Search results for: Jacobian

Authors: Guillaume Morin-Duponchelle, Ahmed Nait Chabane, Benoit Zerr, Pierre Schoesetters

Abstract:

Industrial inspection can be achieved through robotic systems, allowing visual and chemical servoing. A popular scheme for visual servo-controlled robotic is the image-based servoing sys-tems. In this paper, an approach of visual and chemical servoing of a hexapod robot using a visual and chemical Jacobian matrix are proposed. The basic idea behind the visual Jacobian matrix is modeling the differential relationship between the camera system and the robotic control system to detect and track accurately points of interest in confined environments. This approach allows the robot to easily detect and navigates to the QR code or seeks a gas source localization using surge cast algorithm. To track the QR code target, a visual servoing based on Jacobian matrix is used. For chemical servoing, three gas sensors are embedded on the hexapod. A Jacobian matrix applied to the gas concentration measurements allows estimating the direction of the main gas source. The effectiveness of the proposed scheme is first demonstrated on simulation. Finally, a hexapod prototype is designed and built and the experimental validation of the approach is presented and discussed.

Keywords: chemical servoing, hexapod robot, Jacobian matrix, visual servoing, navigation

Procedia PDF Downloads 125

Authors: Chao-Qing Dai

Abstract:

In modern nonlinear science and textile engineering, nonlinear differential-difference equations are often used to describe some nonlinear phenomena. In this paper, we extend the variable coefficient Jacobian elliptic function method, which was used to find new exact travelling wave solutions of nonlinear partial differential equations, to nonlinear differential-difference equations. As illustration, we derive two series of Jacobian elliptic function solutions of the discrete sine-Gordon equation.

Keywords: discrete sine-Gordon equation, variable coefficient Jacobian elliptic function method, exact solutions, equation

Procedia PDF Downloads 668

Authors: Chao-Qing Dai

Abstract:

Two families of exact travelling solutions for the discrete sine-Gordon equation are constructed based on the variable-coefficient Jacobian elliptic function method and different transformations. When the modulus of Jacobian elliptic function solutions tends to 1, soliton solutions can be obtained. Some soliton solutions degenerate into the known solutions in literatures. Moreover, dynamical properties of exact solutions are investigated. Our analysis and results may have potential values for certain applications in modern nonlinear science and textile engineering.

Keywords: exact solutions, variable-coefficient Jacobian elliptic function method, discrete sine-Gordon equation, dynamical behaviors

Procedia PDF Downloads 420

Authors: Zahra Majd, Mohsen Kalantar

Abstract:

Power management and voltage regulation is one of the most important issues in microgrid (MG) control and scheduling. This paper proposes a multiobjective scheduling formulation that consists of active power costs, voltage fluctuations summation, and technical constraints of MG. Furthermore, load flow and reserve constraints are considered to achieve proper voltage regulation. A modified Jacobian matrix is presented for calculating voltage variations and Mont Carlo simulation is used for generating and reducing scenarios. To convert the problem to a mixed integer linear program, a linearization procedure for nonlinear equations is presented. The proposed model is applied to a typical low-voltage MG and two different cases are investigated. The results show the effectiveness of the proposed model.

Keywords: microgrid, energy management system, voltage fluctuations, modified Jacobian matrix

Procedia PDF Downloads 91

Authors: Ramish, Farhan Khalique Awan

Abstract:

Kinematic redundancy within the manipulators presents extended dexterity and manipulability to the manipulators. Redundant serial robotic manipulators are very popular in industries due to its competencies to keep away from singularities during normal operation and fault tolerance because of failure of one or more joints. Such fault tolerant manipulators are extraordinarily beneficial in applications where human interference for repair and overhaul is both impossible or tough; like in case of robotic arms for space programs, nuclear applications and so on. The design of this sort of fault tolerant serial 3 DoF manipulator is presented in this paper. This work was the extension of the author’s previous work of designing the simple 3R serial manipulator. This work is the realization of the previous design with optimizing the link lengths for incorporating the feature of fault tolerance. Various measures have been followed by the researchers to quantify the fault tolerance of such redundant manipulators. The fault tolerance in this work has been described in terms of the worst-case measure of relative manipulability that is, in fact, a local measure of optimization that works properly for certain configuration of the manipulators. An optimum fault tolerant Jacobian matrix has been determined first based on prescribed null space properties after which the link parameters have been described to meet the given Jacobian matrix. A solid model of the manipulator was then developed to realize the mathematically rigorous design. Further work was executed on determining the dynamic properties of the fault tolerant design and simulations of the movement for various trajectories have been carried out to evaluate the joint torques. The mathematical model of the system was derived via the Euler-Lagrange approach after which the same has been tested using the RoboAnalyzer© software. The results have been quite in agreement. From the CAD model and dynamic simulation data, the manipulator was fabricated in the workshop and Advanced Machining lab of NED University of Engineering and Technology.

