A Novel Physics-Informed Learning Framework for Robotics

In this thesis, we propose novel solutions in the context of physics-informed Gaussian Process Regression (GPR), a well-established regression framework that has proven its advantages in several practical applications. Specifically, in the first part of this manuscript, we present the results of preliminary investigations aimed at justifying our interest in physics-informed GPR. Comparisons involving state-of-the-art methods show that physics-informed GPR has the potential to provide accurate and reliable estimates on high-dimensional systems, also when a reduced amount of data samples is available. In the second part, we present our main contribution, a novel multi-output GPR estimator named \textit{Lagrangian Inspired Polynomial} (LIP) estimator. Differently from the previously presented solutions, the LIP estimator embeds the symmetries of Lagrangian mechanics and exploits a specific polynomial characterization to restrict the regression problem to a finite-dimensional functional space where the dynamics are contained. Experimental results both on simulated and real robotics manipulators show that this solution provides accurate performances also with limited data availability, overcoming all the state-of-the-art baselines considered. Moreover, to deal with the non-positiveness of the inertia matrix possibly arising in the GPR framework, we propose a novel algorithm based on constrained optimization. Results show sensible improvements in inertia matrix positiveness, without compromising estimation accuracy. In the third part, we present some use cases of the proposed framework. First, we present an energy-based controller for the swing-up and stabilization of balancing under-actuated robots, which exploits the LIP to derive the estimates of the system energy as well as the dynamics components required. Second, we propose an adaptive robust feedback line