Certain and Uncertain Triangulation in Multiple Camera Vision Systems via LMIs

2013 ◽  
pp. 112-124
Author(s):  
Graziano Chesi ◽  
Yeung Sam Hung
Keyword(s):  
Fundamental Problem ◽  
Real Data ◽  
Computational Time ◽  
Linear Matrix ◽  
Vision Systems ◽  
Standard Case ◽  
Multiple Camera ◽  
L2 Norm ◽  
Reprojection Error ◽  
Image Projections

Triangulation is a fundamental problem in computer vision that consists of estimating the 3D position of a point of the scene from the estimates of its image projections on some cameras and from the estimates of the projection matrices of these cameras. This chapter addresses multiple view L2 triangulation, i.e. triangulation for vision systems with a generic number of cameras where the sought 3D point is searched by minimizing the L2 norm of the image reprojection error. The authors consider the standard case where estimates of all the image points are available (referring to such a case as certain triangulation), and consider also the case where some of such estimates are not available for example due to occlusions (referring to such a case as uncertain triangulation). In the latter case, it is supposed that the unknown image points belong to known regions such as line segments or ellipses. For these problems, the authors propose a unified methodology that exploits the fundamental matrices among the views and provides a candidate 3D point through the solution of a convex optimization problem based on linear matrix inequalities (LMIs). Moreover, the chapter provides a simple condition that allows one to immediately establish whether the found 3D point is optimal. Various examples with synthetic and real data illustrate the proposed technique, showing in particular that the obtained 3D point is almost always optimal in practice, and that its computational time is indeed small.

Certain and Uncertain Triangulation in Multiple Camera Vision Systems via LMIs

2012 ◽  
pp. 53-64
Author(s):  
Graziano Chesi ◽  
Yeung Sam Hung
Keyword(s):  
Fundamental Problem ◽  
Real Data ◽  
Computational Time ◽  
Linear Matrix ◽  
Vision Systems ◽  
Standard Case ◽  
Multiple Camera ◽  
L2 Norm ◽  
Reprojection Error ◽  
Image Projections

Triangulation is a fundamental problem in computer vision that consists of estimating the 3D position of a point of the scene from the estimates of its image projections on some cameras and from the estimates of the projection matrices of these cameras. This chapter addresses multiple view L2 triangulation, i.e. triangulation for vision systems with a generic number of cameras where the sought 3D point is searched by minimizing the L2 norm of the image reprojection error. The authors consider the standard case where estimates of all the image points are available (referring to such a case as certain triangulation), and consider also the case where some of such estimates are not available for example due to occlusions (referring to such a case as uncertain triangulation). In the latter case, it is supposed that the unknown image points belong to known regions such as line segments or ellipses. For these problems, the authors propose a unified methodology that exploits the fundamental matrices among the views and provides a candidate 3D point through the solution of a convex optimization problem based on linear matrix inequalities (LMIs). Moreover, the chapter provides a simple condition that allows one to immediately establish whether the found 3D point is optimal. Various examples with synthetic and real data illustrate the proposed technique, showing in particular that the obtained 3D point is almost always optimal in practice, and that its computational time is indeed small.

Dynamic Analysis of Elastic Link Mechanisms by Reduction of Coordinates

1972 ◽  
Vol 94 (2) ◽  
pp. 577-581 ◽  
Author(s):  
R. C. Winfrey
Keyword(s):  
Dynamic Analysis ◽  
Complete Solution ◽  
Practical Interest ◽  
Elastic Behavior ◽  
Computational Time ◽  
Linear Matrix ◽  
Considerable Saving ◽  
Matrix Differential Equations ◽  
Elastic Link ◽  
Matrix Differential

Techniques for the solution of linear matrix differential equations have previously been applied to the dynamic analysis of a mechanism. However, because the mechanism changes geometry as it rotates, a large number of solutions are necessary to predict the mechanism’s elastic behavior for even a few revolutions. Also, a designer is frequently concerned with the elastic behavior of only one point on the mechanism and has no practical interest in a complete solution. For these reasons, a method is given here for reducing the total number of coordinates to one coordinate at the point of design interest. A considerable saving in computational time is obtained since the dynamic solution involves one degree of freedom instead of many. Further, since any solution will make use of some limiting assumptions, results here indicate that, for design purposes, reducing the coordinates does not significantly affect comparable accuracy.

