This article addresses the problems of online estimations of kinematic and dynamic states of a mechanism from a sequence of noisy measurements. In particular, we focus on a planar four-bar linkage equipped with inertial measurement units (IMUs). Firstly, we describe how the position, velocity, and acceleration of all parts of the mechanism can be derived from IMU signals by means of multibody kinematics. Next, we propose the novel idea of integrating the generic multibody dynamic equations into two variants of Kalman filtering, i.e., the extended Kalman filter (EKF) and the unscented Kalman filter (UKF), in a way that enables us to handle closed-loop, constrained mechanisms, whose state space variables are not independent and would normally prevent the direct use of such estimators. The proposal in this work is to apply those estimators over the manifolds of allowed positions and velocities, by means of estimating a subset of independent coordinates only. The proposed techniques are experimentally validated on a testbed equipped with encoders as a means of establishing the ground-truth. Estimators are run online in real-time, a feature not matched by any previous procedure of those reported in the literature on multibody dynamics.
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