Off-line programming (OLP) system becomes one of the most important programming modules for the robotic belt grinding process, however there lacks research on increasing the grinding dexterous space depending on the...Off-line programming (OLP) system becomes one of the most important programming modules for the robotic belt grinding process, however there lacks research on increasing the grinding dexterous space depending on the OLP system. A new type of grinding robot and a novel robotic belt grinding workcell are forwarded, and their features are briefly introduced. An open and object-oriented off-line programming system is developed for this robotic belt grinding system. The parameters of the trimmed surface are read from the initial graphics exchange specification (IGES) file of the CAD model of the workpiece. The deBoor-Cox basis function is used to sample the grinding target with local contact frame on the workpiece. The numerical formula of inverse kinematics is set up based on Newton's iterative procedure, to calculate the grinding robot configurations corresponding to the grinding targets. After the grinding path is obtained, the OLP system turns to be more effective than the teach-by-showing system. In order to improve the grinding workspace, an optimization algorithm for dynamic tool frame is proposed and performed on the special robotic belt grinding system. The initial tool frame and the interval of neighboring tool frames are defined as the preparation of the algorithm. An optimized tool local frame can be selected to grind the complex surface for a maximum dexterity index of the robot. Under the optimization algorithm, a simulation of grinding a vane is included and comparison of grinding workspace is done before and after the tool frame optimization. By the algorithm, the grinding workspace can be enlarged. Moreover the dynamic tool frame can be considered to add one degree-of-freedom to the grinding kinematical chain, which provides the theoretical support for the improvement of robotic dexterity for the complex surface grinding.展开更多
Off line programming provides an essential link between CAD and CAM, whose development will result in greater use of robotic arc welding. An arc welding system with a robot and a rotating/tilting positioner is one of...Off line programming provides an essential link between CAD and CAM, whose development will result in greater use of robotic arc welding. An arc welding system with a robot and a rotating/tilting positioner is one of the most typical workcells. The inverse kinematics of robot and positioner is the foundation of the off line programming system. The previous researchers only focused on a special solution of the positioner inverse kinematics, which is the solution at down hand welding position. In this paper, we introduce a method for representing welding position. Then a general algorithm of rotating/tilting positioner inverse kinematics is presented, and an approach to find the unique solution of the inverse kinematics is discussed. The simulation experiment results show that the general algorithm can improve the ability of robotic arc welding off line programming system to program all types of welding positions.展开更多
This paper puts forward a communication programming method between robot and external computer based on RPC (Remote Produce Call) communication method, which realizes robot distributed controlling network system model...This paper puts forward a communication programming method between robot and external computer based on RPC (Remote Produce Call) communication method, which realizes robot distributed controlling network system model. And a new Robot off line programming method is built based on this communication method and network model. Further more, as an example, robot auto marking and auto cutting of shipbuilding profile system is developed, which proves the ideas of author’s off line programming and development methods of robot flexible automation system. As a result, this paper presents a new method for developing robot flexible automation system.展开更多
In this paper, we show a clustering method supported on evolutionary algorithms with the paradigm of linear genetic programming. “The Straight-Line Programs (slp)”, which uses a data structure which will be useful t...In this paper, we show a clustering method supported on evolutionary algorithms with the paradigm of linear genetic programming. “The Straight-Line Programs (slp)”, which uses a data structure which will be useful to represent collections of documents. This data structure can be seen as a linear representation of programs, as well as representations in the form of graphs. It has been used as a theoretical model in Computer Algebra, and our purpose is to reuse it in a completely different context. In this case, we apply it to the field of grouping library collections through evolutionary algorithms. We show its efficiency with experimental data we got from traditional library collections.展开更多
