基于自然正交补的冗余驱动并联机构动力学建模  

Dynamics modeling of redundantly-actuated parallel robot based on natural orthogonal complement

作　　者：王耀军[1,2] 张海峰 WANG Yao-jun;ZHANG Hai-feng(School of Automation,Zhejiang Institute of Mechanical and Electrical Engineering,Hangzhou 310053,China;Faculty of Mechanical Engineering and Automation,Zhejiang Sci-Tech University,Hangzhou 310018,China)

机构地区：[1]浙江机电职业技术学院自动化学院,浙江杭州310053 [2]浙江理工大学机械与自动控制学院,浙江杭州310018

出　　处：《机电工程》2022年第10期1440-1447,共8页Journal of Mechanical & Electrical Engineering

基　　金：国家自然科学基金资助项目(51935010,52005448);浙江省自然科学基金资助项目(LQ19E050015)。

摘　　要：为了解决并联机构引入冗余驱动造成驱动力求解不唯一,可能引起内力对抗的问题,对冗余驱动并联机构的动力学建模和驱动力优化进行了研究。首先,以3RRR冗余驱动并联机构为例,基于闭环矢量法确定了机构的位移、速度关系;然后,为克服牛顿-欧拉法方程多、计算量大,以及欧拉-拉格朗日法计算量大、实时性差的问题,基于螺旋理论,提出了应用自然正交补方法建立机构的动力学模型,推导了机构的逆动力学方程;最后,采用无穷大范数法,以最小化最大驱动力为目标优化驱动力,并通过圆轨迹跟踪对其进行了仿真。研究结果表明:应用自然正交补方法建立冗余驱动并联机构的模型,采用最小化最大驱动力优化,将最大驱动器功率由1.5 Nm降低到1.2 Nm,驱动器功率降低了20%;该方法具有形式简洁、系统高效、中间变量少的优点,对冗余驱动机构的建模和后续控制律开发具有较大的参考价值。In order to solve the problem of non-unique solutions of actuating forces(or torques)and potentially antagonistic internal forces,the dynamic modeling and ensuing internal forces distribution and optimization of redundantly-actuated parallel mechanisms were studied.Firstly,taking the 3 RRR redundantly-actuated parallel robot as an example,the solution of displacement and velocity of the mechanism was determined based on the closed-loop vector method.Secondly,by resorting to the screw theory,a dynamic modeling approach was first proposed by means of the natural orthogonal complement,and then applied to obtain the inverse-dynamics equations of the 3 RRR mechanism,that overcomes the shortcomings of both the Newton-Euler and the Euler-Lagrange methods.Finally,the driving forces(or torques)were optimized by infinity-norm solution that minimizes the maximum-driving-torque,with simulation study of a circle trajectory tracking included as a verification.The research results show that,by applying the natural orthogonal complement and the minimization of the maximum-driving-torque,the proposed method decreases the power requirement of the redundant drivers from 1.5 Nm to 1.2 Nm,a significant reduction by 20%;it has the advantages of both simple and efficient derivation,with few intermediate variables,and has great application and reference value for modeling of redundantly-actuated mechanical systems and subsequent control law design.

关 键 词：机构学理论 机构动力学方程 冗余驱动 自然正交补方法 驱动力优化 

分 类 号：TH112[机械工程—机械设计及理论]