Simultaneous estimation of kinematic state and unknown input forces in rigid-link multibody systems
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The knowledge of the external forces (and torques) applied to a multibody system is needed in several applications, such as monitoring or control. Unfortunately, such forces are often difficult to measure and therefore estimation techniques should be adopted. This paper proposes a novel two-stage approach making use nonlinear Kalman filters to estimate both unknown external forces and kinematic state variables in rigid-link multibody systems with negligible joint clearance. The approach consists in splitting the estimation process in two observers running simultaneously: a kinematic observer (first stage) and a force observer (second stage). The first one estimates the kinematic variables (i.e. position, velocity and acceleration) by just using position and acceleration measurements and the kinematic constraint equations, regardless of the knowledge of the external forces. The estimates obtained are then fed into the force observer, which estimates the external forces on the basis of the system dynamic model and the random walk approximation. Numerical assessment of the theory developed is provided through a slider-crank mechanism. The results achieved through the proposed approach are compared with those yielded by traditional unknown input observers based on single-stage dynamic observers, in order to show the advantages and the effectiveness of the new two-stage approach.