模糊逻辑在机器人逆动动学求解中的应用

冗余机器人逆运动学求解的方法很多，多数都不能很好的满足实时控制的要求，本文运用模糊逻辑的思想，构造了一种逆运动学求解方法，其计算量较其它方法大大减小，且满足实时控制的要求，仿真结果也证明了该方法的可行性。     

多机器人协调吊运系统逆运动学分析及优化

针对紧耦合多机器人协调吊运系统的逆运动学问题进行了分析,首先利用几何关系和力旋量平衡方程建立了系统的运动学模型和动力学模型;然后对系统的逆运动学进行分析,将其分为变柔索长度和固定柔索长度两种情况分别进行分析;随后对运动学逆解在某一时刻存在无穷多解、多组解和无解的情况分别给出了解决方法,对存在多组解的情况,提出一优化目标求解最优解;最后结合软件UG/ADAMS/MATLAB建立了系统的实验平台,通过实例仿真计算验证了方法的有效性,为后续进一步研究系统运动稳定性、优化拉力分布和控制算法奠定了基础.     

基于遗传算法的机器人任务优化调度研究

工业机器人应该在尽可能短的周期内完成复杂的任务,以获得高生产率.确定机械手末端执行器访问多个任务点的最佳路径的问题与著名的旅行商问题(TSP)相似,但并不完全相同.为了使TSP适应机器人技术,需要优化的度量是时间而不是距离.另外,任意两点之间的行程时间受机械手构型的选择影响较大.因此,需要考虑运动学逆问题的多重解.逆运动学问题的求解是机器人控制的基础.许多传统的逆运动学问题的解决方法,如几何、迭代和代数方法,对冗余机器人来说是不够的.以此为出发点,基于遗传算法提出了一种新的编码方法来考虑逆运动学问题的多重解,方法适用于任何非冗余度的机械手.仿真实验结果显示,提出的方法能在一定的时间内快速找到最优解或近似最优解.且任何非冗余度机械手的多重配置很容易体现在遗传算法的编码中.     

一种七自由度冗余机械臂的逆运动学优化算法

在建立一种常见的七自由度冗余机械臂D-H模型的基础上,结合固定关节角法和加权最小范数法,提出了一种基于二次计算的逆运动学优化算法.基于加权最小范数法具有回避关节极限以得到优化解的优势,该算法一方面在牺牲一定时间复杂度的条件下进一步提高了逆运动学求解的精度,另一方面基于迭代算法解决了雅克比伪逆不存在时加权最小范数法无法求解的问题.通过仿真结果可以看出,基于加权最小范数法的二次计算法在对期望轨迹的跟踪精度上有了很大提高,并能够较好地解决雅克比伪逆不存在时的求解问题.     

同伦算法在并联机器人运动学中的应用

讨论同伦算法求解并联机器人运动学正问题.通过参系数同伦法大大减少了跟踪路径的数目,从而提高了同伦算法的效率使之对求解一般非线性代数方程组更为可行.采用这一算法,求出了中科院沈阳自动化研究所机器人开放研究实验室的新型并联机器人模型的全部正解.为新模型的机构分析和实时控制提供了理论依据.     

结构动力学逆特征值问题的同伦解法

将结构动力学反问题视为拟乘法逆特征值问题,利用求解非线性方程组的同伦方法来解决结构动力学逆特征值问题,这种方法由于沿同伦路径求解,对初值的选取没有本质的要求,算例说明了这种方法是可行的．     

带复数核的第一类Fredholm积分方程的正则化方法及其应用

本文推广了Ｔｉｋｈｏｎｏｖ正则化方法，导出了带复数核的第一类Ｆｒｅｄｈｏｌｍ积分方程的正则解应满足的正则积分微分方程，并讨论了正则解的收敛性·作为这一方法的应用，数值求解了与二维摇板造波问题相应的一类逆问题，并给出了选择最佳正则参数的一个实用的方法     

实时求解线性规划问题的原对偶神经网络(英文)

本文探讨了线性规划的原问题与对偶问题理论,并在此基础上可开发出一种用于在线求解线性规划的递归神经网络和应用于冗余机器手臂逆运动学的求解问题上.如,Tang等人开展的原对偶神经网络.但鉴于对偶理论的复杂性和多样性,该原对偶神经网络模型仅可以得到线性规划问题的可行解,而本文对该网络模型改进后可得到线性规划问题的最优解.仿真结果证实了这种改进模型在解决线性规划问题上的有效性、正确性和高效率.     

Moore-Penrose广义逆矩阵与线性方程组的解

线性方程组的逆矩阵求解方法只使用于系数矩阵为可逆方阵,对于一般线性方程组可以应用Moore-Penrose广义逆矩阵来研究并表示其通解,本文主要探讨Moore-Penrose广义逆矩阵及一般线性方程组通解和最小范数解.     

二维水翼的局部空泡流研究

运用基于速度势的低阶边界积分方法研究了二维水翼的定常局部空化。通过迭代求解给定了空化数的空泡长度和空泡形状,运动学和动力学边界条件在迭代过程中满足;采用回射流模型和压力恢复闭合模型代替空泡后的高湍流度的二相尾流。计算结果和已发表的数值结果进行了比较。     

Inverse eigenvalue problems

The classical inverse additive and multiplicative inverse eigenvalue problems for matrices are studied. Using general results on the solvability of polynomial systems it is shown that in the complex case these problems are always solvable by a finite number of solutions. In case of real symmetric matrices the inverse problems are reformulated to have a real solution. An algorithm is given to obtain this solution.     

