机器人动力学的李群表示及其应用

采用李群和李代数的方法来描述牛顿一欧拉方程和拉格朗日方程，得到机器人动力学在关节空间和操作空间内单个连杆的递推公式以及整个系统动力学方程的矩阵表达式。分析了机器人动力学的几何特性，并进一步研究了动力学方程的微分形式及其对机器人的设计和最优控制所起的作用。以平面2R为例，分别得到2R机械手在关节空间和操作空间中的动力学方程，推导出机器人在关节空间中动力学的微分形式，分析了机械手的奇异性和复杂性。

Lie Group Representation of Robot Dynamics and Its Applications

By using standard ideas from Lie groups and Lie algebra, the recursive formulation and the Lagrangian formulation were presented. The joint space formulation and the operational space equation of open chain robot system were derived through the matrix, in which the kinematic and inertial parameters appeared explicitly and independently each other. The differentiation of the dynamical equations were showed, which is of paramount importance at a highlevel. At the same time the method made these formulation attractive for applications such as robot design and optimal real-time control. The methods are applied to the analysis of 2-dof planar manipulator.