Off-line programming provides an essential link for CAD/CAM. This paper introduced the principle of developing off-line programming system for laser re-manufacturing. Task and information flow of off-line programming ...Off-line programming provides an essential link for CAD/CAM. This paper introduced the principle of developing off-line programming system for laser re-manufacturing. Task and information flow of off-line programming for laser re-manufacturing robot was analyzed and the software structure of off-line programming based on commercial CAD software was constructed. The off-line programming system developed in this study includes 3-D solid model design, direct slicing for obtaining path data, graphical simulation of the robot and its workcell, kinematic model of the robot, motion planning, and creation of the control program for manufacturing process. The CAD software was used to design models of robot, workpiece, coaxial nozzle, and workspace. Through the application programming interface provided by the CAD software, the VC++ and ATL were chosen to develop such modules as direct slicing for obtaining path data, path planning, process specification, and control program automatic generation. The FANUC Roboguide software was used to realize graphical simulation. By direct slicing, the position and orientation data of robot end-effector was determined. The results show that the proposed system can be applied in laser re-manufacturing robot for manufacturing operations.展开更多
As the end-effector of robot, the induction hard- ening tool is required to keep its orientations perpendicular to the fillets or chamfers of the mould at a distance during its uniform motion along the hardening traje...As the end-effector of robot, the induction hard- ening tool is required to keep its orientations perpendicular to the fillets or chamfers of the mould at a distance during its uniform motion along the hardening trajectory. This trajectory consists of a group of central curves which are parametric curves on the corresponding chamfers or fillets and between two edges of every chamfer or fillet. The trajectory points and the surface normal vectors at these points are obtained by parametric equations of the fillets or chamfers. This study is conducted to join each central curve into the entire hardening trajectory, including handling on the irregular surfaces and unifying the directions of hardening tool motion. According to kinematics of robot, the trajectory points in modeling coordinate system are transferred into the poses of the induction hardening tool in user frame of robot. The kinematical interference of the induction hardening tool and robot joints is checked by Robognide sim- ulation tool. The validity of the robotic off-line programming (OLP) system was verified by experiments.展开更多
Thick walled curve welding are usually joined by multi-layer and multi-pass welding, which quality and efficiency could be improved by off-line programming of robot welding. However, the precision of off-line programm...Thick walled curve welding are usually joined by multi-layer and multi-pass welding, which quality and efficiency could be improved by off-line programming of robot welding. However, the precision of off-line programming welding path was decreased due to the deviation between the off-line planned welding path and the actual welding path. A path planning algorithm and a path compensation algorithm of multi-layer and multi-pass curve welding seam for off-line programming of robot welding are developed in this paper. Experimental results show that the robot off-line programming improves the welding efftcieney and precision for thick walled curve welding seam.展开更多
In this paper, we present a nonmonotone smoothing Newton algorithm for solving the circular cone programming(CCP) problem in which a linear function is minimized or maximized over the intersection of an affine space w...In this paper, we present a nonmonotone smoothing Newton algorithm for solving the circular cone programming(CCP) problem in which a linear function is minimized or maximized over the intersection of an affine space with the circular cone. Based on the relationship between the circular cone and the second-order cone(SOC), we reformulate the CCP problem as the second-order cone problem(SOCP). By extending the nonmonotone line search for unconstrained optimization to the CCP, a nonmonotone smoothing Newton method is proposed for solving the CCP. Under suitable assumptions, the proposed algorithm is shown to be globally and locally quadratically convergent. Some preliminary numerical results indicate the effectiveness of the proposed algorithm for solving the CCP.展开更多
The purpose of this study is to introduce the current applications of off-line programming technology in thermal spraying,including some popular methods of path generation,procedure simulation,robot kinematics optimiz...The purpose of this study is to introduce the current applications of off-line programming technology in thermal spraying,including some popular methods of path generation,procedure simulation,robot kinematics optimization,etc.Indeed this technology reduces the difficulty of robot programming and enormously improves its facility for thermal spraying.At the last part of this paper,presented two examples of off-line programming in thermal spraying which refer to trajectory optimization on a work piece with a great angle and path generation on the complex work piece.The simulations and experiments have proved that off-line programming can effectively improve the production efficiency and the quality of coating.展开更多
Adaptive broadband beamforraing is a key issue in array applications. The adaptive broadband beamformer with tapped delay line (TDL) structure for nonuniform linear array (NLA) is designed according to the rule of...Adaptive broadband beamforraing is a key issue in array applications. The adaptive broadband beamformer with tapped delay line (TDL) structure for nonuniform linear array (NLA) is designed according to the rule of minimizing the beamformer's output power while keeping the distortionless response (DR) in the direction of desired signal and keeping the constant beamwidth (CB) with the prescribed sidelobe level over the whole operating band. This kind of beamforming problem can be solved with the interior-point method after being converted to the form of standard second order cone programming (SOCP). The computer simulations are presented which illustrate the effectiveness of our beamformer.展开更多
