This thesis presents a novel approach for density-based motion planning in dynamic environments. Many state-of-the-art motion planners have difficulties to reach the target in crowded, uncertain environments while keeping the collision probability small. Thus, the main objective for the proposed motion planner is to find trajectories which lead to a target position with minimal collision risk. As we additionally consider an uncertain initial state in form of a given density distribution, we will utilize density-based reachability, i.e., we will estimate the state density distribution which will be reached in the future and use it to compute and minimize the collision risk. The proposed approach consists of three main components: First, a tracking controller will be synthesized such that trajectories starting from all possible initial states stay in the vicinity of a reference trajectory. To guarantee good tracking performance, even under disturbances, we will use contraction theory. The second component is a neural network which approximates the state density distribution for the closed-loop dynamics along the reference trajectory. Finally, a gradient-based optimization procedure will be used to optimize the reference trajectory in order to minimize the collision risk. To evaluate the performance, the motion planning approach is applied to an autonomous car and we show that the approach outperforms state-of-the-art motion planners in a large number of dynamic environments. Furthermore, we demonstrate that the concept can be applied to real-world data without modification.     «

This thesis presents a novel approach for density-based motion planning in dynamic environments. Many state-of-the-art motion planners have difficulties to reach the target in crowded, uncertain environments while keeping the collision probability small. Thus, the main objective for the proposed motion planner is to find trajectories which lead to a target position with minimal collision risk. As we additionally consider an uncertain initial state in form of a given density distribution, we...     »