Keywords: fault tolerant, Graham matrix, Jacobian, kinematics, Lagrange-Euler

Procedia PDF Downloads 222

Authors: Chih-Jer Lin, Jian-Hong Hou

Abstract:

Industry 4.0 is a vision of integrated industry implemented by artificial intelligent computing, software, and Internet technologies. The main goal of industry 4.0 is to deal with the difficulty owing to competitive pressures in the marketplace. For today’s manufacturing factories, the type of production is changed from mass production (high quantity production with low product variety) to medium quantity-high variety production. To offer flexibility, better quality control, and improved productivity, robot manipulators are used to combine material processing, material handling, and part positioning systems into an integrated manufacturing system. To implement the automated system for sheet metal bending operations, motion planning of a 7-degrees of freedom (DOF) robot is studied in this paper. A virtual reality (VR) environment of a bending cell, which consists of the robot and a bending machine, is established using the virtual robot experimentation platform (V-REP) simulator. For sheet metal bending operations, the robot only needs six DOFs for the pick-and-place or tracking tasks. Therefore, this 7 DOF robot has more DOFs than the required to execute a specified task; it can be called a redundant robot. Therefore, this robot has kinematic redundancies to deal with the task-priority problems. For redundant robots, Pseudo-inverse of the Jacobian is the most popular motion planning method, but the pseudo-inverse methods usually lead to a kind of chaotic motion with unpredictable arm configurations as the Jacobian matrix lose ranks. To overcome the above problem, we proposed a method to formulate the motion planning problems as optimization problem. Moreover, a genetic algorithm (GA) based method is proposed to deal with motion planning of the redundant robot. Simulation results validate the proposed method feasible for motion planning of the redundant robot in an automated sheet-metal bending operations.

Keywords: redundant robot, motion planning, genetic algorithm, obstacle avoidance

Procedia PDF Downloads 146

Authors: Khairil Iskandar Othman, Nadhirah Kamal, Zarina Bibi Ibrahim

Abstract:

Block methods for solving stiff systems of ordinary differential equations (ODEs) are based on backward differential formulas (BDF) with PE(CE)2 and Newton method. In this paper, we introduce Modified Newton as a new strategy to get more efficient result. The derivation of BBDF using modified block Newton method is presented. This new block method with predictor-corrector gives more accurate result when compared to the existing BBDF.

Keywords: modified Newton, stiff, BBDF, Jacobian matrix

Procedia PDF Downloads 378

Authors: M. Y. Waziri, M. A. Aliyu

Abstract:

The paper proposes an approach to improve the performance of Broyden’s method for solving systems of nonlinear equations. In this work, we consider the information from two preceding iterates rather than a single preceding iterate to update the Broyden’s matrix that will produce a better approximation of the Jacobian matrix in each iteration. The numerical results verify that the proposed method has clearly enhanced the numerical performance of Broyden’s Method.

Keywords: mulit-step Broyden, nonlinear systems of equations, computational efficiency, iterate

Procedia PDF Downloads 638

Authors: R. B. Ogunrinde, C. C. Jibunoh

Abstract:

In this paper, a spectral decomposition method is developed for the direct integration of stiff and nonstiff homogeneous linear (ODE) systems with linear, constant, or zero right hand sides (RHSs). The method does not require iteration but obtains solutions at any random points of t, by direct evaluation, in the interval of integration. All the numerical solutions obtained for the class of systems coincide with the exact theoretical solutions. In particular, solutions of homogeneous linear systems, i.e. with zero RHS, conform to the exact analytical solutions of the systems in terms of t.

