Analysis And Research On Robot Motion Characteristics Based On Lie Group Lie Algebra

According to the state, characteristics of robot motion divide into two aspects, static characteristics and dynamic characteristics. Singularity, working space, motor dexterity, etc. are static characteristics, working accuracy, reproducibility, stability are dynamic characteristics. The research of those characteristics is, in the final analysis, the study of kinematics, dynamics and control strategy. In this paper Lie groups and Lie algebras, Riemannian geometry of differential geometry are used to analyze above mentioned problems.In this dissertation, first of all, Lie groups and Lie algebras and their geometry method, moving frame method are used to derive the kinematic equations of robots. The set of manipulator effectors’ configurations is Lie group, after researching Lie groups and its differential, the performances of manipulator and its generalized velocity can be gotten. The geometric expression of Lie groups are moving frame method, we set up coordinate in each link, the transformations between the moving frame methods correspond to them between each link, and its relative components are the velocity of manipulator. The robot dynamics is the relationship between movement and force; we combine Lie groups and Lie algebras and Newton-Euler method to derive dynamic equations, which has unified forms and reduces the complexity of computational.Then we derive the joint torque of RRR robot and test and verify the result with software Adams. Then, we plan the trajectories of SCARA and RRR robot using interpolation method in joint space and Riemannian geometry in operating space respectively. When it’s in the operating space, we map the configuration and kinetic energy into surfaces in Euclidean space. Then the shortest line on surface, geodesic curve, is the optimal trajectory of robot, at the same time, it can be visualized in the surface. At last, the characteristics of RP, RRP and SCARA robot are analyzed on the basis of the conclusion above. In a word, we use differential geometry to study robots, unify definition of differential geometry and the concept of robots, which advance the development of robots.