Illustrations of the fiber home positions. The left panel illustrates a fixed fiber-positioning system (parallel positioner), where hexagonal fiber home positions are overlaid with target positions and corresponding patrol radii. The hexagonal mesh, shown in red, represents the fixed home positions of 500 fibers. Each fiber has a defined PR, depicted as purple dashed circles, indicating the region within which the fiber can be repositioned to acquire a target. This setup ensures a structured and consistent fiber distribution while maintaining a limited range of motion for target acquisition. In contrast, the right panel demonstrates a pick-and-place fiber-positioning system (sequential positioner), where 120 fibers (marked in red) are arranged in their home positions around the edge of a FoV and in principle can be allocated to any target. Unlike the fixed system, this approach allows greater flexibility in target allocation by enabling fibers to be placed anywhere to support optimal target allocation. This method enhances target accessibility while maintaining necessary constraints on fiber movement to prevent overlap or mechanical interference.