介绍了STEP-NC的概念、数据模型及其结构特点,然后通过对比MLP(Machining Line Planner)和STEP-NC数控程序对特征和操作的不同定义方法,分析了在MLP中特征及加工工艺与STEP-NC的对应关系,探讨了在MLP中实现输出STEP-NC格式的零件加工程...介绍了STEP-NC的概念、数据模型及其结构特点,然后通过对比MLP(Machining Line Planner)和STEP-NC数控程序对特征和操作的不同定义方法,分析了在MLP中特征及加工工艺与STEP-NC的对应关系,探讨了在MLP中实现输出STEP-NC格式的零件加工程序的方法。展开更多
A study of the interference simulation based on robot welding of the radar pedestal was carried out by using the KUKA Sim Pro simulation software and off-line program technology. Compared with the actual robot welding...A study of the interference simulation based on robot welding of the radar pedestal was carried out by using the KUKA Sim Pro simulation software and off-line program technology. Compared with the actual robot welding process, it was found that the trajectory of the simulated robot welding process in line with that recorded in the actual welding process, and the actual limit and interference appeared at the same place as the simulation process. There was no interference phenomenon on the outside weld-seam; on the internal weld-seam, especially on the weld-joint of support plate connected to the cylinder, a phenomenon of interference appeared. It was helpful to use the simulation method to guide the actual robot welding so as to protect robot from impacting and reduce the weld defects.展开更多
The position synthesis of planar linkages is to locate the center point of the moving joint on a rigid link, whose trajectory is a circle or a straight line. Utilizing the min-max optimization scheme, the fitting curv...The position synthesis of planar linkages is to locate the center point of the moving joint on a rigid link, whose trajectory is a circle or a straight line. Utilizing the min-max optimization scheme, the fitting curve needs to minimize the maximum fitting error to acquire the dimension of a planar binary P-R link. Based on the saddle point programming, the fitting straight line is determined to the planar discrete point-path traced by the point of the rigid body in planar motion. The property and evolution of the defined saddle line error can be revealed from three given separate points. A quartic algebraic equation relating the fitting error and the coordinates is derived, which agrees with the classical theory. The effect of the fourth point is discussed in three cases through the constraint equations. The multi-position saddle line error is obtained by combination and comparison from the saddle point programming. Several examples are presented to illustrate the solution process for the saddle line error of the moving plane. The saddle line error surface and the contour map presented to show the variations of the fitting error in the fixed frame. The discrete kinematic geometry is then set up to disclose the relations of the separate positions of the rigid body, the location of the tracing point on the moving body, and the position and orientation of the saddle line to the point-path. This paper presents a new analytic geometry method for saddle line fitting and provides a theoretical foundation for position synthesis.展开更多
In this paper, the Eigenvalue Complementarity Problem (EiCP) with real symmetric matrices is addressed, which appears in the study of contact problem in mechanics. We discuss a quadratic programming formulation to the...In this paper, the Eigenvalue Complementarity Problem (EiCP) with real symmetric matrices is addressed, which appears in the study of contact problem in mechanics. We discuss a quadratic programming formulation to the problem. The resulting problems are nonlinear programs that can be solved by a line search filter-SQP algorithm.展开更多
Promotion is an essential element in the marketing mix. It is used by businesses to inform, influence and persuade customers to adopt the products and services they offer. Without promotion, business would be stagnant...Promotion is an essential element in the marketing mix. It is used by businesses to inform, influence and persuade customers to adopt the products and services they offer. Without promotion, business would be stagnant and lack substantial growth because the brands would have low visibility in the market. Moreover, today’s vast and assorted markets comprise of customers with different needs and varied behavior. So it is rarely possible for companies to satisfy all customers by treating them alike. Thus there arises a need to divide the market into segments having customers with similar traits/characteristics. After identifying appropriate market segments, firms can design differentiated promotional campaigns for each segment. At the same time there can be a mass market promotional campaign that reaches different segments with a fixed spectrum. Also since promotional effort resources are limited, one must use them judiciously. In this paper, we formulate mathematical programming problem under repeat purchase scenario, which optimally allocates mass promotional effort resources and differentiated promotional effort resources across the segments dynamically in order to maximize the overall sales obtained from multiple products of a product line under budgetary and minimum sales aspiration level constraint on each product under consideration in each segment. The planning horizon is divided into multi periods, the adoption pattern of each product in each segment is observed in every subinterval and accordingly promotional effort allocations are determined for the next period till we reach the end of planning period. The optimization model has been further extended to incorporate minimum aspiration level constraints on total sales for each product under consideration from all the segments taken together. The non linear programming problem so formulated is solved using differential evolution approach. A numerical example has been discussed to illustrate applicability of the model.展开更多
