基于对偶二次规划的六足并联机器人驱动力分配

doi:10.3901/JME.2018.07.020

机械工程学报 ›› 2018, Vol. 54 ›› Issue (7): 20-27.doi: 10.3901/JME.2018.07.020

基于对偶二次规划的六足并联机器人驱动力分配

辛桂阳^1,2, 钟国梁^1,2, 王恒升^1,2, 邓华^1,2

1. 中南大学机电工程学院长沙 410083;
2. 中南大学高性能复杂制造国家重点实验室长沙 410083

收稿日期:2017-03-29 修回日期:2017-11-27 出版日期:2018-04-05 发布日期:2018-04-05
通讯作者: 邓华(通信作者),男,1961年出生,博士,教授,博士研究生导师。主要研究方向为机器人技术,智能控制理论与应用。E-mail:hdeng@csu.edu.cn
作者简介:辛桂阳,男,1990年出生,博士研究生。主要研究方向为机器人建模与基于模型的控制。E-mail:gyxin12@csu.edu.cn;钟国梁,男,1985年出生,博士,讲师,博士研究生导师。主要研究方向为机器人智能控制。E-mail:zhong001985@csu.edu.cn;王恒升,男,1963年出生,博士,教授,博士研究生导师。主要研究方向为控制理论及机电系统运动控制。E-mail:whsheng@csu.edu.cn
基金资助:
国家重点基础研究发展计划（973计划，2013CB035504）资助项目。

Optimal Driving Forces Distribution for a Six-parallel-legged Robot Based on Dual Quadratic Programming Method

XIN Guiyang^1,2, ZHONG Guoliang^1,2, WANG Hengsheng^1,2, DENG Hua^1,2

1. School of Mechanical and Electrical Engineering, Central South University, Changsha 410083;
2. State Key Laboratory of High-performance and Complex Manufacturing, Central South University, Changsha 410083

Received:2017-03-29 Revised:2017-11-27 Online:2018-04-05 Published:2018-04-05

摘要/Abstract

摘要： 针对六足并联机器人冗余驱动问题，提出以降低能耗，提高承载能力为目标的驱动力优化分配方法。通过建立六足并联机器人运动学与动力学模型，得到机器人关节驱动力与脚力间转换关系。在分析机器人动态平衡条件并考虑摩擦约束、最大驱动力约束及触地约束的基础上，建立以驱动力平方和最小为目标函数的二次规划问题。基于QR分解的广义消去法消去等式约束减少约束方程的数量以提高优化问题的求解速度，采用对偶理论将问题转化为对偶二次规划问题可以进一步提高求解速度。分析了多足机器人与多指灵巧手动力学模型的不同，因此两者的二次规划目标函数也存在不同。同时与传统的以内力最小为目标函数的方法比较，表明该方法能够充分利用地面摩擦力以减小驱动力，从而提高承载能力，降低能量消耗。

关键词: 对偶理论, 二次规划, 六足并联机器人, 驱动力分配

Abstract: The active forces distribution algorithm for improving bearing capability and minimizing energy consumption is proposed to solve the redundant actuation problem of a six-parallel-legged robot. The transformation between active joint forces and foot contact forces is established based on the kinematic model and dynamic model. After analyzing the force/moment equilibrium equations of the robot, the quadratic programming optimization model is obtained considering the constraints of friction cone, unilateral constraint and the limits of motors' torques. The solving time of the quadratic programming is reduced by eliminating and simplifying equality and inequality constraints using elimination method based on QR decomposition and dual method. The difference between the objective function of multi-legged robots and multi-finger hands is pointed out because of the difference of their dynamic models. Compared with the traditional method, the proposed algorithm has great advantages in improving bearing capability and minimizing energy consumption due to the efficient utilizing of the contact friction forces.

Key words: dual method, force distribution, quadratic programming, six-parallel-legged robot

中图分类号:

TP242

辛桂阳, 钟国梁, 王恒升, 邓华. 基于对偶二次规划的六足并联机器人驱动力分配[J]. 机械工程学报, 2018, 54(7): 20-27.

XIN Guiyang, ZHONG Guoliang, WANG Hengsheng, DENG Hua. Optimal Driving Forces Distribution for a Six-parallel-legged Robot Based on Dual Quadratic Programming Method[J]. Journal of Mechanical Engineering, 2018, 54(7): 20-27.

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基于对偶二次规划的六足并联机器人驱动力分配

Optimal Driving Forces Distribution for a Six-parallel-legged Robot Based on Dual Quadratic Programming Method

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