Simple Harmonic Generation: an Exact Method of Solution

The general solution for simple harmonic generation is obtained by inverse scattering techniques. The time evolution of the scattering data is found to be much more complicated than in all other cases which are solvable by inverse scattering. It is also pointed out that the instability of the real solutions of simple harmonic generation is related to the singular nature of the scattering data about ζ = 0.     

用3个向量对构造梁振动系统的刚度矩阵

针对梁的离散化模型的刚度矩阵是五对角矩阵,梁振动反问题的实质是实对称五对角矩阵的特征值反问题.该文利用向量对、Moore-Penrose广义逆给出了实对称五对角矩阵向量对反问题存在唯一解的条件,并结合矩阵分块讨论了双对称五对角矩阵向量对反问题解存在唯一的条件,进而计算了次对角线位置元素为负,其它位置元素均为正的实对称五对角矩阵特征值反问题.由于构造梁的离散模型需要的数据可由测试得到,故而其结果适合于模态分析、系统结构的分析与设计等方面应用.最后给出了数值算例,通过数值讨论说明方法的有效性.     

Toward a General Solution of the Three‐Wave Partial Differential Equations

The three‐wave, resonant interaction equations appear in many physical applications. These partial differential equations (PDEs) are known to be completely integrable, and have been solved with initial data that decay rapidly in space, using inverse scattering theory. We present a new way to solve these equations, which makes no use of inverse scattering theory, and which can be used with a wide variety of boundary conditions. A “general solution” of these PDEs would involve six free, real‐valued functions of space. At this time, our “nearly general solution” accepts five free, real‐valued functions of space, and embeds them in convergent series in a deleted neighborhood of a pole.     

A regional inverse eigenvalue problem: solution with application in control theory

A new procedure for the solution of the regional inverse eigenvalueproblem is suggested and applied to the pole-assignment problemof control theory. Algebraic inequalities are derived whichset bounds on the real and imaginary parts of the closed-loopmatrix eigenvalues. As a result, these eigenvalues are locatedinside a prescribed rectangular region in the complex plane,which is better in real applications for controlling the systemperformance by a controller matrix which is computed in a simplerway.     

A regularizing algorithm for the solution of the inverse problem for an inhomogeneous string

We consider uniqueness of the solution of the inverse problem of determining the coefficient of the one-dimensional wave equation on the real halfline. Necessary conditions of existence of a unique solution of this inverse problem are obtained. A Tikhonov regularizing algorithm is constructed for approximate solution of the inverse problem. The algorithm has an efficient numerical implementation.Translated from Vychislitel'naya Matematika i Matematicheskoe Obespechenie EVM, pp. 55–66, 1985.     

The Complexity Analysis of the Inverse Center Location Problem

Given a feasible solution, the inverse optimization problem is to modify some parameters of the original problem as little as possible, and sometimes also with bound restrictions on these adjustments, to make the feasible solution become an optimal solution under the new parameter values. So far it is unknown that for a problem which is solvable in polynomial time, whether its inverse problem is also solvable in polynomial time. In this note we answer this question by considering the inverse center location problem and show that even though the original problem is polynomially solvable, its inverse problem is NP–hard.     

基于Labview的一级环形倒立摆逆系统轨迹法自动摆起控制

利用求解非线性方程两点边值问题,得到逆系统参考轨迹;通过设计逆系统前馈控制及LQR反馈控制器,对参考轨迹实时跟踪。基于QNET 2.0旋转倒立摆实验平台,采用Labview编程软件,实现了一级环形倒立摆的自动摆起与稳定的实物控制。实验结果证明控制算法的有效性,可以使一级环形倒立摆在一个摆周期内自动摆起,并保持稳定状态。与能量法自动起摆实验比较,逆系统算法具有较好的快速性和稳定性。     

Depth sounding: an illustration of some of the pitfalls of inverse scattering problems

The principal objective of this work is to show how various “connections” between the estimator and the predictor affect the solution of an inverse scattering problem as it is formulated in the frequency domain. We show that when there is little or no connection, it is impossible to obtain a solution. The other extreme, i.e., identity of the estimator and predictor (inverse crime [1]), enables solutions to be obtained, whatever the particular choices of the estimator or predictor, but these solutions are not trivial, as is written in [1], in that they are not unique. Moreover, we show that by a suitable change of external variables (e.g., frequency), one can lift the degeneracy and thereby spot the correct solution, which is unique. In this respect, the inverse crime turns out to be useful in that it enables one to devise methods for resolving the nonuniqueness issue of inverse problems. More generally, we show that successful inversion, in both the frequency and time domains, can be accomplished only when the discrepancy between the estimator and the predictor is small.     

On the Uniqueness of Solutions of a Nonlinear Elliptic Problem Arising in the Confinement of a Plasma in a Stellarator Device

We study the uniqueness of solutions of a semilinear elliptic problem obtained from an inverse formulation when the nonlinear terms of the equation are prescribed in a general class of real functions. The inverse problem arises in the modeling of the magnetic confinement of a plasma in a Stellarator device. The uniqueness proof relies on an -estimate on the solution of an auxiliary nonlocal problem formulated in terms of the relative rearrangement of a datum with respect to the solution. Accepted 21 March 1997