Strain accuracy enhancement of stereo digital image correlation for objects deformation with large rotations

We propose a full-field stereo digital image correlation (DIC) strain measurement method in order to overcome the poor accuracy while measuring the deformation under large rotations. Such drawback comes from the missing of considering rotation movements of the deformed objects when calculating their strain values. To address that, we first used a DIC matching algorithm combined with rotated subset and feature point detection to obtain displacement fields. By employing a singular value decomposition (SVD) method, we then can calculate rotation matrices of the strain windows before and after deformations. Finally, in order to eliminate the strain errors caused by rotation, we introduced the rotation matrices into the classical pointwise least square (PLS) DIC strain calculation method. Both numerical simulations and experiments are performed, and the accuracy and effectiveness of the proposed method are confirmed by the experimental results.

Enhanced Potential Field-Based Collision Avoidance in Cluttered Three-Dimensional Urban Environments

With the various applications of unmanned aerial vehicles (UAVs), the number of UAVs will increase in limited airspace, leading to an increased risk collision. To reduce such potential risk, this work proposes a collision avoidance strategy for UAVs using an enhanced potential field (EPF) approach in cluttered three-dimensional urban environments. Using the EPF formulated in a two-dimensional environment, the avoidance maneuvers for both horizontal and vertical planes are generated by introducing rotation matrices, and these maneuvers are combined by applying a weighting factor. The numerical simulations with various meaningful scenarios are conducted to validate the performance of the proposed approach. To mimic practical situations, UAV dynamics and sensor limitations were considered. The simulation results show that the proposed approach provides an efficient, reliable, and collision-free path without local minima and unreachable goal issues.

Dwelling on the Connection Between SO(3) and Rotation Matrices in Rigid Multibody Dynamics – Part 1: Description of an Index-3 DAE Solution Approach

In rigid multibody dynamics simulation using absolute coordinates, a choice must be made in relation to how to keep track of the attitude of a body in 3D motion. The commonly used choices of Euler angles and Euler parameters each have drawbacks, e.g., singularities, and carrying along extra normalization constraint equations, respectively. This contribution revisits an approach that works directly with the orientation matrix and thus eschews the need for generalized coordinates used at each time step to produce the orientation matrix A. The approach is informed by the fact that rotation matrices belong to the SO(3) Lie matrix group. The numerical solution of the dynamics problem is anchored by an implicit first order integration method that discretizes, without index reduction, the index 3 Differential Algebraic Equations (DAEs) of multibody dynamics. The approach handles closed loops and arbitrary collections of joints. Our main contribution is the outlining of a systematic way for computing the first order variations of both the constraint equations and the reaction forces associated with arbitrary joints. These first order variations in turn anchor a Newton method that is used to solve both the Kinematics and Dynamics problems. The salient observation is that one can express the first order variation of kinematic quantities that enter the kinematic constraint equations, constraint forces, external forces, etc., in terms of Euler infinitesimal rotation vectors. This opens the door to a systematic approach to formulating a Newton method that provides at each iteration an orthonormal rotation matrix A. The Newton step calls for repeatedly solving linear systems of the form Gδ = e, yet evaluating the iteration matrix G and residuals e is inexpensive, to the point where in the Part 2 companion contribution the proposed formulation is shown to be two times faster for Kinematics and Dynamics analysis when compared to the Euler parameter and Euler angle approaches in conjunction with a set of four mechanisms.

OBJECT TRACKING CONTROL USING A GIMBAL MECHANISM

This work describes a control solution for real time object tracking in images acquired for a RPAS on an object inspection environment. This, controlling a 3-axis gimbal mechanism to control a camera orientation embedded to a RPAS, using its image processed for feedback. The objective of control is to maintain the target of interest at the center of the image plane. The proposed solution uses a YOLOv3 object detection model in order to detect the target object and determine, thru rotation matrices, the new desired angles to converge the object’s position to the center of the image. To compare results of the proposed control, a linear control was tuned using a linear PI algorithm. Simulation and practice experiments successfully tracked the desired object in real time using YOLOv3 in both control approaches presented.

Model independent analysis of Dirac CP violating phase for some well-known mixing scenarios

In this paper, we present a model independent analysis of Leptonic CP violation for some well-known mixing scenarios. In particular, we considered modified schemes for bimaximal (BM), democratic (DC), hexagonal (HG) and tribimaximal (TBM) mixing for our numerical investigation. These model independent corrections to mixing matrices are parametrized in terms of complex rotation matrices [Formula: see text] with related modified PMNS matrix of the forms [Formula: see text] where [Formula: see text] is a complex rotation in [Formula: see text] sector and [Formula: see text] is unperturbed mixing scheme. We present generic formulae for mixing angles, Dirac CP phase [Formula: see text] and Jarlskog invariant [Formula: see text] in terms of correction parameters. The parameter space of each modified mixing case is scanned for fitting neutrino mixing angles using [Formula: see text] approach and the corresponding predictions for Leptonic CP phase [Formula: see text] and Jarlskog invariant [Formula: see text] has been evaluated from allowed parameter space. The obtained ranges are reported for all viable cases.

A quaternion-group knowledge graph embedding model

Capturing the composite embedding representation of a multi-hop relation path is an extremely vital task in knowledge graph completion. Recently, rotation-based relation embedding models have been widely studied to embed composite relations into complex vector space. However, these models make some over-simplified assumptions on the composite relations, resulting the relations to be commutative. To tackle this problem, this paper proposes a novel knowledge graph embedding model, named QuatGE, which can provide sufficient modeling capabilities for complex composite relations. In particular, our method models each relation as a rotation operator in quaternion group-based space. The advantages of our model are twofold: (1) Since the quaternion group is a non-commutative group (i.e., non-Abelian group), the corresponding rotation matrices of composite relations can be non-commutative; (2) The model has a more expressive setting with stronger modeling capabilities, which is flexible to model and infer the complete relation patterns, including: symmetry/anti-symmetry, inversion and commutative/non-commutative composition. Experimental results on four benchmark datasets show that the proposed method outperforms the existing state-of-the-art models for link prediction, especially on composite relations.