Clustering and PCA for Reconstructing Two Perpendicular Planes Using Ultrasonic Sensors

Abstract

In this paper, the authors make use of sonar transducers to detect the corner of two orthogonal panels and they propose a strategy for accurately reconstructing the surfaces. In order to point a linear array of four sensors at the desired position, the motion of a digital motor is appropriately controlled. When the sensors are directed towards the intersection between the planes, longer times of flight are observed because of multiple reflections. All the concerned distances have to be excluded and that is why an indicator based on the output signal energy is introduced. A clustering technique allows for the partitioning of the dataset in three clusters and the indicator selects the subset containing misrepresented information. The remaining distances are corrected so as to take into consideration the directivity and they permit the plotting of two sets of points in a three-dimensional space. In order to leave out the outliers, each set is filtered by means of a confidence ellipsoid which is defined by the Principal Component Analysis (PCA). The best-fit planes are obtained based on the principal directions and the variances. Experimental tests and results are shown demonstrating the effectiveness of this new approach.

New Methods for Robotic Perception by Using in-Air Sonar Data

“…The sonar sensor array used in all the tests is described in [4][5][6][7][8][9][10][11] and is reproduced here for clarity. It is composed of two types of ultrasonic sensors: the Hagisonic AniBat HG-M40DAI and the HG-M40DNI [12].…”

“…The same sensor array has also been used for evaluating the orientation of a wall; in this case, the tripod has been rotated in such a way that the array rotation axis z is perpendicular to the xy plane to obtain a right-handed orientation (as in Figure 2). All the technical details of the electronic boards that were realized -the sensor electrical connections and rectangular driving signal generation with a frequency of 12.5 Hz, the duty cycle of 4% and the amplitude of 4 V -are fully described in [4][5][6][7][8][9][10][11]. The TOF is estimated by the period that elapsed from the rising edge of the input pulse to the rising edge of the output pulse, while all the output signals were acquired by the acquisition board NI-USB 6210 [14].…”

“…The authors dealt with this problem by developing and testing algorithms for obstacle detection and reconstruction using in-air sonar sensors [4][5][6][7][8][9][10][11]. The present article involves recently published studies and summarizes all the significant findings in a unique contribution.…”

“…They realized an array of four ultrasonic sensors moved by a digital modular actuator [4] and utilized it to scan corners, planes, corridors and rooms [4][5][6][7][8][9][10][11]; the reconstruction algorithms used the digital sonic signals and the analogue full-waveforms. Moreover, they carefully examined the physical phenomenon of multiple reflections in the zone close to the intersection, introducing new reconstruction strategies based on powerful mathematical tools, such as Fuzzy C-Means (FCM) algorithm [4][5][6][7][8][9][10][11], RANdom SAmple Consensus (RANSAC) fitting [4][5][6]9], Principal Component Analysis (PCA) [7][8]9,11] and a function inspired by the Gibbs entropy [10].…”

“…Moreover, they carefully examined the physical phenomenon of multiple reflections in the zone close to the intersection, introducing new reconstruction strategies based on powerful mathematical tools, such as Fuzzy C-Means (FCM) algorithm [4][5][6][7][8][9][10][11], RANdom SAmple Consensus (RANSAC) fitting [4][5][6]9], Principal Component Analysis (PCA) [7][8]9,11] and a function inspired by the Gibbs entropy [10].…”