This paper presents an explicit formula based on reparameterization technique for progressively computing a simple root of a smooth function,which may have wide applications in robotics,geomagnetic navigation,geometri...This paper presents an explicit formula based on reparameterization technique for progressively computing a simple root of a smooth function,which may have wide applications in robotics,geomagnetic navigation,geometric processing and computer graphics.Comparing with Newton-like method,it can achieve convergence rate 2 by adding one more functional evaluation,improve the computational stability and ensure the convergence,and also obtain higher convergence rate and higher efficiency index.Compared with clipping methods for polynomials,it doesn't need to bound the polynomials,directly bound the roots and can also work well for non-polynomial functions with much higher computational efficiency.Comparing with previous progressive methods,it achieves a much higher computational efficiency and is extended to solve bivariate equation system.Numerical examples show its much better performance on approximation error,computational efficiency and computational stability.展开更多
Aimed at the real-time forward kinematics solving problem of Stewart parallel manipulator in the control course, a mixed algorithm combining immune evolutionary algorithm and numerical iterative scheme is proposed. Fi...Aimed at the real-time forward kinematics solving problem of Stewart parallel manipulator in the control course, a mixed algorithm combining immune evolutionary algorithm and numerical iterative scheme is proposed. Firstly taking advantage of simpleness of inverse kinematics, the forward kinematics is transformed to an optimal problem. Immune evolutionary algorithm is employed to find approximate solution of this optimal problem in manipulator＇s workspace. Then using above solution as iterative initialization, a speedy numerical iterative scheme is proposed to get more precise solution. In the manipulator running course, the iteration initialization can be selected as the last period position and orientation. Because the initialization is closed to correct solution, solving precision is high and speed is rapid enough to satisfy real-time requirement. This mixed forward kinematics algorithm is applied to real Stewart parallel manipulator in the real-time control course. The examination result shows that the algorithm is very efficient and practical.展开更多
A new iterating method based on homotopy function is developed in this paper. All solutions can be found easily without the need of choosing proper initial values. Compared to the homotopy continuation method, the sol...A new iterating method based on homotopy function is developed in this paper. All solutions can be found easily without the need of choosing proper initial values. Compared to the homotopy continuation method, the solution process of the present method is simplified, and the computation efficiency as well as the reliability for obtaining all solutions is also improved. By application of the method to the mechanisms problems, the results are satisfactory.展开更多
The exploitation of rocket guidance technology on the basis of the guidance law of Space Shuttle and Pegasus rocket was performed. A new efficient method of numerical iteration solution to the boundary value problem w...The exploitation of rocket guidance technology on the basis of the guidance law of Space Shuttle and Pegasus rocket was performed. A new efficient method of numerical iteration solution to the boundary value problem was put forward. The numerical simulation results have shown that the method features good performances of stability, robustness, high precision, and algebraic formulas in real computation. By virtue of modern DSP （digital signal processor ） high speed chip technology, the algorithm can be used in real time and can adaot to the requirements of the big primary bias of rocket guidance.展开更多
WT5”BZ]On the basis of the theory of complex functions the authors derive the boundary integral equations for the flow discharging from an outlet in a dam in an auxiliary plane. Assuming that the integral variables a...WT5”BZ]On the basis of the theory of complex functions the authors derive the boundary integral equations for the flow discharging from an outlet in a dam in an auxiliary plane. Assuming that the integral variables are constants in small integral intervals, one can directly integrate the boundary integral equations. With the use of the boundary stream coordinates, the boundary integral equations in the physical plane are obtained. Therefore the angle of the solid boundaries is a known function of stream coordinates in the physical plane instead of an unknown function in the complex potential plane or auxiliary plane. As a result we avoid the difficulty for seeking the mapping function which conformally maps the physical plane onto the complex potential or auxiliary plane. A synchronous iterative method for the flow rate and the flow pattern is presented. The flow rate, the pressure distributions at the solid walls and the profiles of the free jet are calculated. The numerical results are in excellent agreement with the experimental results.[WT5”HZ]展开更多
基金Supported by the National Natural Science Foundation of China (61972120)。
文摘This paper presents an explicit formula based on reparameterization technique for progressively computing a simple root of a smooth function,which may have wide applications in robotics,geomagnetic navigation,geometric processing and computer graphics.Comparing with Newton-like method,it can achieve convergence rate 2 by adding one more functional evaluation,improve the computational stability and ensure the convergence,and also obtain higher convergence rate and higher efficiency index.Compared with clipping methods for polynomials,it doesn't need to bound the polynomials,directly bound the roots and can also work well for non-polynomial functions with much higher computational efficiency.Comparing with previous progressive methods,it achieves a much higher computational efficiency and is extended to solve bivariate equation system.Numerical examples show its much better performance on approximation error,computational efficiency and computational stability.
文摘Aimed at the real-time forward kinematics solving problem of Stewart parallel manipulator in the control course, a mixed algorithm combining immune evolutionary algorithm and numerical iterative scheme is proposed. Firstly taking advantage of simpleness of inverse kinematics, the forward kinematics is transformed to an optimal problem. Immune evolutionary algorithm is employed to find approximate solution of this optimal problem in manipulator＇s workspace. Then using above solution as iterative initialization, a speedy numerical iterative scheme is proposed to get more precise solution. In the manipulator running course, the iteration initialization can be selected as the last period position and orientation. Because the initialization is closed to correct solution, solving precision is high and speed is rapid enough to satisfy real-time requirement. This mixed forward kinematics algorithm is applied to real Stewart parallel manipulator in the real-time control course. The examination result shows that the algorithm is very efficient and practical.
文摘A new iterating method based on homotopy function is developed in this paper. All solutions can be found easily without the need of choosing proper initial values. Compared to the homotopy continuation method, the solution process of the present method is simplified, and the computation efficiency as well as the reliability for obtaining all solutions is also improved. By application of the method to the mechanisms problems, the results are satisfactory.
文摘The exploitation of rocket guidance technology on the basis of the guidance law of Space Shuttle and Pegasus rocket was performed. A new efficient method of numerical iteration solution to the boundary value problem was put forward. The numerical simulation results have shown that the method features good performances of stability, robustness, high precision, and algebraic formulas in real computation. By virtue of modern DSP （digital signal processor ） high speed chip technology, the algorithm can be used in real time and can adaot to the requirements of the big primary bias of rocket guidance.
文摘WT5”BZ]On the basis of the theory of complex functions the authors derive the boundary integral equations for the flow discharging from an outlet in a dam in an auxiliary plane. Assuming that the integral variables are constants in small integral intervals, one can directly integrate the boundary integral equations. With the use of the boundary stream coordinates, the boundary integral equations in the physical plane are obtained. Therefore the angle of the solid boundaries is a known function of stream coordinates in the physical plane instead of an unknown function in the complex potential plane or auxiliary plane. As a result we avoid the difficulty for seeking the mapping function which conformally maps the physical plane onto the complex potential or auxiliary plane. A synchronous iterative method for the flow rate and the flow pattern is presented. The flow rate, the pressure distributions at the solid walls and the profiles of the free jet are calculated. The numerical results are in excellent agreement with the experimental results.[WT5”HZ]
