A New Strategy for Spatial Reconstruction of Orthogonal Planes Using a Rotating Array of Ultrasonic Sensors

In this paper, the authors present a new strategy for accurately reconstructing an L-shaped obstacle such as some wooden panels opportunely connected so as to form a right angle. The mechatronics scanning system consists of four inexpensive ultrasonic sensors moved in three-dimensional (3-D) space by means of a digital motor. The motor rotation is controlled in order to point the sensor array at the target and to obtain distance measurements for each shaft position. Ultrasonic distance sensors propagate large beams and feel the significant effect of multiple reflections. For the sake of excluding all misrepresented distance values at the intersection of the planes, the proposed approach uses powerful mathematical tools together with a physical indicator based on the reflected signal energy. The Fuzzy C-Means (FCM) classification allows partitioning a data set, and the introduced physical indicator is able to select the specific cluster corresponding to the spurious distances. Each remaining cluster permits to calculate the equation of a plane because it is referred to the distance values deriving from a direct reflection. These distances are then transformed considering the sensors directivity and the direction of reflection so as to obtain two sets of 3-D points. Finally, the reconstruction of each plane is achieved by the RANdom SAmple Consensus (RANSAC) in such a way as to better fit these points. The details of this strategy and the experimental tests are shown, demonstrating the applicability and the good results.