Thickness measurements using an ultrasonic contact test is a well-known nondestructive evaluation technique. However, its implementation in a robotic system with a closed-loop feedback control for artificial intelligent measurements requires precise information of positioning and force of the ultrasonic probe. In this work, we describe an ultrasonic probe developed in our lab that uses a semispherical soft membrane made from an elastomer. The aim is to develop a methodology for precise positioning and force control of a dry contact ultrasonic probe based on the ultrasonic signal information processed using sparse matrix optimization and Fourier analysis techniques. The results show that the proposed methodology makes easy to achieve a fine tuning of the probe orientation with high sensitivity to load and misalignment in order to perform accurate thickness measurements.