Deep learning of multibody minimal coordinates for state and input estimation with Kalman filtering

In general, multibody models are described with a set of redundant coordinates and additional constraints. Their dynamics is thus expressed through differential algebraic equations. As an alternative, the minimal coordinate formulation permits to describe a rigid system with the minimal number of variables leading to ordinary differential equations which can be employed in a coupled state/input estimation scheme. However, in some cases the explicit relation between the full-system coordinates and the minimal coordinates may not be available or analytically obtainable, as for closed-loop mechanisms. In this work, a previously presented deep learning framework to find the non-linear mapping and reduce a generic multibody model from redundant to minimal coordinates is employed. The resulting equations are then exploited in an extended Kalman filter where the unknown inputs are considered as augmented states and jointly estimated. The necessary derivatives are given and it is shown that acceleration measurements are sufficient for the estimation. The method is experimentally validated on a slider–crank mechanism.