Weed competition is one of the most limiting factors affecting crop yield and profitability. Robotic weeding systems have demonstrated their potential to save herbicide usage and thereby minimize costs and adverse impacts on the environment. We introduce the software and hardware design of an automatic system for micro-volume herbicide spray using a mobile robot for early-stage weed control. The system is equipped with a stereo camera, one inertial measurement unit, and multiple linearly actuating spray nozzles. To enable the system, we propose a new scene representation from the perspective of spray operation. We represent the space occupied by weeds as candidate line segments for spray and then construct a directed acyclic graph (DAG) that embraces the feasible nozzle paths among weeds. Based on the new scene representation, we formulate an optimal <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$K$</tex-math></inline-formula> -nozzle assignment/motion planning problem and develop a binary linear programming-based algorithm to assign nozzles to the candidate line segments for optimal coverage. We built the system and conducted both simulation and field experiments. Evaluation on rough soil surfaces with artificial targets has shown that the lateral errors of herbicide spray are at sub-centimeter levels. Simulation results demonstrate that the proposed assignment algorithm can provide good coverage within the intra-row regions.