We present a control approach for autonomous vehicles based on deep reinforcement learning. A neural network agent is trained to map its estimated state to acceleration and steering commands given the objective of reaching a specific target state while considering detected obstacles. Learning is performed using state-of-the-art proximal policy optimization in combination with a simulated environment. Training from scratch takes five to nine hours. The resulting agent is evaluated within simulation and subsequently applied to control a full-size research vehicle. For this, the autonomous exploration of a parking lot is considered, including turning maneuvers and obstacle avoidance. Altogether, this work is among the first examples to successfully apply deep reinforcement learning to a real vehicle.

Complete coverage path planning (CCPP) is vital in mobile robot applications. Optimizing CCPP is particularly significant in precision agriculture, where it enhances resource utilization, reduces soil compaction, and boosts crop yields. This work offers a comprehensive approach to CCPP for agricultural vehicles with curvature constraints. Our methodology comprises four key stages. First, it decomposes complex agricultural areas into simpler cells, each equipped with guidance tracks, forming a fixed track system. The subsequent route planning and smooth path planning stages compute a path that adheres to path constraints, optimally traverses the cells, and aligns with the track system. We use the generalized traveling salesman problem (GTSP) to determine the optimal traversing sequence. Additionally, we introduce an algorithm for calculating paths that are both smooth and curvature-constrained within individual cells, as well as paths that enable seamless transitions between cells, resulting in a smooth, curvature-constraint coverage path. Our modular approach allows method flexibility at each step. We evaluate our method on real agricultural fields, demonstrating its effectiveness in minimizing path length, ensuring efficient coverage, and adhering to curvature constraints. This work establishes a strong foundation for precise and efficient agricultural coverage path planning, with potential for further real-world applications and enhancements.

A numerical method for the approximation of reachable sets of linear control systems is discussed. The method is based on the formulation of suitable optimal control problems with varying objective function, whose discretization by Runge–Kutta methods leads to finite-dimensional convex optimization problems. It turns out that the order of approximation for the reachable set depends on the particular choice of the Runge–Kutta method in combination with the selection strategy used for control approximation. For an inappropriate combination, the expected order of convergence cannot be achieved in general. The method is illustrated by two test examples using different Runge–Kutta methods and selection strategies, in which the run times are analysed, the order of convergence is estimated numerically and compared with theoretical results in similar areas.