Robot skills learning with Riemannian manifolds: Leveraging geometry-awareness in robot learning, optimization and control

Humans exhibit outstanding learning and adaptation capabilities while performing various types of manipulation tasks. When learning new skills, humans are able to extract important information by observing examples of a task and efficiently refine a priori knowledge to master new tasks. However, learning does not happen in isolation, and the planning and control abilities of humans also play a crucial role to properly execute manipulation tasks of varying complexity. In the last years, a lot of attention has been devoted to the problem of providing robots with close-to-human-level abilities. In this context, this thesis proposes to enhance robot learning and control capabilities by introducing domain knowledge into the corresponding models. Our approaches, built on Riemannian manifolds, exploit the geometry of non-Euclidean spaces, which are ubiquitous in robotics to represent rigid-body orientations, inertia matrices, manipulability ellipsoids, or controller gain matrices.

We initially consider the problem of transferring skills to a robot and propose a probabilistic framework to learn symmetric positive definite (SPD) matrices from demonstrations. Given a learned reference trajectory in the form of SPD matrices, the goal of the robot is to reproduce the task by tracking this sequence using appropriate controllers. This challenge is tackled in the second part of this thesis. We focus on a specific application and propose a complete geometry-aware framework to learn, control and transfer posture-dependent task requirements from humans to robots via manipulability profiles. The third part of this thesis focuses on refining the skills learned by the robot and on adapting them to new situations by introducing a geometry-aware Bayesian optimization framework. Overall, this thesis proves that geometry-awareness is crucial for successfully learning, controlling and refining non-Euclidean parameters in addition to providing a proper mathematical treatment of the different problems. Finally, the last part of this work shows that domain knowledge can be introduced not only through geometry-awareness, but also through structure-awareness, which may be considered either as prior models or as intrinsically present in the data. With its final part, this thesis emphasizes that domain knowledge, that can be introduced into robot learning algorithms through various means, may be significant for providing robots with close-to-humans abilities.