面向冗余度机械臂QP问题求解的E47和94LVI数值算法

J4 ›› 2015, Vol. 37 ›› Issue (07): 1405-1411.

面向冗余度机械臂QP问题求解的E47和94LVI数值算法

谢清，张雨浓，余晓填，郭东生，金龙

（1.中山大学信息科学与技术学院，广东广州 510006；
2.广东顺德中山大学卡内基梅隆大学国际联合研究院,广东顺德 528300；
3.华南理工大学自主系统和网络控制教育部重点实验室,广东广州 510640）

收稿日期:2014-02-04 修回日期:2014-09-05 出版日期:2015-07-25 发布日期:2015-07-25
基金资助:
国家自然科学基金资助项目（61075121和60935001）；广东省大学生创新训练资助项目（1055813063）；自主系统与网络控制教育部重点实验室开放基金资助项目(2013A07)

Numerical algorithms E47 and 94LVI for quadratic programming
problems solving of redundant robot manipulators

XIE Qing，ZHANG Yunong，YU Xiaotian，GUO Dongsheng，JIN Long

（1.School of Information Science and Technology,Sun Yatsen University,Guangzhou 510006;
2.Shunde International Joint Research Institute,SYSUCMU,Shunde 528300;
3.Key Laboratory of Autonomous Systems and Networked Control of Ministry of Education,
South China University of Technology,Guangzhou 510640,China）

Received:2014-02-04 Revised:2014-09-05 Online:2015-07-25 Published:2015-07-25

摘要/Abstract

摘要：

冗余度机械臂的二次规划(QP)问题同时受制于等式约束、不等式约束和双端约束，且面向冗余度机械臂实时控制的该类QP问题的求解对运算实时性有较高要求。考虑同时受制于上述三种约束的二次规划问题的求解，给出并研究两种数值算法(E47和94LVI算法)。这类带约束的二次规划问题被等价转换为分段线性投影方程。应用E47和94LVI算法求解上述分段线性投影方程，从而得到二次规划问题的最优数值解。同时，通过大量的数值实验，研究两种算法面向冗余度机械臂的QP问题求解性能，并给出E47、94LVI算法与经典有效集算法的对比实验结果。最终证实了E47和94LVI两种算法在求解二次规划问题上的高效性和优越性。

关键词: 二次规划, 数值算法, E47算法, 94LVI算法, 冗余度机械臂

Abstract:

The quadratic programming (QP) problems of redundant robot manipulators, which have high requirement for realtime calculation,are subject to equality,inequality and bound constraints.For solving such QP problems with these constraints,we present and study two numerical algorithms (named as E47 and 94LVI).Such QP problems are converted equivalently to piecewiselinear projection equations (PLPE).Resultant PLPE can be solved by E47 and 94LVI algorithms,and thus the optimal numerical solutions to the QP problems are obtained.In addition, by means of abundant numerical experiments,the performances of these two algorithms on QP solving for redundant robot manipulators are proved.Comparative numerical results of E47,94LVI and those of the conventional activeset algorithms are also presented.Finally,the efficiency and superiority of the E47 and 94LVI algorithms for QP solving are well validated.

Key words: quadratic programming;numerical algorithms;E47 algorithm;94LVI algorithm;redundant robot manipulators

谢清，张雨浓，余晓填，郭东生，金龙. 面向冗余度机械臂QP问题求解的E47和94LVI数值算法[J]. J4, 2015, 37(07): 1405-1411.

XIE Qing，ZHANG Yunong，YU Xiaotian，GUO Dongsheng，JIN Long. Numerical algorithms E47 and 94LVI for quadratic programming
problems solving of redundant robot manipulators [J]. J4, 2015, 37(07): 1405-1411.

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