A kind of direct methods is presented for the solution of optimal control problems with state constraints. These methods are sequential quadratic programming methods. At every iteration a quadratic programming which i...A kind of direct methods is presented for the solution of optimal control problems with state constraints. These methods are sequential quadratic programming methods. At every iteration a quadratic programming which is obtained by quadratic approximation to Lagrangian function and linear approximations to constraints is solved to get a search direction for a merit function. The merit function is formulated by augmenting the Lagrangian function with a penalty term. A line search is carried out along the search direction to determine a step length such that the merit function is decreased. The methods presented in this paper include continuous sequential quadratic programming methods and discreate sequential quadratic programming methods.展开更多
基金supported by National Hi-tech Research and Development Program of China (863 Program, Grant No. 2007AA04Z2443)State Key Laboratory for Man ufacturing Systems Engineering of Xi’an Jiaotong University of China
文摘Off-line programming (OLP) system becomes one of the most important programming modules for the robotic belt grinding process, however there lacks research on increasing the grinding dexterous space depending on the OLP system. A new type of grinding robot and a novel robotic belt grinding workcell are forwarded, and their features are briefly introduced. An open and object-oriented off-line programming system is developed for this robotic belt grinding system. The parameters of the trimmed surface are read from the initial graphics exchange specification (IGES) file of the CAD model of the workpiece. The deBoor-Cox basis function is used to sample the grinding target with local contact frame on the workpiece. The numerical formula of inverse kinematics is set up based on Newton's iterative procedure, to calculate the grinding robot configurations corresponding to the grinding targets. After the grinding path is obtained, the OLP system turns to be more effective than the teach-by-showing system. In order to improve the grinding workspace, an optimization algorithm for dynamic tool frame is proposed and performed on the special robotic belt grinding system. The initial tool frame and the interval of neighboring tool frames are defined as the preparation of the algorithm. An optimized tool local frame can be selected to grind the complex surface for a maximum dexterity index of the robot. Under the optimization algorithm, a simulation of grinding a vane is included and comparison of grinding workspace is done before and after the tool frame optimization. By the algorithm, the grinding workspace can be enlarged. Moreover the dynamic tool frame can be considered to add one degree-of-freedom to the grinding kinematical chain, which provides the theoretical support for the improvement of robotic dexterity for the complex surface grinding.
基金ThispaperissupportedbyNationalNatureScienceFoundation (No .5 96 35 16 0 )AdvancedUniversityDoctoralSubjectFoundation (No .980 2 1311)
文摘Off line programming provides an essential link between CAD and CAM, whose development will result in greater use of robotic arc welding. An arc welding system with a robot and a rotating/tilting positioner is one of the most typical workcells. The inverse kinematics of robot and positioner is the foundation of the off line programming system. The previous researchers only focused on a special solution of the positioner inverse kinematics, which is the solution at down hand welding position. In this paper, we introduce a method for representing welding position. Then a general algorithm of rotating/tilting positioner inverse kinematics is presented, and an approach to find the unique solution of the inverse kinematics is discussed. The simulation experiment results show that the general algorithm can improve the ability of robotic arc welding off line programming system to program all types of welding positions.
文摘This paper puts forward a communication programming method between robot and external computer based on RPC (Remote Produce Call) communication method, which realizes robot distributed controlling network system model. And a new Robot off line programming method is built based on this communication method and network model. Further more, as an example, robot auto marking and auto cutting of shipbuilding profile system is developed, which proves the ideas of author’s off line programming and development methods of robot flexible automation system. As a result, this paper presents a new method for developing robot flexible automation system.
文摘In this paper, we show a clustering method supported on evolutionary algorithms with the paradigm of linear genetic programming. “The Straight-Line Programs (slp)”, which uses a data structure which will be useful to represent collections of documents. This data structure can be seen as a linear representation of programs, as well as representations in the form of graphs. It has been used as a theoretical model in Computer Algebra, and our purpose is to reuse it in a completely different context. In this case, we apply it to the field of grouping library collections through evolutionary algorithms. We show its efficiency with experimental data we got from traditional library collections.
