# A data-efficient geometrically inspired polynomial kernel for robot inverse dynamics

## TL;DR

This paper presents a novel polynomial kernel for Gaussian Process Regression that improves data efficiency and generalization in robot inverse dynamics estimation, reducing reliance on prior models.

## Contribution

Introduction of the Geometrically Inspired Polynomial Kernel (GIP) for more data-efficient and less biased inverse dynamics estimation in robotics.

## Key findings

- GIP kernel defines a finite-dimensional RKHS containing the inverse dynamics function.
- The approach outperforms other data-driven estimators in data efficiency and generalization.
- The method requires less prior information than traditional model-based estimators.

## Abstract

In this paper, we introduce a novel data-driven inverse dynamics estimator based on Gaussian Process Regression. Driven by the fact that the inverse dynamics can be described as a polynomial function on a suitable input space, we propose the use of a novel kernel, called Geometrically Inspired Polynomial Kernel (GIP). The resulting estimator behaves similarly to model-based approaches as concerns data efficiency. Indeed, we proved that the GIP kernel defines a finite-dimensional Reproducing Kernel Hilbert Space that contains the inverse dynamics function computed through the Rigid Body Dynamics. The proposed kernel is based on the recently introduced Multiplicative Polynomial Kernel, a redefinition of the classical polynomial kernel equipped with a set of parameters that allows for a higher regularization. We tested the proposed approach in a simulated environment, and also in real experiments with a UR10 robot. The obtained results confirm that, compared to other data-driven estimators, the proposed approach is more data-efficient and exhibits better generalization properties. Instead, with respect to model-based estimators, our approach requires less prior information and is not affected by model bias.