Robotic drilling for aerospace structures demands a high positioning accuracy of the robot, which is usually achieved through error measurement and compensation. In this paper, we report the development of a practical...Robotic drilling for aerospace structures demands a high positioning accuracy of the robot, which is usually achieved through error measurement and compensation. In this paper, we report the development of a practical monocular vision system for measurement of the relative error between the drill tool center point(TCP) and the reference hole. First, the principle of relative error measurement with the vision system is explained, followed by a detailed discussion on the hardware components, software components, and system integration. The elliptical contour extraction algorithm is presented for accurate and robust reference hole detection. System calibration is of key importance to the measurement accuracy of a vision system. A new method is proposed for the simultaneous calibration of camera internal parameters and hand-eye relationship with a dedicated calibration board. Extensive measurement experiments have been performed on a robotic drilling system. Experimental results show that the measurement accuracy of the developed vision system is higher than 0.15 mm, which meets the requirement of robotic drilling for aircraft structures.展开更多
In this paper,we investigate the superconvergence property and the L∞-error estimates of mixed finite element methods for a semilinear elliptic control problem with an integral constraint.The state and co-state are a...In this paper,we investigate the superconvergence property and the L∞-error estimates of mixed finite element methods for a semilinear elliptic control problem with an integral constraint.The state and co-state are approximated by the order one Raviart-Thomas mixed finite element space and the control variable is approximated by piecewise constant functions or piecewise linear functions.We derive some superconvergence results for the control variable and the state variables when the control is approximated by piecewise constant functions.Moreover,we derive L∞-error estimates for both the control variable and the state variables when the control is discretized by piecewise linear functions.Finally,some numerical examples are given to demonstrate the theoretical results.展开更多
This article is devoted to studying the application of the weak Galerkin(WG)finite element method to the elliptic eigenvalue problem with an emphasis on obtaining lower bounds.The WG method uses discontinuous polynomi...This article is devoted to studying the application of the weak Galerkin(WG)finite element method to the elliptic eigenvalue problem with an emphasis on obtaining lower bounds.The WG method uses discontinuous polynomials on polygonal or polyhedral finite element partitions.The non-conforming finite element space of the WG method is the key of the lower bound property.It also makes the WG method more robust and flexible in solving eigenvalue problems.We demonstrate that the WG method can achieve arbitrary high convergence order.This is in contrast with existing nonconforming finite element methods which can provide lower bound approximations by linear finite elements.Numerical results are presented to demonstrate the efficiency and accuracy of the theoretical results.展开更多
A discontinuous Galerkin(DG)scheme for solving semilinear elliptic problem is developed and analyzed in this paper.The DG finite element discretization is first established,then the corresponding well-posedness is pro...A discontinuous Galerkin(DG)scheme for solving semilinear elliptic problem is developed and analyzed in this paper.The DG finite element discretization is first established,then the corresponding well-posedness is provided by using Brouwer’s fixed point method.Some optimal priori error estimates under both DG norm and L^(2)norm are presented,respectively.Numerical results are given to illustrate the efficiency of the proposed approach.展开更多
基金supported by the National Natural Science Foundation of China(Nos.51205352 and 51221004)
文摘Robotic drilling for aerospace structures demands a high positioning accuracy of the robot, which is usually achieved through error measurement and compensation. In this paper, we report the development of a practical monocular vision system for measurement of the relative error between the drill tool center point(TCP) and the reference hole. First, the principle of relative error measurement with the vision system is explained, followed by a detailed discussion on the hardware components, software components, and system integration. The elliptical contour extraction algorithm is presented for accurate and robust reference hole detection. System calibration is of key importance to the measurement accuracy of a vision system. A new method is proposed for the simultaneous calibration of camera internal parameters and hand-eye relationship with a dedicated calibration board. Extensive measurement experiments have been performed on a robotic drilling system. Experimental results show that the measurement accuracy of the developed vision system is higher than 0.15 mm, which meets the requirement of robotic drilling for aircraft structures.
基金supported by Guangdong Province Universities and Colleges Pearl River Scholar Funded Scheme(2008)National Science Foundation of China(10971074)+1 种基金Specialized Research Fund for the Doctoral Program of Higher Education(20114407110009)the Foundation for High-level Talent Faculty of Guangdong Provincial University,and Hunan Provincial Innovation Foundation for Postgraduate CX2010B247.
文摘In this paper,we investigate the superconvergence property and the L∞-error estimates of mixed finite element methods for a semilinear elliptic control problem with an integral constraint.The state and co-state are approximated by the order one Raviart-Thomas mixed finite element space and the control variable is approximated by piecewise constant functions or piecewise linear functions.We derive some superconvergence results for the control variable and the state variables when the control is approximated by piecewise constant functions.Moreover,we derive L∞-error estimates for both the control variable and the state variables when the control is discretized by piecewise linear functions.Finally,some numerical examples are given to demonstrate the theoretical results.
基金supported in part by China Natural National Science Foundation(91630201,U1530116,11771179)by the Program for Cheung Kong Scholars of Ministry of Education of China,Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education,Jilin University,Changchun,130012,P.R.China+3 种基金supported in part by the National Natural Science Foundation of China(NSFC 11471031,91430216)and the U.S.National Science Foundation(DMS–1419040)supported by Science Challenge Project(No.TZ2016002)National Natural Science Foundations of China(NSFC 11771434,91330202,11371026,91430108,11771322,11626033,11601368)the National Center for Mathematics and Interdisciplinary Science,CAS.
文摘This article is devoted to studying the application of the weak Galerkin(WG)finite element method to the elliptic eigenvalue problem with an emphasis on obtaining lower bounds.The WG method uses discontinuous polynomials on polygonal or polyhedral finite element partitions.The non-conforming finite element space of the WG method is the key of the lower bound property.It also makes the WG method more robust and flexible in solving eigenvalue problems.We demonstrate that the WG method can achieve arbitrary high convergence order.This is in contrast with existing nonconforming finite element methods which can provide lower bound approximations by linear finite elements.Numerical results are presented to demonstrate the efficiency and accuracy of the theoretical results.
基金The second and third authors are supported by the National Natural Science Foundation of China(No.12071160)the Guangdong Basic and Applied Basic Research Foundation(No.2019A1515010724)+2 种基金The second author is also supported by the National Natural Science Foundation of China(No.11671159)The third author is also supported by National Natural Science Foundation of China(No.12101250)the Science and Technology Projects in Guangzhou(No.202201010644).
文摘A discontinuous Galerkin(DG)scheme for solving semilinear elliptic problem is developed and analyzed in this paper.The DG finite element discretization is first established,then the corresponding well-posedness is provided by using Brouwer’s fixed point method.Some optimal priori error estimates under both DG norm and L^(2)norm are presented,respectively.Numerical results are given to illustrate the efficiency of the proposed approach.