基金Supported by the Science and Technology Development Project of Tianjin Colleges and Universities (No. 20071108)the Key Project of Tianjin Science and Technology Committee (No.08ZCKFGX02300)
文摘Off-line programming provides an essential link for CAD/CAM. This paper introduced the principle of developing off-line programming system for laser re-manufacturing. Task and information flow of off-line programming for laser re-manufacturing robot was analyzed and the software structure of off-line programming based on commercial CAD software was constructed. The off-line programming system developed in this study includes 3-D solid model design, direct slicing for obtaining path data, graphical simulation of the robot and its workcell, kinematic model of the robot, motion planning, and creation of the control program for manufacturing process. The CAD software was used to design models of robot, workpiece, coaxial nozzle, and workspace. Through the application programming interface provided by the CAD software, the VC++ and ATL were chosen to develop such modules as direct slicing for obtaining path data, path planning, process specification, and control program automatic generation. The FANUC Roboguide software was used to realize graphical simulation. By direct slicing, the position and orientation data of robot end-effector was determined. The results show that the proposed system can be applied in laser re-manufacturing robot for manufacturing operations.
文摘As the end-effector of robot, the induction hard- ening tool is required to keep its orientations perpendicular to the fillets or chamfers of the mould at a distance during its uniform motion along the hardening trajectory. This trajectory consists of a group of central curves which are parametric curves on the corresponding chamfers or fillets and between two edges of every chamfer or fillet. The trajectory points and the surface normal vectors at these points are obtained by parametric equations of the fillets or chamfers. This study is conducted to join each central curve into the entire hardening trajectory, including handling on the irregular surfaces and unifying the directions of hardening tool motion. According to kinematics of robot, the trajectory points in modeling coordinate system are transferred into the poses of the induction hardening tool in user frame of robot. The kinematical interference of the induction hardening tool and robot joints is checked by Robognide sim- ulation tool. The validity of the robotic off-line programming (OLP) system was verified by experiments.
文摘Thick walled curve welding are usually joined by multi-layer and multi-pass welding, which quality and efficiency could be improved by off-line programming of robot welding. However, the precision of off-line programming welding path was decreased due to the deviation between the off-line planned welding path and the actual welding path. A path planning algorithm and a path compensation algorithm of multi-layer and multi-pass curve welding seam for off-line programming of robot welding are developed in this paper. Experimental results show that the robot off-line programming improves the welding efftcieney and precision for thick walled curve welding seam.
基金supported by the National Natural Science Foundation of China(11401126,71471140 and 11361018)Guangxi Natural Science Foundation(2016GXNSFBA380102 and 2014GXNSFFA118001)+2 种基金Guangxi Key Laboratory of Cryptography and Information Security(GCIS201618)Guangxi Key Laboratory of Automatic Detecting Technology and Instruments(YQ15112 and YQ16112)China
文摘In this paper, we present a nonmonotone smoothing Newton algorithm for solving the circular cone programming(CCP) problem in which a linear function is minimized or maximized over the intersection of an affine space with the circular cone. Based on the relationship between the circular cone and the second-order cone(SOC), we reformulate the CCP problem as the second-order cone problem(SOCP). By extending the nonmonotone line search for unconstrained optimization to the CCP, a nonmonotone smoothing Newton method is proposed for solving the CCP. Under suitable assumptions, the proposed algorithm is shown to be globally and locally quadratically convergent. Some preliminary numerical results indicate the effectiveness of the proposed algorithm for solving the CCP.
文摘The purpose of this study is to introduce the current applications of off-line programming technology in thermal spraying,including some popular methods of path generation,procedure simulation,robot kinematics optimization,etc.Indeed this technology reduces the difficulty of robot programming and enormously improves its facility for thermal spraying.At the last part of this paper,presented two examples of off-line programming in thermal spraying which refer to trajectory optimization on a work piece with a great angle and path generation on the complex work piece.The simulations and experiments have proved that off-line programming can effectively improve the production efficiency and the quality of coating.
基金supported by the National Nature Science Foundation of China (60472101)President Award of ChineseAcademy of Sciences(O729031511).
文摘Adaptive broadband beamforraing is a key issue in array applications. The adaptive broadband beamformer with tapped delay line (TDL) structure for nonuniform linear array (NLA) is designed according to the rule of minimizing the beamformer's output power while keeping the distortionless response (DR) in the direction of desired signal and keeping the constant beamwidth (CB) with the prescribed sidelobe level over the whole operating band. This kind of beamforming problem can be solved with the interior-point method after being converted to the form of standard second order cone programming (SOCP). The computer simulations are presented which illustrate the effectiveness of our beamformer.
