Dario Richiedei

State estimation is a key requirement for the control of multibody systems, yet full state measurements are rarely available in practice. This necessitates the use of observers. While extended Kalman filters (eKFs) are widely used for nonlinear systems, their reliance on local linearizations often results in approximation errors. The Koopman operator framework offers an alternative by transforming nonlinear dynamics into a higher-dimensional linear representation, theoretically valid over the entire state space for systems with only one isolated fixed point. In this work, we propose a Koopman-based observer that integrates a Kalman filter for state estimation in nonlinear multibody systems. The Koopman operator is approximated using a deep neural network trained on system trajectories. We evaluate the method in simulation on two representative systems: a cable-driven parallel robot and a planar parallel robot. Results show that our Koopman-based observer consistently achieves lower estimation errors than a conventional eKF, demonstrating its potential for accurate and robust state estimation in nonlinear control applications.

This paper proposes a method for solving inverse dynamics of an underactuated gantry crane driving a spatial double pendulum, consisting of a cable moving a spatial rigid-body attached to the pendulum terminal mass. The outcomes of the method are both the control forces to be commanded to the torque (or current) control loops and the reference position of the actuated coordinates. The system has 6 degrees of freedom, and just two coordinates are actuated. The reference is imposed to the two Cartesian coordinates of the tip of the rigid-body, while the actuated coordinates are the two displacements of the moving platform. The goal is to ensure precise tracking during transients and at steady states, both in terms of time and space, by compensating for the oscillating attitude of the suspended load. This (non-collocated) definition of input and output leads to a non-minimum phase system. Additionally, inertial and viscous properties of the system make it non-flat; therefore, inverse dynamics should be solved through a differential-algebraic approach. Given the presence of an unstable internal dynamics, stabilization process is carried out in this paper through the concept of output redefinition, which is exploited to stabilize the computation. Numerical simulations are provided to show the effectiveness of the method, also by means of the comparison with a benchmark technique.

The forward dynamics of multibody systems is widely exploited in engineering applications to simulate the behavior of complex mechanical systems undergoing kinematic constraints. It relies on the integration of the equations of motion of the system. However, the numerical integration error causes the simulation to violate the position and velocity kinematic constraint. In this paper a novel Constraint Enforcement method based on the application of the prediction-correction scheme of the Extended Kalman Filter is proposed and it will be denoted (CE-EKF). First, the equations of motion of the system are integrated to provide thesimulation output estimate, i.e., the prediction. Then, the Kalman Filter computes the correction to ensure that the corrected simulation output is consistent with respect to the constraint equations. Besides proposing such the novel theoretical framework for the application of the Extended Kalman Filter in the suppression of constraints violation. In this work the numerical application of the method is provided for a redundant mechanism. The provided results highlight the effectiveness of the proposed method in comparison with other methodsproposed in the literature.

State estimation is a key requirement for the control of multibody systems, yet full state measurements are rarely available in practice. This necessitates the use of observers. While extended Kalman filters (eKFs) are widely used for nonlinear systems, their reliance on local linearizations often results in approximation errors. The Koopman operator framework offers an alternative by transforming nonlinear dynamics into a higher-dimensional linear representation, theoretically valid over the entire state space. In this work, we propose a Koopman-based observer that integrates a Kalman filter for state estimation in nonlinear multibody systems. The Koopman operator is approximated using a deep neural network trained on system trajectories. We evaluate the method in simulation on two representative systems: a cable-driven parallel robot and a planar parallel robot. Results show that our Koopman-based observer consistently achieves lower estimation errors than a conventional eKF, demonstrating its potential for accurate and robust state estimation in nonlinear control applications.