Efficient and Robust Modeling of Nonlinear Mechanical Systems

The development of efficient and robust dynamic models is fundamental in the field of systems and control engineering. In this paper, a new formulation for the dynamic model of nonlinear mechanical systems, that can be applied to different automotive and robotic case studies, is proposed, together with a modeling procedure allowing to automatically obtain the model formulation. Compared with the Euler-Lagrange formulation, the proposed model is shown to give superior performances in terms of robustness against measurement noise for systems exhibiting dependence on some external variables, as well as in terms of execution time when computing the inverse dynamics of the system.

💡 Research Summary

The paper introduces a novel formulation for modeling nonlinear mechanical systems that overcomes several limitations of the traditional Euler‑Lagrange approach. The classic Euler‑Lagrange equations are expressed as (M(x)\ddot{x}+N(x,\dot{x})\dot{x}=\tau), where the inertia matrix (M) and the Coriolis/centrifugal matrix (N) must be derived explicitly. This derivation becomes cumbersome for systems with external variable dependencies (e.g., gear ratios, roller tilt angles) and is sensitive to measurement noise, especially when the external variables’ derivatives are required.

The authors propose a “factorized” model:
\