This research introduces two efficient methods to estimate the collision risk of planned trajectories in autonomous driving under uncertain driving conditions. Deterministic collision checks of planned trajectories are often inaccurate or overly conservative, as noisy perception, localization errors, and uncertain predictions of other traffic participants introduce significant uncertainty into the planning process. This paper presents two semi-analytic methods to compute the collision probability of planned trajectories with arbitrary convex obstacles. The first approach evaluates the probability of spatial overlap between an autonomous vehicle and surrounding obstacles, while the second estimates the collision probability based on stochastic boundary crossings. Both formulations incorporate full state uncertainties, including position, orientation, and velocity, and achieve high accuracy at computational costs suitable for real-time planning. Simulation studies verify that the proposed methods closely match Monte Carlo results while providing significant runtime advantages, enabling their use in risk-aware trajectory planning. The collision estimation methods are available as open-source software: https://github.com/TUM-AVS/Collision-Probability-Estimation

While classic control theory offers state of the art solutions in many problem scenarios, it is often desired to improve beyond the structure of such solutions and surpass their limitations. To this end, \emph{\gls{rpl}} offers a formulation to improve existing controllers with reinforcement learning (RL) by learning an additive "residual" to the output of a given controller. However, the applicability of such an approach highly depends on the structure of the controller. Often, internal feedback signals of the controller limit an RL algorithm to adequately change the policy and, hence, learn the task. We propose a new formulation that addresses these limitations by also modifying the feedback signals to the controller with an RL policy and show superior performance of our approach on a contact-rich peg-insertion task under position and orientation uncertainty. In addition, we use a recent impedance control architecture as control framework and show the difficulties of standard RPL. Furthermore, we introduce an adaptive curriculum for the given task to gradually increase the task difficulty in terms of position and orientation uncertainty. A video showing the results can be found at https://youtu.be/SAZm_Krze7U .