Lie-theory-based dynamic model identification of serial robots considering nonlinear friction and optimal excitation trajectory

Accurate dynamic model is essential for the model-based control of robotic systems. However, on the one hand, the nonlinearity of the friction is seldom treated in robot dynamics. On the other hand, few of the previous studies reasonably balance the calculation time-consuming and the quality for the excitation trajectory optimization. To address these challenges, this article gives a Lie-theory-based dynamic modeling scheme of multi-degree-of-freedom (DoF) serial robots involving nonlinear friction and excitation trajectory optimization. First, we introduce two coefficients to describe the Stribeck characteristics of Coulomb and static friction and consider the dependency of friction on load torque, so as to propose an improved Stribeck friction model. Whereafter, the improved friction model is simplified in a no-load scenario, a novel nonlinear dynamic model is linearized to capture the features of viscous friction across the entire velocity range. Additionally, a new optimization algorithm of excitation trajectories is presented considering the benefits of three different optimization criteria to design the optimal excitation trajectory. On the basis of the above, we retrieve a feasible dynamic parameter set of serial robots through the hybrid least square algorithm. Finally, our research is supported by simulation and experimental analyses of different combinations on the seven-DoF Franka Emika robot. The results show that the proposed friction has better accuracy performance, and the modified optimization algorithm can reduce the overall time required for the optimization process while maintaining the quality of the identification results.