Convex polytopic modeling for flexible joints industrial robot using TP-model transformation

This paper presents a method for converting nonlinear flexible joint robot system into linear convex polytopic model by using the tensor product (TP) model transformation. The robot link position and velocity information was taken as variable parameters, and the dynamic equation of flexible joint robot was equidistant partitioned and stored in a tensor within the variable parameter range. Then, the tensor's singular values and the corresponding eigenvector were computed by using high order singular value decomposition. The weighting functions of polytopic model were constructed with the resulting eigenvectors, and then finite vertex LTI system was obtained. The simulation results show that the convex polytopic model can accurately represents the nonlinear dynamics model of flexible joint robot in the parameter range. This modeling approach is the foundation of designing multi-model robust controller based on LMIs for flexible joint robot.