A well-planned robot dispatching platform reduces costs and increases efficiency for companies while also reducing carbon emissions and achieving sustainable development. At the moment, the solution to the difficulty of warehouse logistics is use of multiple distribution centers with autonomous mobile robots (AMR). To solve this problem, this paper establishes a semi-closed model of multiple distribution centers, considering the number of cycles and the number of vehicles. An improved ant colony algorithm is proposed to improve the heuristic function based on the node distance relationship to improve the quality of path search. Dynamic variable pheromone concentration and volatility factors are set to accelerate the convergence speed of the algorithm while effectively reducing the problem of the premature algorithm. The traditional ant colony algorithm and the improved ant colony algorithm are used to solve the established model. In addition, the results show that the traditional ant colony algorithm has a certain rate of dominance in the single-day cost of the closed distribution model, but the overall comprehensive cost is lower than that of the improved ant colony algorithm. The single-day cost of the semi-open multi-distribution center logistics and distribution model is lower than that of the closed multi-distribution center logistics and distribution model, and the 7 day average cost is reduced by 12%. The improved ant colony algorithm can save about 119 kWh of electricity under the same target volume requirement, which achieves the company’s goals of cost reduction and increased efficiency, as well as green and sustainable development.