scholarly journals Minimising the computational time of a waveform based location algorithm

2021 ◽  
Author(s):  
Emmanouil Parastatidis ◽  
Stella Pytharouli ◽  
Lina Stankovic ◽  
Vladimir Stankovic ◽  
Peidong Shi
Keyword(s):  
Computer Architecture ◽  
Time Window ◽  
Real Data ◽  
Computational Time ◽  
Enhanced Geothermal Systems ◽  
Geothermal Systems ◽  
Migration Method ◽  
Location Algorithm ◽  
Hypocentral Location ◽  
Grid Interval

<p>Accurate and fast localisation of microseismic events is a requirement for a number of applications, e.g. mining, enhanced geothermal systems. New methods for event localisation have been proposed over the last decades. The waveform-based methods are of the most recent developed ones and their main advantage is the ability to locate weak seismic events. Despite this, these methods are demanding in terms of computational time, making real-time seismic event localisation very difficult. In this work, we further develop a waveform-based method, the Multichannel coherency migration method (MCM), to improve the computational time. The computational time for the MCM algorithm has been reported to linearly depend on several parameters, such as the number of stations, the length of the waveform time window, the computer architecture, and the volume of the area we are searching for the hypocentre. To minimise the computational time we need to decrease one or more of the above parameters without compromising the accuracy of the result. We break the localisation procedure into several steps: (1) we locate the event with a relatively large spatial grid interval which will give less potential hypocentral locations and less calculations as a result. (2) Based on the results of step (1) and the locations of maximum coherencies we decrease the grid volume to a quarter of the original volume and the spatial interval to half the original, focusing only around the area identified in step (1). Step (2) is repeated several times for decreased grid volumes and spatial intervals until the hypocentral location does not significantly change any more. We tested this approach on both synthetic and real data. We find that while the accuracy of the hypocentre is not compromised, the computational time is up to  125,000 times shorter.    </p>

L2 norm-based finite-time stability and boundedness of singular distributed parameter systems with parabolic type

2020 ◽  
pp. 095965182096689
Author(s):  
Xingyu Zhou ◽  
Haoping Wang ◽  
Yang Tian
Keyword(s):  
Finite Time ◽  
Sufficient Conditions ◽  
Parabolic Type ◽  
Distributed Parameter Systems ◽  
Temperature Control System ◽  
Linear Matrix ◽  
Distributed Parameter ◽  
Time Stability ◽  
Finite Time Stability ◽  
L2 Norm

In this study, the problem of finite-time stability and boundedness for parabolic singular distributed parameter systems in the sense of [Formula: see text] norm is investigated. First, two new results on [Formula: see text] norm-based finite-time stability and finite-time boundedness for above-mentioned systems, inspired by the light of partial differential equations theory and Lyapunov functional method, are presented. Then, some sufficient conditions of [Formula: see text] norm-based finite-time stability and boundedness are established by virtue of differential inequalities and linear matrix inequalities. Furthermore, the distributed state feedback controllers are constructed to guarantee the [Formula: see text] norm-based finite-time stable and bounded of the closed-loop singular distributed parameter systems. Finally, numerical simulations on a specific numerical example and the building temperature control system equipped with air conditioning are given to demonstrate the validity of the proposed methods.

