Dynamic Modeling And Analysis Of Space Manipulator Based On Screw Theory And Lie Group-Lie Algebra

The space manipulator used in space mission has the characteristics of microgravity,large span,large self-weight ratio and low damping.When the manipulator endures a large load,the flexible effect is very strong,which produces obvious elastic vibration in a wide range of motion.For the small load,the behavior is approximately rigid,and the elastic vibration is not obvious.Establishing an accurate and efficient dynamic model is a prerequisite basis for a series of work such as the design of space manipulator,dynamic behavior analysis,controller design and debugging.To this end,in view of these two situations,this article has carried on the research to the related dynamics problem of the space manipulator,the main content has:Based on the screw theory and the Lie group-Lie algebra mathematical method,the position and attitude vectors of the space manipulator are expressed as a unified screw,and the kinematic exponent product formula of the space manipulator is established.The exponential form kinematics formula can describe the whole motion of the manipulator in the inertial coordinate system and provide a complete and clear geometric description,avoiding the singularity brought by the traditional DH coordinate method.At the same time,which Also describes the geometric meaning of object movement more clearly,avoids the disadvantages of mathematical abstract symbols and greatly simplifies the analysis and solution of the system.The article also discusses the relationship between the spin index product method and the D-H parameter method,and the properties of Jacobi's matrix.A space six-degree-freedom manipulator is taken as object to verify the model.For small loads,an efficient recursive dynamics model of space rigid manipulator is established.Under the condition of light load,the space manipulator approximates a rigid motion.Based on the space rigid body motion described by screw theory,the traditional Newton-Euler kinematics modeling method is improved.Using mathematical and physical models,through detailed derivation,an efficient recursive dynamics model for computational efficiency was developed to obtain the recursive inverse kinematics and forward kinetic recursive algorithms for the recursive open-loop multi-body system with n-degree of freedom.Finally,a four-link manipulator is taken as a research model,and its simulation calculation is carried out to verify the correctness of the dynamic model.For large loads,a dynamic model of flexible manipulator under coupling deformation was established.Under heavy load,the rigid model is no longer applicable,and the coupling deformation(transverse deformation,longitudinal deformation and torsional deformation)of the flexible manipulator is described by the space deformation screw.By combining the generalized flexibility matrix of the manipulator and the generalized inertia matrix,Rayleigh-Ritz method to establish a decoupled dynamic model of space flexible manipulator.A simplified cantilever beam was used to study the characteristic frequency of the flexible manipulator under coupling deformation.Finally,a decoupling dynamic equation was established for a flexible manipulator with a joint axis perpendicular to each other,and the simulation and verification are carried out to verify the correctness of the model.