Learning Positive Definite Inertia Matrices in Black-Box Inverse Dynamics Models via Gaussian Processes: a Constraint Learning Approach

Inverse dynamics models are crucial for robotic control, but traditional physics-based models require precise system parameters that can be difficult to obtain. While data-driven black-box models offer a valid alternative, they usually lack physical plausibility, limiting their use with standard control methods. This paper presents a method for black-box inverse dynamics identification using Gaussian Processes Regression (GPR) that promotes physical consistency, by enforcing the positive definiteness of the inertia matrix. In particular, we unveil how to estimate the inertia matrix elements from black-box models, and we integrate positivity constraints into the empirical risk minimization problem. Experimental validation demonstrates that our approach significantly improves physical consistency with minimal loss in estimation accuracy, outperforming unconstrained models that may yield non-physical behaviors and consequently poor control performances.