基于旋量理论的移动机械手动力学建模

Dynamic Modeling of Mobile Manipulator Based on Screw Theory

应用旋量理论可以方便地建立固定基开链或闭链机器人系统的动力学模型,但是,能否和怎样把它用在移动机械手等这些非固定基系统的动力学建模还值得探讨。本文基于旋量理论研究了移动机械手系统的动力学建模方法。首先通过构造虚拟连杆把移动机械手转换成等效的固定基单自由度关节的开链系统。然后应用刚体旋量的指数积公式导出移动平台的运动约束方程,通过建立移动机械手各刚体的雅克比矩阵,推导出刚体和整个系统的动能。最后利用Lagrange-d′ Alemert原理建立了移动机械手系统的动力学模型。

The screw theory can be easily used to build up the dynamic model of a base-fixed open-chain or closed-chain robot, however, for the mobile manipulators, its application is worth exploring. Based on the screw theory, a method of the dynamics modeling for the mobile manipulator is proposed. First, by constructing virtual links, the mobile manipulator can be transformed into an equivalent base-fixed openchain robot composed by joints with single degree of freedom. Then, by applying exponential product formula of rigid screw, the kinetic constraint equations of mobile platform can be derived, and, by building Jacobin matrix of each rigid body, both rigid bodies＇ and the whole systems＇ kinetic energy can be found out. Finally, the dynamic model of mobile manipulator can be built up based on Lagrange-d＇Alemertprinciple.