An Improved Method for Scheduling Aircraft Ground Handling Operations From a Global Perspective

2019 ◽  
Vol 36 (04) ◽  
pp. 1950020 ◽  
Author(s):  
Silvia Padrón ◽  
Daniel Guimarans
Keyword(s):  
Time Windows ◽  
Pareto Frontier ◽  
Solution Space ◽  
Real Data ◽  
Global Perspective ◽  
Computational Time ◽  
Efficient Utilization ◽  
Ground Handling ◽  
And Performance

The turnaround is a critical airport process where a set of interrelated operations need to be performed to get an aircraft ready for its next flight. These activities are carried out by different vehicles, which need to be coordinated to guarantee an efficient utilization of resources. Due to the relations between operations, the order in which these resources are scheduled has a critical influence on the planning and performance of the turnaround. In this work, we present a novel methodology for solving the proposed bi-objective ground handling scheduling problem from a global perspective. This means solving a set of interconnected routing problems with restrictive time windows for each operation. We first explore the solution space using a fast heuristic, focusing then on the most promising solutions to intensify the search in the vicinity of the Pareto frontier. This two-step schema permits significantly reducing the required computational time, which, in turn, allows a more thorough exploration of solutions. Different experiments over real data from two Spanish airports have been conducted to assess the proposed methodology. Our results show that the new method not only outperforms previous approaches in terms of computational requirements, but can also improve the quality of scheduling solutions.

Distributed Parameter-Dependent Modeling and Control of Flexible Structures

2004 ◽  
Vol 127 (2) ◽  
pp. 230-239 ◽  
Author(s):  
Fen Wu ◽  
Suat E. Yildizoglu
Keyword(s):  
Optimization Problems ◽  
Flexible Structures ◽  
Synthesis Condition ◽  
Distributed Model ◽  
Linear Matrix ◽  
Distributed Parameter ◽  
Modeling And Control ◽  
L2 Norm ◽  
And Control ◽  
Parameter Dependent

In this paper, distributed parameter-dependent modeling and control approaches are proposed for flexible structures. The distributed model is motivated from distributed control design, which is advantageous in reducing control implementation cost and increasing control system reliability. This modeling approach mainly relies on a central finite difference scheme to capture the distributed nature of the flexible system. Based on the proposed distributed model, a sufficient synthesis condition for the design of a distributed output-feedback controller is presented using induced L2 norm as the performance criterion. The controller synthesis condition is formulated as linear matrix inequalities, which are convex optimization problems and can be solved efficiently using interior-point algorithms. The distributed controller inherits the same structure as the plant, which results in a localized control architecture and a simple implementation scheme. These modeling and control approaches are demonstrated on a non-uniform cantilever beam problem through simulation studies.

scholarly journals Robust Control of a Class of Nonlinear Discrete-Time Systems: Design and Experimental Results on a Real-Time Emulator

Actuators ◽  
2021 ◽  
Vol 10 (11) ◽  
pp. 303
Author(s):  
Noussaiba Gasmi ◽  
Mohamed Boutayeb ◽  
Assem Thabet ◽  
Ghazi Bel Haj Frej ◽  
Mohamed Aoun
Keyword(s):  
Real Time ◽  
Systems Design ◽  
Linear Matrix ◽  
Numerical Comparison ◽  
Matrix Inequality ◽  
Standard Case ◽  
Software Algorithms ◽  
New Strategy ◽  
The One ◽  
Window Approach

The aim of this study is to develop a new observer-based stabilization strategy for a class of Lipschitz uncertain systems. This new strategy improves the performances of existing methods and ensures better convergence conditions. Sliding window approach involves previous estimated states and measurements in the observer and the control law structures which increase the number of decision variables in the constraint to be solved and offers less restrictive Linear Matrix Inequality (LMI) conditions. The established sufficient stability conditions are in the form of Bilinear Matrix Inequality (BMI) which is solved in two steps. First, by using a slack variable technique and an appropriate reformulation of the Young’s inequality. Second, by introducing a useful approach to transform the obtained constraint to a more suitable one easily tractable by standard software algorithms. A comparison with the standard case is provided to show the superiority of the proposed H∞ observer-based controller which offers greater degree of freedom. The accuracy and the potential of the proposed process are shown through real time implementation of the one-link flexible joint robot to ARDUINO UNO R3 device and numerical comparison with some existing results.

scholarly journals Truncation Mixture R-Vine Copulas

2021 ◽  
Author(s):  
Fadhah Alanazi
Keyword(s):  
Simulation Study ◽  
Real Data ◽  
Computational Time ◽  
Model Parameters ◽  
Copula Models ◽  
Truncation Level ◽  
Truncation Method ◽  
Tree Estimation ◽  
Vine Copula ◽  
Vine Copulas

