The Basic Principle And Symmetry Of Wall-climbing Robot System

The wall climbing robot is a kind of bionic robot that can assist people to work in complex and dangerous environments.It has a wide range of application fields.Therefore,it has received extensive attention in materials science,mechanics,physics,mathematics,biology,modern science and engineering technology.We study the basic principles and symmetry of the wall climbing robot system.Previous studies on the dynamics of wall climbing robots are mostly based on Newton mechanics.In this thesis,the method of Lagrange mechanics will be adopted to establish the motion equation of the wall climbing robot system by selecting appropriate generalized coordinates.And taking the analysis method of Lie group to study the symmetry and motion principle of the wall-climbing robot system.The symmetry and motion principle of the wall-climbing robot system were studied by Lie group analysis method.The motion pattern of the wall-climbing robot system is decomposed into the motion of limbs and body.The kinetic energy of the wall-climbing robot system is given.By analyzing its motion process,the potential energy,Lagrange function and the nonholonomic constraints of the system are given and the motion differential equation of the system is given;The Hamiltonian action of a nonholonomic wall-climbing robot system is defined by introducing the infinitesimal transformation of time and generalized coordinates,and the basic variational formula of the Hamiltonian action is calculated.The definition of Noether symmetric transformation and generalized quasi-symmetric transformation,the criterion and the existence of Noether conserved quantity for the wall-climbing robot system are given,and the Noether theorem for the wall-climbing robot system is proposed.Based on the infinitesimal transformation of time and generalized coordinates,the infinitesimal generating element vector is introduced,and the Lie symmetry determination equation,limiting equation and additional limiting equation of the wall-climbing robot system are given.The Lie symmetry theorem of the wall-climbing robot system is proposed,and the conservation quantity of Lie symmetry exists in the system is given;Taking a wall-climbing robot on a cone as an example,the Lie symmetry theory of the wall-climbing robot system is verified;Finally,by integrating the conserved quantities of the nonholonomic wall-climbing robot system,the exact solution of the body motion and the numerical solution of the limb motion of the nonholonomic wall-climbing robot system were obtained,and the motion law of the nonholonomic wall-climbing robot system was obtained.This thesis presents a new symmetric solution method for multi-body flexible robot systems.