Structure-Preserving Learning of Nonholonomic Dynamics

TL;DR

This paper introduces a Gaussian process framework with a specialized kernel that preserves the nonholonomic constraints in learned dynamics, ensuring physically consistent motions in robotics applications.

Contribution

It develops a nonholonomic matrix-valued kernel for GPs that guarantees constraint satisfaction and provides theoretical analysis of its properties and consistency.

Findings

Kernel ensures learned vector fields satisfy nonholonomic constraints.

The approach guarantees physically consistent motions in simulations.

The method is validated through numerical simulations on a vertical rolling disk.

Abstract

Data-driven modeling is playing an increasing role in robotics and control, yet standard learning methods typically ignore the geometric structure of nonholonomic systems. As a consequence, the learned dynamics may violate the nonholonomic constraints and produce physically inconsistent motions. In this paper, we introduce a structure-preserving Gaussian process (GP) framework for learning nonholonomic dynamics. Our main ingredient is a nonholonomic matrix-valued kernel that incorporates the constraint distribution directly into the GP prior. This construction ensures that the learned vector field satisfies the nonholonomic constraints for all inputs. We show that the proposed kernel is positive semidefinite, characterize its associated reproducing kernel Hilbert space as a space of admissible vector fields, and prove that the resulting estimator admits a coordinate representation adapted to the constraint distribution. We also establish the consistency of the learned model. Numerical simulations on a vertical rolling disk illustrate the effectiveness of the proposed approach.