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.

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This work presents the dynamic modeling and active vibration control of planar multilink manipulators having flexible links. Since the eigenvalue problem of such continuous structures is strongly dependent on the posture configuration, at first an efficient matrix formulation is provided in order to derive exact natural frequencies and mode shapes of a robot in its general posture. The analytical modal data are used to develop the forced vibration model; this is accomplished through the analytical decoupling of the modal coordinates of the manipulator; to this latter end, orthogonality conditions of modal shapes sets of planar multilink manipulators are demonstrated. The suppression of vibrations is challenged through a full-state linear quadratic regulator controller by optimally placing collocated sensor/actuator pairs. An optimal stochastic observer is designed in line with the noise-corrupted truncated model, i.e. the continuous Kalman-Bucy filter. The simulation results demonstrate that the presented matrix formulation for deriving exact modal data is effective, and the designed control method, along with the forcedvibration solving strategy, is feasible and efficient.

This paper introduces two analytical matrix descriptions of the differential eigenvalue problem concerning each admissible posture of a two-link flexible manipulator. In the hypothesis of the Euler-Bernoulli beam theory, analytical natural frequencies and mode shapes are derived through both formulations, which are obtained according to an axial and transverse dynamic characterization of the manipulator links. As is demonstrated by several simulations, such formulations give identical analytical results, though having very different matrix structures. Moreover, additional simulations through a finite element package confirm the analytical predictions of both methods presented herein.

Timoshenko's theory is adopted in order to accurately describe the freely vibrating dynamics of a multilink flexible manipulator. It is herein presented an analytical modelling strategy that extends previous works through a more refined model which accounts for elastic complicating effects along with lumped inertial loads which are typically mounted on joints of manipulators; in this regard, more accurate results are provided. The eigenproblem is presented from an analytical point of view through a matrix formulation, thus providing an essentially closed formula. Apart from the limitations of the implementing calculator, the formulation can take into account an arbitrary number of links in an arbitrary settled configuration, thus allowing relevant analytical analysis and avoiding the need to recur to nonimmediate numerical schemes. Once the analytical model is introduced, solutions are compared to both those achieved by previous models and those obtained by a finite elements method.