Learning Rotations

Many problems in computer vision today are solved via deep learning. Tasks like pose estimation from images, pose estimation from point clouds or structure from motion can all be formulated as a regression on rotations. However, there is no unique way of parametrizing rotations mathematically: matrices, quaternions, axis-angle representation or Euler angles are all commonly used in the field. Some of them, however, present intrinsic limitations, including discontinuities, gimbal lock or antipodal symmetry. These limitations may make the learning of rotations via neural networks a challenging problem, potentially introducing large errors. Following recent literature, we propose three case studies: a sanity check, a pose estimation from 3D point clouds and an inverse kinematic problem. We do so by employing a full geometric algebra (GA) description of rotations. We compare the GA formulation with a 6D continuous representation previously presented in the literature in terms of regression error and reconstruction accuracy. We empirically demonstrate that parametrizing rotations as bivectors outperforms the 6D representation. The GA approach overcomes the continuity issue of representations as the 6D representation does, but it also needs fewer parameters to be learned and offers an enhanced robustness to noise. GA hence provides a broader framework for describing rotations in a simple and compact way that is suitable for regression tasks via deep learning, showing high regression accuracy and good generalizability in realistic high-noise scenarios.

Recovery of the parameters of a focal zone by the data of earthquakes

We present an approach for solving the inverse kinematic problem of seismic with internal sources, based on the method of multidimensional data approximation on irregular grids. The times of arrival of elastic waves to the seismic stations are considered as known. The hodographs from earthquake to the stations are approximated for further determining the velocities of longitudinal and transverse waves using the eikonal equation. The ratio of these velocities determines the Poisson’s ratio, and the other elastic parameters of the medium can be found in units of the density. The results of implementation of the approach, based on the real data, are presented.

Trajectory Planning for a 3-SPS-U Tensegrity Mechanism

This article presents the actuation strategy of a 2-DOF tensegrity type mechanism that employs three tension springs and a passive universal joint. This mechanism is proposed to be incorporated as an articulation unit for a piping inspection robot in order to overcome pipe bends and junctions. In the event of a junction, external actuations are required to allow the mechanism as well as the robot to follow a certain direction. Using DC-motors coupled with encoders, experiments are carried out on a test bench of the tensegrity mechanism. The actuation of the mobile platform is performed using cables that pass through each spring. By correlating the architecture to a 3-SPS-U parallel mechanism, the singularity-free workspace of the mechanism is analyzed to identify the tilt limits. A closed-loop PID controller is implemented using a microcomputer to perform a linear trajectory within the singularity-free workspace. The Inverse Kinematic Problem (IKP) is solved by passing input tilt angles to the controller. With the help of a force control algorithm, the experiments are carried out under no-load conditions for vertical and horizontal orientations of the mechanism. The error data of the joint positions and the motor torques are then interpreted for both orientations of the mechanism.

LOCALIZATION OF MICROSEISMIC EVENTS USING PHYSICS-INFORMED NEURAL NETWORK SOLUTION TO THE EIKONAL EQUATION

The paper demonstrates an algorithm for using physics-informed neural networks in workflow of processing microseismic data regarding the problem of localization of microseismic events. The proposed algorithm involves the use of a physics-informed neural network solution to the eikonal equation to calculate the traveltimes of the first arrivals. As a result, the network solution is compared with the observed arrival times to solve the inverse kinematic problem to determine the coordinates of the event locations. Using a synthetic 3D example, it was shown that the average absolute error of the arrival time misfit was less than 0.25 ms, and the average localization error did not exceed 4.5 meters.

Exploiting Redundancies for Workspace Enlargement and Joint Trajectory Optimisation of a Kinematically Redundant Hybrid Parallel Robot

In this paper, possibilities for workspace enlargement and joint trajectory optimisation of a (6+3)-degree-of-freedom kinematically redundant hybrid parallel robot are investigated. The inverse kinematic problem of the robot can be solved analytically, which is a desirable property of redundant robots, and is implemented in the investigations. A new method for detecting mechanical interferences between two links which are not directly connected is proposed for evaluating the workspace. Redundant degrees of freedom are optimised in order to further expand the workspace. An approach for determining the desired redundant joint coordinates is developed so that a performance index can be minimised approximately when the robot is following a prescribed Cartesian trajectory. The presented approaches are readily applicable to other kinematically redundant hybrid parallel robots proposed by the authors.

