State observer of multibody systems formulated using differential algebraic equations

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Abstract Multibody dynamics comprises methodologies for the design and analysis of mechanical systems, with Kalman filters being the principal state estimation methods. The Kalman filters are generally formulated for unconstrained systems, the dynamics of which are described by ordinary differential equations in state-space models. However, multibody systems are constrained systems, and the commonly used method to describe their dynamics involves using differential algebraic equations (DAEs) comprising differential and algebraic equations. The differential equations also include the Lagrange multipliers. Hence, incorporating multibody systems, described by DAEs into the scheme of Kalman filters, cannot be achieved straightforwardly, which facilitates different strategies being addressed. This study develops a novel method for converting DAEs into a state-space model. A transition model of the time derivatives of Lagrange multipliers and a Lagrange multiplier constraint vector are devised and used in the state and output equations, respectively. The continuous- and discrete-time extended Kalman filters (CEKF and DEKF) are constructed using the proposed state-space model, and state estimations are simulated on the benchmark planar four- and five-bar linkages. Further, a demonstration of system observability is conducted, and sensitivity to the initial state estimates is studied. These tests demonstrate that the proposed state-space model achieves observable systems and that both the CEKF and DEKF, constructed using the proposed state-space model, can estimate the states with a wide range of initial conditions.