Keywords: spectral decomposition, linear RHS, homogeneous linear systems, eigenvalues of the Jacobian

Procedia PDF Downloads 330

Authors: Marc Diesse, Hochschule Heilbronn

Abstract:

We address the question of identifying the configuration space singularities of linkages, i.e., points where the configuration space is not locally a submanifold of Euclidean space. Because the configuration space cannot be smoothly parameterized at such points, these singularity types have a significantly negative impact on the kinematics of the linkage. It is known that Jacobian methods do not provide sufficient conditions for the existence of CS-singularities. Herein, we present several additional algebraic criteria that provide the sufficient conditions. Further, we use those criteria to analyze certain classes of planar linkages. These examples will also show how the presented criteria can be checked using algorithmic methods.

Keywords: linkages, configuration space-singularities, real algebraic geometry, analytic geometry

Procedia PDF Downloads 148

Authors: Adriano Trono, Federico Pinto, Diego Turello, Marcelo A. Ceballos

Abstract:

Numerical modeling of dynamic soil-structure interaction problems requires an adequate representation of the unbounded characteristics of the ground, material non-linearity of soils, and geometrical non-linearities such as large displacements due to rocking of the structure. In order to account for these effects simultaneously, it is often required that the equations of motion are solved in the time domain. However, boundary conditions in conventional finite element codes generally present shortcomings in fully absorbing the energy of outgoing waves. In this sense, the Perfectly Matched Layers (PML) technique allows a satisfactory absorption of inclined body waves, as well as surface waves. However, the PML domain is inherently unstable, meaning that it its instability does not depend upon the discretization considered. One way to stabilize the PML domain is to use multiaxial stretching functions. This development is questionable because some Jacobian terms of the coordinate transformation are not accounted for. For this reason, the resulting absorbing layer element is often referred to as "uncorrected M-PML” in the literature. In this work, the strong formulation of the "corrected M-PML” absorbing layer is proposed using multiaxial stretching functions that incorporate all terms of the coordinate transformation. The results of the stable model are compared with reference solutions obtained from extended domain models.

Keywords: mixed finite elements, multiaxial stretching functions, perfectly matched layer, soil-structure interaction

Procedia PDF Downloads 70

Authors: Shiji Hu, Lei Li, Wanting Zhou, DaoHong Yang

Abstract:

The data encryption, is the foundation of today’s communication. On this basis, how to improve the speed of data encryption and decryption is always a problem that scholars work for. In this paper, we proposed an elliptic curve crypto processor architecture based on SM2 prime field. In terms of hardware implementation, we optimized the algorithms in different stages of the structure. In finite field modulo operation, we proposed an optimized improvement of Karatsuba-Ofman multiplication algorithm, and shorten the critical path through pipeline structure in the algorithm implementation. Based on SM2 recommended prime field, a fast modular reduction algorithm is used to reduce 512-bit wide data obtained from the multiplication unit. The radix-4 extended Euclidean algorithm was used to realize the conversion between affine coordinate system and Jacobi projective coordinate system. In the parallel scheduling of point operations on elliptic curves, we proposed a three-level parallel structure of point addition and point double based on the Jacobian projective coordinate system. Combined with the scalar multiplication algorithm, we added mutual pre-operation to the point addition and double point operation to improve the efficiency of the scalar point multiplication. The proposed ECC hardware architecture was verified and implemented on Xilinx Virtex-7 and ZYNQ-7 platforms, and each 256-bit scalar multiplication operation took 0.275ms. The performance for handling scalar multiplication is 32 times that of CPU(dual-core ARM Cortex-A9).

Keywords: Elliptic curve cryptosystems, SM2, modular multiplication, point multiplication.

