Title: Generalization of Task Parameterized Dynamical Systems using Gaussian Process Transportation

Abstract: Learning from Interactive Demonstrations has revolutionized the way non-expert humans teach robots. It is enough to kinesthetically move the robot around to teach pick-and-place, dressing, or cleaning policies. However, the main challenge is correctly generalizing to novel situations, e.g., different surfaces to clean or different arm postures to dress. This article proposes a novel task parameterization and generalization to transport the original robot policy, i.e., position, velocity, orientation, and stiffness. Unlike the state of the art, only a set of points are tracked during the demonstration and the execution, e.g., a point cloud of the surface to clean. We then propose to fit a non-linear transformation that would deform the space and then the original policy using the paired source and target point sets. The use of function approximators like Gaussian Processes allows us to generalize, or transport, the policy from every space location while estimating the uncertainty of the resulting policy due to the limited points in the task parameterization point set and the reduced number of demonstrations. We compare the algorithm's performance with state-of-the-art task parameterization alternatives and analyze the effect of different function approximators. We also validated the algorithm on robot manipulation tasks, i.e., different posture arm dressing, different location product reshelving, and different shape surface cleaning.