非完整蛇形机器人系统的Lie对称性和守恒量

Lie symmetry and conserved quantity of non-holonomic snake robot system

研究了蛇形机器人系统的Lie对称性和守恒量,给出该系统的Lie对称性积分方法。将蛇形机器人等效为一个由n节连杆构成的动力学系统,选择了恰当的广义坐标,给出蛇形机器人的动能、势能、Lagrange函数,以及所受的非完整约束,建立了蛇形机器人系统的第二类Lagrange方程;引入关于时间和广义坐标的无限小变换、相应的无限小变换的生成元矢量场及其扩展形式,基于蛇形机器人系统的运动微分方程在无限小变换下的不变性,给出了蛇形机器人系统的Lie对称性确定方程和限制方程,提出了该系统的Lie对称性定理,并以3自由度非完整蛇形机器人系统为例研究其Lie对称性和守恒量,验证了本文提出的Lie对称性理论。

The Lie symmetry and conserved quantity of the snake robot system are studied,and the Lie symmetry integration method of the system is given.The snake-like robot is equivalent to a dynamic system composed of n-links,the appropriate generalized coordinates are selected,the kinetic energy,potential energy,Lagrange equation and the non-holonomic constraints of the snake-like robot are given,and the second type of Lagrange equation of the robot system is established.Introducing the infinitesimal transformation of time and generalized coordinates and the corresponding infinitesimal transformation’s generator vector field and its extended form,based on the invariance of the motion differential equation of the snake-like robot system under infinitesimal transformations,the snake-like robot is given.The system’s Lie symmetry determination equation and limiting equation are proposed,the system’s Lie symmetry theorem is proposed,and its Lie symmetry and conserved quantity are studied with a 3-degree-of-freedom non-holonomic snake robot system as an example,and the proposed Lie symmetry is verified.