*Article* **A Discrete-Time Extended Kalman Filter Approach Tailored for Multibody Models: State-Input Estimation**

**Rocco Adduci 1,2,***∗***, Martijn Vermaut 1,2, Frank Naets 1,2, Jan Croes 1,2 and Wim Desmet 1,2**


**Abstract:** Model-based force estimation is an emerging methodology in the mechatronic community given the possibility to exploit physically inspired high-fidelity models in tandem with ready-to-use cheap sensors. In this work, an inverse input load identification methodology is presented combining high-fidelity multibody models with a Kalman filter-based estimator and providing the means for an accurate and computationally efficient state-input estimation strategy. A particular challenge addressed in this work is the handling of the redundant state-description encountered in common multibody model descriptions. A novel linearization framework is proposed on the time-discretized equations in order to extract the required system model matrices for the Kalman filter. The presented framework is experimentally validated on a slider-crank mechanism. The nonlinear kinematics and dynamics are well represented through a rigid multibody model with lumped flexibilities to account for localized interaction phenomena among bodies. The proposed methodology is validated estimating the input torque delivered by a driver electro-motor together with the system states and comparing the experimental data with the estimated quantities. The results show the stability and accuracy of the estimation framework by only employing the angular motor velocity, measured by the motor encoder sensor and available in most of the commercial electro-motors.

**Keywords:** multibody dynamics; Kalman filtering; coupled states-inputs estimation; virtual sensors; slider-crank mechanism
