The Kinetic Equations And Integral Methods Of Snake-like Robot Systems

In this paper,the kinetic equations and integral methods of snake soft robot systems are studied.Soft robot is a kind of bionic robot that human beings can get inspiration from the nature to design and manufacture,which has the characteristics of high structural softness,good environmental adaptability,strong affinity and diverse functions.Among soft robots,snake-like robots have been widely used in many fields due to their flexible motion mode,and become a new hot spot in the field of soft robots research.In this paper,the Lie group analysis method is introduced into the snake-like robot systems.The snake-like robot is equivalent to dynamical systems composed of n-links.The appropriate generalized coordinates are selected and the kinetic energy,potential energy,Lagrange function and nonholonomic constraints of the snake-like robot systems are given.The Routh equation of the snake-like robot systems is established.On this basis,the following three issues are respectively studied:First,the algebraic structure and Poisson's integral theory of snake-like robot systems are studied.The generalized momentum,Hamiltonian function,generalized Hamilton canonical equations and their contravariant algebraic forms are obtained for snake-like robot systems.The Lie-admissible algebra structures of the snake-like robot systems are proved and partial Poisson's integral methods are applied to the snake-like robot systems.The first integral methods of the snake-like robot systems are given.Secondly,the Noether symmetries and conserved quantities of the snake-like robot systems are studied,and the Noether symmetries integration methods of the systems are given.By introducing the infinitesimal transformations with respect to the time and generalized coordinates,the Hamilton action of the snake-like robot systems is quantized.Based on the invariance principle of the Hamiltonian action under the infinitesimal transformation,the definition and criterion and existing Noether conser-ved quantity of the snake-like robot systems are given.The Noether's symmetry theorem of the snake-like robot systems are given.Thirdly,the Lie symmetries and conserved quantities of the snake-like robot systems are studied,and the Lie symmetries integration methods of the systems are given.By introducing the infinitesimal transformations with respect to the time and generalized coordinates and the corresponding infinitesimal transformation's generati-ve element vector field and its extension form,the invariance of the differential equations based on the snake-like robot systems under the infinitesimal transformatio-n,the deterministic equations and limit equations of the snake-like robot systems are established,the structural equations and the corresponding conserved quantities of the systems are obtained.