Inverse and forward kinematics and workspace analysis of a novel 5-DOF (3T2R) parallel–serial (hybrid) manipulator

The proposed study provides a solution of the inverse and forward kinematic problems and workspace analysis for a five-degree-of-freedom parallel–serial manipulator, in which the parallel kinematic chain is made in the form of a tripod and the serial kinematic chain is made in the form of two carriages displaced in perpendicular directions. The proposed manipulator allows to realize five independent movements—three translations and two rotations motion pattern (3T2R). Analytical relationships between the coordinates of the end-effector and five controlled movements provided by manipulator’s drives (generalized coordinates) were determined. The approach of reachable workspace calculation was defined with respect to available design constraints of the manipulator based on the obtained algorithms of the inverse and forward kinematics. Case studies are considered based on the obtained algorithms of inverse and forward kinematics. For the inverse kinematic problem, the solution is obtained in accordance with the given laws of position and orientation change of the end-effector, corresponding to the motion along a spiral-helical trajectory. For the forward kinematic problem, various assemblies of the manipulator are obtained at the same given values of the generalized coordinates. An example of reachable workspace designing finalizes the proposed study. Dimensions and extreme values of the end-effector orientation angles are calculated.

Kinematics Analysis of 6-DoF Articulated Robot with Spherical Wrist

The aim of the paper is to study the kinematics of the manipulator. The articulated robot with a spherical wrist has been used for this purpose. The Comau NM45 Manipulator has been chosen for the kinematic model study. The manipulator contains six revolution joints. Pieper’s approach has been employed to study the kinematics (inverse) of the robot manipulator. Using this approach, the inverse kinematic problem is divided into two small less complex problems. This reduces the time of analysing the manipulator kinematically. The forward and inverse kinematics has been performed, and mathematical solutions are detailed based on D-H (Denavit–Hartenberg) parameters. The kinematics solution has been verified by solving the manipulator’s motion. It has been observed that the model is accurate as the motion trajectory was smoothly followed by the manipulator.

Using a Cable-Driven Parallel Robot with Applications in 3D Concrete Printing

In construction, a large-scale 3D printing method for construction is used to build houses quickly, based on Computerized Aid Design. Currently, the construction industry is beginning to apply quite a lot of 3D printing technologies to create buildings that require a quick construction time and complex structures that classical methods cannot implement. In this paper, a Cable-Driven Parallel Robot (CDPR) is described for the 3D printing of concrete for building a house. The CDPR structures are designed to be suitable for 3D printing in a large workspace. A linear programming algorithm was used to quickly calculate the inverse kinematic problem with the force equilibrium condition for the moving platform; this method is suitable for the flexible configuration of a CDPR corresponding to the various spaces. Cable sagging was also analyzed by the Trust-Region-Dogleg algorithm to increase the accuracy of the inverse kinematic problem for controlling the robot to perform basic trajectory interpolation movements. The paper also covers the design and analysis of a concrete extruder for the 3D printing method. The analytical results are experimented with based on a prototype of the CDPR to evaluate the work ability and suitability of this design. The results show that this design is suitable for 3D printing in construction, with high precision and a stable trajectory printing. The robot configuration can be easily adjusted and calculated to suit the construction space, while maintaining rigidity as well as an adequate operating space. The actuators are compact, easy to disassemble and move, and capable of accommodating a wide variety of dimensions.

Modeling of Inverse Kinematic of 3-DoF Robot, Using Unit Quaternions and Artificial Neural Network

SUMMARY This paper presents a novel method for modeling a 3-degree of freedom open kinematic chain using quaternions algebra and neural network to solve the inverse kinematic problem. The structure of the network was composed of 3 hidden layers with 25 neurons per layer and 1 output layer. The network was trained using the Bayesian regularization backpropagation. The inverse kinematic problem was modeled as a system of six nonlinear equations and six unknowns. Finally, both models were tested using a straight path to compare the results between the Newton–Raphson method and the network training.