Procedia PDF Downloads 98

Authors: Sidrah Ahmed

Abstract:

The river and lakes flows are modeled mathematically by shallow water equations that are depth-averaged Reynolds Averaged Navier-Stokes equations under Boussinesq approximation. The temperature stratification dynamics influence the water quality and mixing characteristics. It is mainly due to the atmospheric conditions including air temperature, wind velocity, and radiative forcing. The experimental observations are commonly taken along vertical scales and are not sufficient to estimate small turbulence effects of temperature variations induced characteristics of shallow flows. Wind shear stress over the water surface influence flow patterns, heat fluxes and thermodynamics of water bodies as well. Hence it is crucial to couple temperature gradients with shallow water model to estimate the atmospheric effects on flow patterns. The Ripa system has been introduced to study ocean currents as a variant of shallow water equations with addition of temperature variations within the flow. Ripa model is a hyperbolic system of partial differential equations because all the eigenvalues of the system’s Jacobian matrix are real and distinct. The time steps of a numerical scheme are estimated with the eigenvalues of the system. The solution to Riemann problem of the Ripa model is composed of shocks, contact and rarefaction waves. Solving Ripa model with Riemann initial data with the central schemes is difficult due to the eigen structure of the system.This works presents the comparison of four different finite difference schemes for the numerical solution of Riemann problem for Ripa model. These schemes include Lax-Friedrichs, Lax-Wendroff, MacCormack scheme and a higher order finite difference scheme with WENO method. The numerical flux functions in both dimensions are approximated according to these methods. The temporal accuracy is achieved by employing TVD Runge Kutta method. The numerical tests are presented to examine the accuracy and robustness of the applied methods. It is revealed that Lax-Freidrichs scheme produces results with oscillations while Lax-Wendroff and higher order difference scheme produce quite better results.

Keywords: finite difference schemes, Riemann problem, shallow water equations, temperature gradients

Procedia PDF Downloads 203

Authors: Suleyman Ogul Ertugrul, Mustafa Turgut, Serkan Inandı, Mustafa Gorkem Coban, Mustafa Kıgılı, Ali Mert, Oguzhan Kesmez, Murat Ozancı, Caglar Uyulan

Abstract:

In high-performance automotive engineering, the realistic simulation of suspension systems is crucial for enhancing vehicle dynamics and handling. This study focuses on the double wishbone suspension system, prevalent in racing vehicles due to its superior control and stability characteristics. Utilizing MATLAB and Adams Car simulation software, we conduct a comprehensive analysis of displacement behaviors and damper sizing under various dynamic conditions. The initial phase involves using MATLAB to simulate the entire suspension system, allowing for the preliminary determination of damper size based on the system's response under simulated conditions. Following this, manual calculations of wheel loads are performed to assess the forces acting on the front and rear suspensions during scenarios such as braking, cornering, maximum vertical loads, and acceleration. Further dynamic force analysis is carried out using MATLAB Simulink, focusing on the interactions between suspension components during key movements such as bumps and rebounds. This simulation helps in formulating precise force equations and in calculating the stiffness of the suspension springs. To enhance the accuracy of our findings, we focus on a detailed kinematic and dynamic analysis. This includes the creation of kinematic loops, derivation of relevant equations, and computation of Jacobian matrices to accurately determine damper travel and compression metrics. The calculated spring stiffness is crucial in selecting appropriate springs to ensure optimal suspension performance. To validate and refine our results, we replicate the analyses using the Adams Car software, renowned for its detailed handling of vehicular dynamics. The goal is to achieve a robust, reliable suspension setup that maximizes performance under the extreme conditions encountered in racing scenarios. This study exemplifies the integration of theoretical mechanics with advanced simulation tools to achieve a high-performance suspension setup that can significantly improve race car performance, providing a methodology that can be adapted for different types of racing vehicles.

Keywords: FSAE, suspension system, Adams Car, kinematic

Procedia PDF Downloads 51

Authors: Aitor Bilbao, Dragos Axinte, John Billingham

Abstract:

