Abstract:

In this extended abstract we present two recent contributions in the context of Physics Informed black-box inverse dynamics identification using Gaussian Processes (GPs). The first contribution consists in a novel kernel, named Geometrically inspired Polynomial Kernel (GIP) for single joint GP-based inverse dynamics identification. Driven by the fact that the inverse dynamics can be described as a polynomial function on a suitable input space, the GIP kernel restricts the regression problem to a finite-dimensional space which contains the inverse dynamics function, thus leading to improved data efficiency and generalization properties. The second contribution consists in the derivation of a multidimensional GP framework, named Lagrangian GPR, which overcomes the single joint approach and learns the inverse dynamics in a multidimensional setting. Exploiting the properties of GPs in connection with linear operators, Lagrangian GPR allows to impose by design the known symmetric structure of the Euler-Lagrange equation on the learned models. Moreover, since information is shared between different degrees of freedom (DOFs), this approach strongly improves data efficiency and generalization properties.