Research On Noether’s Symmetries And Conservation Quantites Of Bipedal Robot

Biped robots,as a key component of robotics,represent cutting-edge robotic technology and the highest-level robotic research.Compared with other types of robots,biped robots reveal that more extensive applications can be developed across different research fields and disciplines such as sports biomechanics,haptics,neurology,analog simulation,and sensor network,so the research on biped robots can greatly help a country’s sci-tech development;compared with other mobile robots such as wheeled or tracked ones,biped robots are more flexible,more adaptable to different terrains,and more similar to human characteristics,thus showing higher research value;in the future research,primary consideration should be the stability of biped robots;meanwhile,biped robots are energy-efficient in movement.Nowadays,with the rapid development of biped robots,more and more scholars have been engaged in the research thereof and their research significance is increasing,thus making biped robots a research focus.The kinetic stability of robots constitutes an important part of robotic research.Given the fundamental role the symmetry theory of robotic systems plays in the study of kinetic stability,the symmetry study of robotic systems is indispensable to the stability design of bipedal robots.In this paper,the structural design and dynamics of bipedal robots were analyzed,the bipedal structure and walking process of humans were studied,and a kinetic model of bipedal robotic systems was constructed according to the structural characteristics of human legs.Besides,the symmetry and conserved quantity of bipedal robotic systems were also studied based on the Noether symmetry theory.For a start,the Noether symmetry theory of constrained dynamics system was introduced,defining the criterion,derivation process,and conservation formulas for Noether symmetry transformation,Noether quasi-symmetry transformation and Noether generalized quasi-symmetry transformation.Then,a simple model of bipedal robots was established to describe the motion law of the legs of bipedal robotic systems walking straightly on a flat surface.Besides,the corresponding generalized coordinates were selected to write the kinetic equation of the bipedal robotic system with the Lagrange function,based on which the kinetic behavior of the bipedal robot was studied.Last but not least,through the infinitesimal transformation of time and generalized coordinates,the Hamiltonian actions of general complete robotic systems were obtained.The Noether symmetry theory was applied to study the basic principles and symmetry properties of bipedal robotic systems and calculate the conserved quantity of the bipedal robotic system.Meanwhile,the validity of the Noether conserved quantity of the bipedal robotic system on the horizontal plane was verified through Matlab.Further,we adopt the discrete variational algorithm for the numerical simulation of bipedal robot system,gives the motion of bipedal robot system,through the simulation results: discrete variational algorithm can be well applied to the calculation of robot system,has certain reference value.The study of robotic system symmetry is of great theoretical significance and practical value for it could help improve robot modeling,reduce the number of equations used to describe robot motion,and lay a solid foundation for the efficient numerical simulation of robotic systems.