Uncovering hidden mixture correlation among variables have been investigating in the literature using mixture R-vine copula models. These models are hierarchical in nature. They provides a huge flexibility for modelling multivariate data. As the dimensions increases, the number of the model parameters that need to be estimated is increased dramatically, which becomes along with huge computational times and efforts. This situation becomes even much more harder and complicated in the mixture Regular vine models. Incorporating truncation method with mixture Regular vine models will reduce the computation difficulty for the mixture based models. In this paper, tree-by-tree estimation mixture model is joined with the truncation method, in order to reduce the computational time and the number of the parameters that need to be estimated in the mixture vine copula models. A simulation study and a real data applications illustrated the performance of the method. In addition, the real data applications show the affect of the mixture components on the truncation level.

scholarly journals Routing and Spectrum Allocation in Spectrum-Sliced Elastic Optical Path Networks: A Primal-Dual Framework

Electronics ◽  
2021 ◽  
Vol 10 (22) ◽  
pp. 2809
Author(s):  
Yang Wang ◽  
Chaoyang Li ◽  
Qian Hu ◽  
Jabree Flor ◽  
Maryam Jalalitabar
Keyword(s):  
Heuristic Algorithms ◽  
Fundamental Problem ◽  
Optimal Solution ◽  
Optical Path ◽  
Spectrum Allocation ◽  
Computational Time ◽  
Solution Quality ◽  
Traffic Demand ◽  
Primal Dual ◽  
Routing And Spectrum Allocation

The recent decade has witnessed a tremendous growth of Internet traffic, which is expected to continue climbing for the foreseeable future. As a new paradigm, Spectrum-sliced Elastic Optical Path (SLICE) networks promise abundant (elastic) bandwidth to address the traffic explosion, while bearing other inherent advantages including enhanced signal quality and extended reachability. The fundamental problem in SLICE networks is to route each traffic demand along a lightpath with continuously and consecutively available sub-carriers, which is known as the Routing and Spectrum Allocation (RSA) problem. Given its NP-Hardness, the solutions to the RSA problem can be classified into two categories: optimal solutions using link-based, path-based, and channel-based Integer Linear Programming (ILP) models, which require extensive computational time; and sub-optimal heuristic and meta-heuristic algorithms, which have no guarantee on the solution quality. In this work, inspired by a channel-based ILP model, we propose a novel primal-dual framework to address the RSA problem, which can obtain a near-optimal solution with guaranteed per-instance closeness to the optimal solution.

A Passive Fault-Tolerant Switched Control Approach for Linear Multivariable Systems: Application to a Quadcopter Unmanned Aerial Vehicle Model

2019 ◽  
Vol 142 (3) ◽  
Author(s):  
Hasan Başak ◽  
Emre Kemer ◽  
Emmanuel Prempain
Keyword(s):  
Output Feedback ◽  
State Feedback ◽  
Fault Tolerant ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Passive State ◽  
Linear Matrix ◽  
Control Approach ◽  
Linear Time Invariant ◽  
L2 Norm

Abstract This paper proposes synthesis algorithms for the design of passive state- and output-feedback fault-tolerant controllers. Sufficient conditions for the existence and the construction of such fault-tolerant controllers are given in terms of linear matrix inequalities (LMIs) which can be solved efficiently. The state-feedback fault-tolerant controller consists of a family of state-feedback gains switched appropriately according to a stabilizing switching signal so that the closed-loop system satisfies a performance requirement expressed in terms of system L2 norm. Similarly, the output feedback controller consists of a family of full-order linear, time-invariant controllers switched according to a stabilizing signal that depends only on the controller states. Both approaches are passive in the sense that they do not rely on the detection and/or the estimation of the faults. The proposed approaches are tested on a nonlinear model of a quadcopter. Simulation results show that satisfactory stability, tracking, and disturbance rejection are maintained despite of time-varying actuator faults.

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