Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Physically Consistent Modeling & Identification of Nonlinear Friction with Dissipative Gaussian Processes

Rui Dai, Giulio Evangelisti, Sandra Hirche

TL;DR

This work tackles friction identification in Euler–Lagrange systems by enforcing physical passivity through a dissipative Gaussian Process (GP). It introduces matrix-vector structured GPs for damping, with both full and diagonal damping matrices, and proves deterministic positive semidefiniteness guarantees for the damping estimates, ensuring system passivity. The approach embeds prior physical structure into GP priors and kernels, and constrains hyperparameters during training to maintain passivity, yielding improved data efficiency and accurate aerodynamic torque modeling on an ONERA–AIRBUS aircraft benchmark. Experimental results show that the full-damping GP achieves the best tracking accuracy and data efficiency, while passivity is numerically preserved under the proposed constraints, highlighting the method’s practical relevance for safe data-driven control of mechanical systems.

Abstract

Friction modeling has always been a challenging problem due to the complexity of real physical systems. Although a few state-of-the-art structured data-driven methods show their efficiency in nonlinear system modeling, deterministic passivity as one of the significant characteristics of friction is rarely considered in these methods. To address this issue, we propose a Gaussian Process based model that preserves the inherent structural properties such as passivity. A matrix-vector physical structure is considered in our approaches to ensure physical consistency, in particular, enabling a guarantee of positive semi-definiteness of the damping matrix. An aircraft benchmark simulation is employed to demonstrate the efficacy of our methodology. Estimation accuracy and data efficiency are increased substantially by considering and enforcing more structured physical knowledge. Also, the fulfillment of the dissipative nature of the aerodynamics is validated numerically.

Physically Consistent Modeling & Identification of Nonlinear Friction with Dissipative Gaussian Processes

TL;DR

This work tackles friction identification in Euler–Lagrange systems by enforcing physical passivity through a dissipative Gaussian Process (GP). It introduces matrix-vector structured GPs for damping, with both full and diagonal damping matrices, and proves deterministic positive semidefiniteness guarantees for the damping estimates, ensuring system passivity. The approach embeds prior physical structure into GP priors and kernels, and constrains hyperparameters during training to maintain passivity, yielding improved data efficiency and accurate aerodynamic torque modeling on an ONERA–AIRBUS aircraft benchmark. Experimental results show that the full-damping GP achieves the best tracking accuracy and data efficiency, while passivity is numerically preserved under the proposed constraints, highlighting the method’s practical relevance for safe data-driven control of mechanical systems.

Abstract

Friction modeling has always been a challenging problem due to the complexity of real physical systems. Although a few state-of-the-art structured data-driven methods show their efficiency in nonlinear system modeling, deterministic passivity as one of the significant characteristics of friction is rarely considered in these methods. To address this issue, we propose a Gaussian Process based model that preserves the inherent structural properties such as passivity. A matrix-vector physical structure is considered in our approaches to ensure physical consistency, in particular, enabling a guarantee of positive semi-definiteness of the damping matrix. An aircraft benchmark simulation is employed to demonstrate the efficacy of our methodology. Estimation accuracy and data efficiency are increased substantially by considering and enforcing more structured physical knowledge. Also, the fulfillment of the dissipative nature of the aerodynamics is validated numerically.
Paper Structure (17 sections, 3 theorems, 27 equations, 2 figures, 1 table)

This paper contains 17 sections, 3 theorems, 27 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Related Work
  3. Contribution and Structure
  4. Notation
  5. Problem Formulation and Passivity
  6. Gaussian Process Framework
  7. Dissipative Gaussian Processes
  8. Matrix-vector Structured Gaussian Processes for Full Damping Matrices
  9. GP Structure and Formulation
  10. Positive Semidefiniteness
  11. Matrix-vector Structured Gaussian Processes for Diagonal Damping Matrices
  12. GP Structure and Formulation
  13. Positive Semidefiniteness
  14. Simulation and Results
  15. Tracking Performance and Data Efficiency
  16. ...and 2 more sections

Key Result

lemma 1

Under Ass. ass: full independent damping matrix and the independent GP models eq: full D element GP model, denoting $\boldsymbol{k}_{d_n} = [k_{d_{mn}}\left(\Dot{\boldsymbol{q}}, \Dot{\boldsymbol{q}}^{\prime}\right)]_{m=1}^{N}$ as the n-th column of the matrix kernel associated with $\boldsymbol{D}(

Figures (2)

  • Figure 1: Training results based on trajectory and volume space
  • Figure 2: Dissipated power distribution from the collected test data and the corresponding estimation based on constrained and unconstrained methods

Theorems & Definitions (6)

  • lemma 1
  • proof
  • Theorem 1
  • proof
  • Corollary 1
  • proof