The inverse problem in Energy Beam (EB) Processes consists of defining the control parameters, in particular the 2D beam path (position and orientation of the beam as a function of time), to arrive at a prescribed solution (freeform surface). This inverse problem is well understood for conventional machining, because the cutting tool geometry is well defined and the material removal is a time independent process. In contrast, EB machining is achieved through the local interaction of a beam of particular characteristics (e.g. energy distribution), which leads to a surface-dependent removal rate. Furthermore, EB machining is a time-dependent process in which not only the beam varies with the dwell time, but any acceleration/deceleration of the machine/beam delivery system, when performing raster paths will influence the actual geometry of the surface to be generated. Two different EB processes, Abrasive Water Machining (AWJM) and Pulsed Laser Ablation (PLA), are studied. Even though they are considered as independent different technologies, both can be described as time-dependent processes. AWJM can be considered as a continuous process and the etched material depends on the feed speed of the jet at each instant during the process. On the other hand, PLA processes are usually defined as discrete systems and the total removed material is calculated by the summation of the different pulses shot during the process. The overlapping of these shots depends on the feed speed and the frequency between two consecutive shots. However, if the feed speed is sufficiently slow compared with the frequency, then consecutive shots are close enough and the behaviour can be similar to a continuous process. Using this approximation a generic continuous model can be described for both processes. The inverse problem is usually solved for this kind of process by simply controlling dwell time in proportion to the required depth of milling at each single pixel on the surface using a linear model of the process. However, this approach does not always lead to the good solution since linear models are only valid when shallow surfaces are etched. The solution of the inverse problem is improved by using a discrete adjoint optimization algorithm. Moreover, the calculation of the Jacobian matrix consumes less computation time than finite difference approaches. The influence of the dynamics of the machine on the actual movement of the jet is also important and should be taken into account. When the parameters of the controller are not known or cannot be changed, a simple approximation is used for the choice of the slope of a step profile. Several experimental tests are performed for both technologies to show the usefulness of this approach.

Keywords: abrasive waterjet machining, energy beam processes, inverse problem, pulsed laser ablation

Procedia PDF Downloads 275

Authors: Timur S. Zaripov, Artur K. Gilfanov, Sergei S. Sazhin, Steven M. Begg, Morgan R. Heikal

Abstract:

The calculation of the concentration of inertial droplets in complex flows is encountered in the modelling of numerous engineering and environmental phenomena; for example, fuel droplets in internal combustion engines and airborne pollutant particles. The results of recent research, focused on the development of methods for calculating concentration and their implementation in the commercial CFD code, ANSYS Fluent, is presented here. The study is motivated by the investigation of the mixture preparation processes in internal combustion engines with direct injection of fuel sprays. Two methods are used in our analysis; the Fully Lagrangian method (also known as the Osiptsov method) and the Eulerian approach. The Osiptsov method predicts droplet concentrations along path lines by solving the equations for the components of the Jacobian of the Eulerian-Lagrangian transformation. This method significantly decreases the computational requirements as it does not require counting of large numbers of tracked droplets as in the case of the conventional Lagrangian approach. In the Eulerian approach the average droplet velocity is expressed as a function of the carrier phase velocity as an expansion over the droplet response time and transport equation can be solved in the Eulerian form. The advantage of the method is that droplet velocity can be found without solving additional partial differential equations for the droplet velocity field. The predictions from the two approaches were compared in the analysis of the problem of a dilute gas-droplet flow around an infinitely long, circular cylinder. The concentrations of inertial droplets, with Stokes numbers of 0.05, 0.1, 0.2, in steady-state and transient laminar flow conditions, were determined at various Reynolds numbers. In the steady-state case, flows with Reynolds numbers of 1, 10, and 100 were investigated. It has been shown that the results predicted using both methods are almost identical at small Reynolds and Stokes numbers. For larger values of these numbers (Stokes — 0.1, 0.2; Reynolds — 10, 100) the Eulerian approach predicted a wider spread in concentration in the perturbations caused by the cylinder that can be attributed to the averaged droplet velocity field. The transient droplet flow case was investigated for a Reynolds number of 200. Both methods predicted a high droplet concentration in the zones of high strain rate and low concentrations in zones of high vorticity. The maxima of droplet concentration predicted by the Osiptsov method was up to two orders of magnitude greater than that predicted by the Eulerian method; a significant variation for an approach widely used in engineering applications. Based on the results of these comparisons, the Osiptsov method has resulted in a more precise description of the local properties of the inertial droplet flow. The method has been applied to the analysis of the results of experimental observations of a liquid gasoline spray at representative fuel injection pressure conditions. The preliminary results show good qualitative agreement between the predictions of the model and experimental data.

Keywords: internal combustion engines, Eulerian approach, fully Lagrangian approach, gasoline fuel sprays, droplets and particle concentrations

Procedia PDF Downloads 257