NOETHER SYMMETRIES AND CONSERVED QUANTITIES OF WALL CLIMBING ROBOT SYSTEM

The wall climbing robot's motion is a kind of imitation gecko's crawling motion. The wall climbing robot's motion can be divided into four limbs driving the body's movement. The previous research is based on Newton's mechanics. In this paper, Lagrange mechanics method is used to establish the motion equation of the wall climbing robot system, and the Noether symmetry theory of the system is established by using the Lie group analysis method, and the motion law of the wall climbing robot is obtained. Firstly, the kinetic energy, potential energy, Lagrange functions and nonholonomic constraints of nonholonomic wall climbing robot system are given, and the Lagrange equation of nonholonomic wall climbing robot system is established. Secondly, by introducing infinitesimal transformation of time and generalized coordinates, the basic variational formulas of Hamilton action and Hamilton action of nonholonomic wall climbing robot system are proposed. Thirdly, the wall climbing robot system is given The definition, criterion and existing Noether conserved quantity of Noether symmetry transformation and generalized quasi symmetry transformation are introduced. The Noether theorem of non conservative holonomic system and non conservative nonholonomic wall climbing robot system is proposed. Finally, taking the wall climbing robot on the conic surface as an example, the given conserved quantity is directly integrated, and the exact solution of the whole motion of the wall climbing robot on the conical surface and the motion of the limbs are given The numerical results show that the motion law of the wall climbing robot is found and the Noether symmetry theory of the nonholonomic wall climbing robot system is well verified. This paper proposes a new symmetry solution method for Lie group analysis method applied to other complex robot systems and flexible robot systems.