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

Abstract

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

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

“…Alternatively, in [ 13 ] a kinematic state observer is presented. It combines the constrained kinematic MB equations with nonlinear estimators.…”

Synthesis of an Extended Kalman Filter for Cable-Driven Parallel Robots

“…[11,12]), that is in contrast usually not available. To overcome this issue, state observers can be designed and implemented [13,14].…”

Multi-domain optimization of the eigenstructure of controlled underactuated vibrating systems

“…In the implementation of state-feedback control, it is a common need to replace the measured, actual state (q and q) with the estimated one (Caracciolo et al 2008). Indeed, measurement of all the state variables in structures or in multibody systems is usually very difficult (Palomba et al 2017;Sanjurjo et al 2018). Estimation is provided by a state observer (or state estimator), which reconstructs missing state variables by merging the model, expressed as a first-order state-space model, and a meaningful set of measurements with a prediction-correction logic (Palomba et al 2017).…”

“…Indeed, measurement of all the state variables in structures or in multibody systems is usually very difficult (Palomba et al 2017;Sanjurjo et al 2018). Estimation is provided by a state observer (or state estimator), which reconstructs missing state variables by merging the model, expressed as a first-order state-space model, and a meaningful set of measurements with a prediction-correction logic (Palomba et al 2017). In the light of a concurrent design, the effect of the state observer should be included in the overall approach too, and the limitations due to the computational effort required for real time estimation should be investigated.…”