Kinematic state estimation for rigid-link multibody systems by means of nonlinear constraint equations

In the multibody field the design of state observers proves useful for several tasks, ranging from the synthesis of control schemes and fault detection strategies, to the identification of uncertain parameters. State observers are designed to obtain accurate estimates of unmeasurable or unmeasured variables. Their accuracy and performance depend on both the models used and the measurement sets. In multibody systems, if it is reasonable to neglect joint clearance and to assume that links are rigid, the estimates of kinematic variables (i.e. position, velocity and acceleration) can be carried out very effectively using kinematic models, i.e. models based on kinematic constraint nonlinear equations, which provide much less uncertain models than dynamic equations. Under the aforementioned assumptions, this paper proposes a general theory, valid for both open-chain and closed-chain multibody systems, to design observers based on nonlinear kinematic models. The concurrent use of kinematic models and nonlinear estimators is original in the multibody field and represents the chief contribution of the paper. The soundness of the proposed theory is proved through numerical and experimental tests on both open-chain and closed-chain multibody systems. Finally, a comparison is given between the kinematic estimations computed through two nonlinear observers (the extended Kalman filter, EKF, and the spherical simplex unscented Kalman filter, SS-UKF), in order to demonstrate the benefits of the SS-UKF in nonlinear estimation.