Automation technologies can help to increase the efficiency and sustainability of agricultural operations such as pest and weed control while reducing operating costs. In this paper, a global path planner for automated, mechanic weed removal along crop rows of complex-shaped fields using electric field robots is proposed. The input data of the planner includes the contours of the field and static obstacles, the start and target poses of the robots as well as the recorded tracks of a sowing machine. First, adjacent plant rows are determined and grouped into subfields based on the recorded tracks and the specifications of the sowing machine. Next, the plant rows within each subfield are covered by individual field robot tracks according to the working width of the mounted weeder. The autonomous processing of an entire field requires a dedicated navigation strategy enabling successive transfers between the various subfields such as headlands and the main field. Hence, a collision-free route network is constructed by extrapolating and interconnecting the outermost field robot tracks of each subfield. The route network is represented as a weighted graph and Dijkstra's algorithm is applied to efficiently route the robots between consecutive subfields. The travel distance on the field is minimized by optimizing the processing order of subfields using a genetic algorithm. According to the computed sequence, a field-covering global path is constructed, which is proportionally divided and allocated to a variable number of field robots and optionally involves return trips to mobile charging stations. The transfer routes along the route network are smoothed using Dubins paths in order to satisfy the kinematic constraints of the vehicles. The planning algorithm is successfully validated with sample data and prospectively tested in practice within the Fraunhofer lighthouse project Cognitive Agriculture (COGNAC).