Advantages of a physics-embedding kernel for robot inverse dynamics identification

The Geometrically Inspired Polynomial Kernel (GIP) [1] has been recently proposed in the context of black box inverse dynamics estimation based on Gaussian Processes, driven by the fact that the inverse dynamics map derived from the Lagrangian equations is a polynomial function in a suitable feature space. In this paper, we further investigate the advantages of the GIP kernel comparing it with the state of the art Radial Basis Function Kernel (RBF). In particular, we extend the analysis of the generalization properties, by comparing estimation accuracy and reliability of the confidence intervals returned. Moreover, we evaluate the structural properties induced by the two kernels considering their ability to estimate inertial, Coriolis and gravitational components of the inverse dynamics map. Numerical experiments confirm that the GIP kernel has better generalization properties and returns more reliable estimates of the prediction variance. Moreover, its superior ability to estimate inertial, Coriolis and gravitational torques components, suggests that it better encodes the underlying structural properties of the unknown inverse dynamics map.