Basic Theory And Noether Symmetry Analysis Of The Soft Robots System

Soft robot is a kind of new type of bionic robot composed of soft materials.It has unlimited degrees of freedom in theory,complex structure and difficult theoretical analysis.This paper combines the methods of analytical mechanics and elastic mechanics to study the basic theory and symmetry theory of the soft robot system dynamics,and provides theoretical and technical support for the rapid development,design,control and application of soft robots.Firstly,the deformation of the soft robot is analyzed.Unlike the general particle system,the soft robot is deformed by the external force,and its internal force does not work,that is,strain energy is generated.Based on ideal constraints,introducing degrees of freedom and generalized coordinates,the principle of virtual displacement generalized to soft robot systems is proposed:the sum of the elemental work done by the external forces acting on the system in any virtual displacement is always equal to the virtual memory stored in the soft robot system strain energy.The principle of virtual displacement provides great convenience for solving the static problems of soft robots.Introducing inertial force,combining the principle of virtual displacement and the principle of D'Alembert,the general equations of dynamics of soft robot systems are derived,and the research of soft robots is extended from statics to dynamics.Starting from the general dynamic equations of soft robot systems,the Hamilton principle is derived,and then the Lagrange equation of the soft robot system is established,and the basic theoretical framework of the soft robot system dynamics is constructed.By calculating the kinetic energy and generalized force of the soft robot system and using the Lagrange equation,the differential equation of motion of the soft robot can be obtained.Using the Lie group analysis method,based on the invariant nature of Hamiltonian action under infinitesimal transformation,three definitions and criteria for Noether symmetry transformation are given,and the Noether symmetry of soft robot system and the resulting conserved quantities are studied.Noether theorem of soft robot system is established.