A Closed-Form Approach to Determine the Base Inertial Parameters of Complex Structured Robotic Systems

The dynamic performance and steady-state control errors of many control schemes improve with increasing model accuracy. This paper presents a method to determine the symbolic expressions of the base inertial parameters and the corresponding regressor matrix for models of robotic systems that are linear in the parameters. This is achieved using a transformation based on the row space of the initially rank-deficient observation matrix. Compared to the state-of-the-art methods the proposed approach can handle complex multibody structures for instance dynamic models with non-collocation of the position and the torque sensors. In addition it applies for general linear parameter models. The procedure of the algorithm is demonstrated considering the double pendulum dynamics as a closed-form example. Furthermore, the performance of the approach is experimentally validated with the 7 degree of freedom medical robot DLR MIRO.