Uncertainty in Robotics - Tractable Inference and Policy Optimization

English The goal in robotics is to bring the robot and the world from some initial state into a desired state. For instance, we may want the robot to move to a particular place, or we may want it to arrange a set of external objects in a specific way. In order to achieve this, the robot needs to physically interact with the world. However, our models describing this interaction are an imperfect representation of reality and their predictions are hence subject to a large degree of uncertainty. In this thesis we investigate two key problems which arise as a consequence of this uncertainty. First, we consider the filtering problem, i.e. estimating the underlying state of our robot and the world given sensory information. We analyze the limitations of the two most widely used filtering methods in robotics, the particle filter (PF) and the Gaussian filter (GF), and we propose according extensions. The key problem of the PF is the exponential growth of the computational cost with the state dimension. We identify certain independence structures among the state and observation variables which occur in robotics, and we show how PFs can be extended to exploit those. These extensions allow us to apply PFs to such systems even if they have a high-dimensional state-space. In contrast, the main drawback of the GF is that its parametric form can be too restrictive to accurately capture the dependences in systems with nonlinear observation models. We show how the GF can be seen as the optimal approximation to the exact posterior distribution, subject to some constraints. This new perspective then motivates extensions to relax this constraint, which can greatly improve the filtering accuracy in nonlinear systems. As a concrete application for the proposed PF and GF extensions, we consider the problem of 3D object and manipulator tracking using depth cameras. We evaluate the proposed tracking methods extensively to show their accuracy under difficult conditions, such as heavy occlusions and fast motion. A second consequence of the uncertainty in our physics model is that we are not able to accurately predict how well a certain controller will perform on the real robot. Unfortunately, in robotics problems the number of experiments required to fully explore the parameter space of a controller is often prohibitively large. Hence, we may not be able to identify the global