. Leibniz, “Letter to Jacobus Bernoulli,” in: C. I. Gerhardt, ed., Leibniz’ Mathematische Schriften, Vol. III, Abt. 1, Berlin (1855), S. 13–20; G. Olms, Hildesheim (1962).
Medical Tactile Inc., http://www.medicaltactile.com.
Palpometer Systems, Inc., http://www.palpometer.ca.
Pressure Profile Systems, Inc., http://www.pressureprofile.com.
Tachi Laboratory. The University of Tokyo Graduate School of Information Science and Technology, http://www.star.t.u-tokyo.ac.jp.
Tekscan, Inc., http://www.tekscan.com.
V. A. Vinokurov, Particle from Medium. Mathematical Methods and Models [in Russian] (2002), http://vinokur.narod.ru/vinbook.html.
V. A. Vinokurov, Mathematical Description of a Finite Compression of Complex Rigid Bodies [in Russian] (2008), http://vinokur.narod.ru/findef.pdf.
V. A. Vinokurov and V. A. Sadovnichy, Mathematical Description of Artificial Sense-of-Touch Systems [in Russian] (2008), http://vinokur.narod.ru/sat.pdf.
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 15, No. 4, pp. 5–28, 2009.
Rights and permissions
About this article
Cite this article
Vinokurov, V.A., Sadovnichy, V.A. Mathematical description of artificial sense-of-touch systems. J Math Sci 169, 413–429 (2010). https://doi.org/10.1007/s10958-010-0054-3
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-010-0054-3