CAJ | 학술논문

为考虑柔索垂度影响采用抛物线方程来描述大跨度柔索的构形,推导出索端张力与索端位移和索长变化之间的关系.基于柔索力学方程建立索牵引机器人的动力学模型,模型中作用在末端执行器上的柔索合力与柔索长度和末端执行器的位姿直接相关.为便于在控制设计中引入力学模型,对动力学方程进行线性展开,得到作用在末端执行器上的柔索合力增量与索长变化和末端执行器位移之间的关系.作用在末端执行器上的柔索合力可以表示为其期望值与相应的增量之和,该增量是由索长误差及末端执行器位姿误差引起的.控制设计时首先采用李雅普诺夫法针对柔索合力设计反馈控制器,然后利用前述的增量关系构造出基于末端执行器位姿反馈,以索长调整量为控制输出的非线性控制器.该控制器在本质上为一带补偿项的非线性PD控制,控制器参数可随系统状态的变化而自动调整.数值算例证明了控制算法的有效性.
위고필유색수도영향채용포물선방정래묘술대과도유색적구형,추도출색단장력여색단위이화색장변화지간적관계.기우유색역학방정건립색견인궤기인적동역학모형,모형중작용재말단집행기상적유색합력여유색장도화말단집행기적위자직접상관.위편우재공제설계중인입역학모형,대동역학방정진행선성전개,득도작용재말단집행기상적유색합력증량여색장변화화말단집행기위이지간적관계.작용재말단집행기상적유색합력가이표시위기기망치여상응적증량지화,해증량시유색장오차급말단집행기위자오차인기적.공제설계시수선채용리아보낙부법침대유색합력설계반궤공제기,연후이용전술적증량관계구조출기우말단집행기위자반궤,이색장조정량위공제수출적비선성공제기.해공제기재본질상위일대보상항적비선성PD공제,공제기삼수가수계통상태적변화이자동조정.수치산예증명료공제산법적유효성.
Parabolic equation is utilized to represent the curve of a long span cable. The relationship among cable force, cable end displacement and cable length variation is derived by using parabolic equation. Dynamics model of cable-driven robots is established on the basis of cable mechanical equation, which shows that the resultant cable force acting on the end-effector is directly related to cable length and end-effector pose. A linear expansion of the mechanical equation is carried out to facilitate introducing the mechanical model into the control design, then the relationship between the cable force increment acting on end-effector and the cable length variation and the end-effector displacement is obtained. The cable force on end-effector can be expressed as the addition of its desired value and a corresponding increment resulting from the error of cable length and the error of end-effector pose. In the control design, a feedback controller is first designed for the cable force by using Lyapunov method. Then, by utilizing the above-mentioned incremental relationship, a nonlinear controller based on the end-effector pose feedback is constructed, in which the cable length adjustment quantity serves as the controller for output control. It is essentially a nonlinear PD controller with compensation terms. Controller parameters can be adjusted automatically along with the variation of system state. Numerical examples validate the control algorithm.