基于微分几何的欠驱动机器人动力学建模和控制

应用位形流形最小嵌入模型，对带有二阶非完整约束的欠驱动机器人动力学建模和控制进行研究。采用位形流形最小嵌入模型，简化了动力学方程，为欠驱动机器人动力学建模和控制的进一步研究奠定了基础。首先用一个齐次线性方程组表示被动关节的存在，给出基于嵌入模型的动力学方程解的结构。通过引入计算转矩控制法，给出另一个和主动关节及控制输入有关的齐次线性方程组，分析控制输入和这两个方程组解之间的关系，得到一个与控制输入及这两个方程组的解相关的欠定线性方程组，求解该欠定线性方程组，得到欠驱动机器人改进的动力学方程，进而可以运用全驱动机器人控制法来实现最小嵌入模型的控制，解决了由全驱动机器人控制法实现欠驱动机器人关节空间控制的问题。最后以平面二杆欠驱动机器人为例，验证了所得理论的可行性和有效性。

UNDERACTUATED ROBOT DYNAMIC MODELLING AND CONTROL BASED ON DIFFERENTIAL GEOMETRY

The second order nonholonomic constraint underac- tuated robot dynamic modeling and control are investigated by applying configuration manifold minimum embedding model. So the dynamic equation is reduced and the basis for further study on underactuated robot's dynamic modeling and control is found.The existence of passive joints is expressed by one homogeneous linear equation.And solution structure for dynamic equation based on minimum embedding model is posed.Another homogeneous linear equation associated with actuated joints and control inputs is presented by introducing computed torque.And one underdetermined linear equation set related with control inputs and theirs solutions is formulated by analyzing the relationship between control inputs and solutions of the two equations.Improved dynamic equation of underactuated robot is developed by solving the equations.The minimum embedding model control is performed by full actuated robot control law.And the underactuated robot joint space control is realized.Finally,the above principle feasibility and effectiveness are illustrated with a planar two bar underactuated robot.