基金Funded by Anhui Provincial Natural Science Foundation of China(GFKJ2015B002)Quality Engineering Project of Anhui province(2014zy122)
文摘A study of the interference simulation based on robot welding of the radar pedestal was carried out by using the KUKA Sim Pro simulation software and off-line program technology. Compared with the actual robot welding process, it was found that the trajectory of the simulated robot welding process in line with that recorded in the actual welding process, and the actual limit and interference appeared at the same place as the simulation process. There was no interference phenomenon on the outside weld-seam; on the internal weld-seam, especially on the weld-joint of support plate connected to the cylinder, a phenomenon of interference appeared. It was helpful to use the simulation method to guide the actual robot welding so as to protect robot from impacting and reduce the weld defects.
基金Supported by National Natural Science Foundation of China(Grant No.51275067)
文摘The position synthesis of planar linkages is to locate the center point of the moving joint on a rigid link, whose trajectory is a circle or a straight line. Utilizing the min-max optimization scheme, the fitting curve needs to minimize the maximum fitting error to acquire the dimension of a planar binary P-R link. Based on the saddle point programming, the fitting straight line is determined to the planar discrete point-path traced by the point of the rigid body in planar motion. The property and evolution of the defined saddle line error can be revealed from three given separate points. A quartic algebraic equation relating the fitting error and the coordinates is derived, which agrees with the classical theory. The effect of the fourth point is discussed in three cases through the constraint equations. The multi-position saddle line error is obtained by combination and comparison from the saddle point programming. Several examples are presented to illustrate the solution process for the saddle line error of the moving plane. The saddle line error surface and the contour map presented to show the variations of the fitting error in the fixed frame. The discrete kinematic geometry is then set up to disclose the relations of the separate positions of the rigid body, the location of the tracing point on the moving body, and the position and orientation of the saddle line to the point-path. This paper presents a new analytic geometry method for saddle line fitting and provides a theoretical foundation for position synthesis.
文摘In this paper, the Eigenvalue Complementarity Problem (EiCP) with real symmetric matrices is addressed, which appears in the study of contact problem in mechanics. We discuss a quadratic programming formulation to the problem. The resulting problems are nonlinear programs that can be solved by a line search filter-SQP algorithm.
文摘Promotion is an essential element in the marketing mix. It is used by businesses to inform, influence and persuade customers to adopt the products and services they offer. Without promotion, business would be stagnant and lack substantial growth because the brands would have low visibility in the market. Moreover, today’s vast and assorted markets comprise of customers with different needs and varied behavior. So it is rarely possible for companies to satisfy all customers by treating them alike. Thus there arises a need to divide the market into segments having customers with similar traits/characteristics. After identifying appropriate market segments, firms can design differentiated promotional campaigns for each segment. At the same time there can be a mass market promotional campaign that reaches different segments with a fixed spectrum. Also since promotional effort resources are limited, one must use them judiciously. In this paper, we formulate mathematical programming problem under repeat purchase scenario, which optimally allocates mass promotional effort resources and differentiated promotional effort resources across the segments dynamically in order to maximize the overall sales obtained from multiple products of a product line under budgetary and minimum sales aspiration level constraint on each product under consideration in each segment. The planning horizon is divided into multi periods, the adoption pattern of each product in each segment is observed in every subinterval and accordingly promotional effort allocations are determined for the next period till we reach the end of planning period. The optimization model has been further extended to incorporate minimum aspiration level constraints on total sales for each product under consideration from all the segments taken together. The non linear programming problem so formulated is solved using differential evolution approach. A numerical example has been discussed to illustrate applicability of the model.
文摘A kind of direct methods is presented for the solution of optimal control problems with state constraints. These methods are sequential quadratic programming methods. At every iteration a quadratic programming which is obtained by quadratic approximation to Lagrangian function and linear approximations to constraints is solved to get a search direction for a merit function. The merit function is formulated by augmenting the Lagrangian function with a penalty term. A line search is carried out along the search direction to determine a step length such that the merit function is decreased. The methods presented in this paper include continuous sequential quadratic programming methods and discreate sequential quadratic programming methods.