Topograhical image reconstruction via differential geometry in the ultrasonic tactile sensing system

Abstract

This paper describes a topographic image reconstruction via differential geometry using a proposed acoustical tactile sensing probe. The proposed tactile sensing system has an ability to identify the principal curvatures of the object surface by detecting reflected wave fronts. Two major difficulties, however, exist in the principal curvature identification. The first reason is that the wave front reflected by the paraboloidal surface cannot be described in the combination of the plane waves nor the spherical waves strictly. The second is that the principal curvature identification process becomes ill-posed due to the nonlinear relationship between the principal curvatures and propagation time of flight. Avoiding these difficulties, the proposed sensing system seeks the unique point over the manifold which satisfies the Snell’s law. After the principal curvature estimation at several points over the object surface, the topographic image of the surface can be reconstructed via geometrical connection. Connecting identified principal curvatures and principal direction, the differential geometrical method then provides a smooth surface description and discrimination following plane and paraboloidal surfaces: (1) plane, (2) paraboloid, (3) elliptic paraboloid, (4) hyperbolic paraboloid. Further, several acoustical experiments show that the tactile sensor can identify the principal direction and curvatures of the paraboloidal surfaces.