State Estimator of Errorekf and UKF Based on Generalized-A Method for Constrained Multibody Systems

Multibody dynamics models inherently contain comprehensive physical information of complex systems, while multibody integrators enable efficient prediction of dynamic behaviors. The advancements in these two research interests have made it a natural progression to integrate multibody dynamics models and multibody integrators into state estimators. However, their integration faced several challenges: nonlinear discrete formulations, reformulation of differential-algebraic equations (DAEs), constraint violation correction, and integrator selection. With ongoing research, the first three issues have been largely resolved for low-order rigid multibody systems. Nevertheless, current one-step prediction methods predominantly rely on explicit integrators or low-order implicit integrators, which suffer from inefficiencies in state estimation and inadequate constraint violation correction. This study proposes the framework that embeds the generalized-α integrator - a high-order multibody integrator - within the error Extended Kalman filter(errorEKF) architecture and Unscented Kalman filter(UKF). The generalized-α integrator is employed for one-step state prediction which directly solves the original DAEs, ensuring that states remain strictly on the constraint manifold. Comparative studies with this two Kalman filter-based state estimators are conducted on two benchmarks: a four-bar mechanism and a five-bar mechanism. The results shown that both state estimators based on the generalized-α integration method have good estimation accuracy. In terms of computational efficiency, the estimated computational efficiency of ErrEKF is significantly higher than that of UKF.