基于递归 Gibbs-Appell 的柔性空间机器人建模与特性分析

Dynamic modeling and characteristic analysis of space robots with multiple flexible factors were studied by Recursive Gibbs-Appell modeling method. Firstly， the deformation of link and joints was described by concentrated stiffness and Timoshenko beam theory. Secondly，the homogeneous transformation matrix T₄×₄ was simplified by using the rotation matrix R₃×₃ and the translation vector L₁×3，and the difficulty of recursive kinematics was reduced. The inverse dynamics model of the flexible space robot was derived by using the recursive Gibbs function and the potential energy function. Thirdly， the mass inertia matrix and coupling matrix were obtained by inverse recursive method. The forward dynamic model of the space robot was obtained. The numerical simulation results showed that the relative deviation between Matlab and Adams simulation results did not exceed 0.1%， and the Z bending deformation was more than 10³ orders of magnitude relative to the X shear deformation and Y torsional deformation，which verified the correctness of the model. Within a certain range， when the joint stiffness increased by 50 N·m/rad， the maximum deformation increment of the connecting rod did not exceed 1.5×10⁻³ m， and when the joint friction increased by 5 times， the maximum deformation increment of the link did not exceed 2×10⁻³ m，the incremental deformation of the windsurfing board had the same trend.