Two-stage approach to state and force estimation in rigid-link multibody systems
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A novel two-stage approach is presented for improving the estimates of both the kinematic state and the unknown external forces in rigid-link multibody systems with negligible joint clearance. The approach is said to be a two-stage one because the estimation process is carried out by two observers running simultaneously and only partially coupled in order to reduce model uncertainties. Nonlinear Kalman filters are employed at both stages. In the first stage, a kinematic observer estimates an augmented system state (i.e., positions, velocities and accelerations) by employing the kinematic constraint equations and some measurements of kinematic quantities as inputs and outputs. Therefore, it is unbiased by external forces and uncertainties on any dynamic parameters. In the second stage, a force observer estimates the external forces by employing dynamic models. The input of the force observer is the kinematic state, while the correction is performed through some direct or indirect measurements of the known forces. 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 a single-stage dynamic estimation. An extensive statistical analysis is carried out at varying levels of measurement noise. Two different strategies are followed in the synthesis of the non-linear Kalman filters. The comparison clearly shows the advantages and the effectiveness of the new two-stage approach.