Port-Hamiltonian multibody dynamics: Lagrangian formulation, consistent interconnection, structure-preserving simulation and index-reduction
This work provides a consistent and structure-preserving approach for multibody dynamics simulation, which is incremental but beneficial for energy-based control design in mechanical engineering.
The authors tackled the modeling and simulation of constrained mechanical systems by introducing a port-Hamiltonian framework derived from Lagrangian equations, resulting in a method that ensures constant mass matrices and enables stable long-term simulations with robust energy and angular momentum conservation.
This work introduces a port-Hamiltonian (PH) model for constrained mechanical systems, which is directly derived from the Lagrangian equations of motion. The present PH framework incorporates a singularity-free director representation of rigid body rotations, resulting in constant mass matrices. It is shown that the power-preserving interconnection of PH rigid-body subsystems is mathematically equivalent to the classical description of ideal joints using kinematic pairs. This establishes a PH multibody dynamics framework that is consistent with traditional modeling paradigms. Notably, the PH structure of the governing index-2 differential-algebraic equations enables the application of an implicit, structure preserving midpoint time integration. The proposed scheme is able to satisfy both the balance laws for total energy and angular momentum as well as the position-level constraints. These properties make the proposed method remarkably robust and enable stable long-term simulations. Furthermore, a variationally derived index-reduction strategy is incorporated that enforces velocity-level constraints in addition to position-level constraints while preserving the port-Hamiltonian structure. Numerical examples illustrate the favorable properties of the proposed formulation, which is well-suited for energy-based control design.