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

arXiv: https://arxiv.org/abs/1904.13317 · HTML: https://mlsanity.com/paper/1904.13317/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Apr 2019.

## Built on by (most cited first, 2 of 2)

- [A Black-Box Physics-Informed Estimator based on Gaussian Process Regression for Robot Inverse Dynamics Identification](https://mlsanity.com/paper/2310.06585/) (2023)
- [Joint torques prediction of a robotic arm using neural networks](https://mlsanity.com/paper/2405.00695/) (2024)

## Abstract (arXiv)

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.