Constrained maximum likelihood estimation of the principal curvatures on the object surface in an ultrasonic tactile sensing

Abstract

The maximum likelihood estimation (MLE) provides a robust solution in matched-field imaging (MFI), which has evolved from various underwater acoustic applications successfully. In the identification of the principal curvatures during the medical or robotic applications of acoustic tactile sensing, matched field processing offers a reasonable detection of the reflected wavefront. Two major difficulties, however, are there in the principal curvature identification. The first reason is that the wavefront reflected by the elliptic paraboloidal or the hyperbolic 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. The MFI scenario, therefore, can solve the nonlinear optimization problem in order to identify the curvature. In this paper, the proposed identification algorithm seeks the unique KKT (Karush–Kuhn–Tucker) point in the augmented Lagrange function of the constrained likelihood function, which is defined over the observed signal field. Furthermore, several acoustical experiments show that the proposed tactile sensor can identify the principal curvatures of the following surface cases: (1) plane, (2) paraboloid, (3) elliptic paraboloid, and (4) hyperbolic paraboloid.