In order to solve the problem of sharp fluctuations in demand in the terminal delivery of logistics drones and the situation that traditional positioning models lack robustness, this paper puts forward a robust positioning model (RFL-LU) that takes into consideration the demand uncertainties and the physical constraints of drones (such as endurance and no-fly zones, and so on). This model aims at minimizing the total cost of construction, transportation, and maintenance, and also combines the advantages of the set covering model and the P - median model. It incorporates an uncertainty budget Γ to adjust the degree of robustness, and then transforms the nonlinear robust constraints into linear ones through dual transformation, ensuring that the capacity of the take - off and landing points can cover both the nominal demand and the fluctuating increment. In order to efficiently address the model issues, an improved tabu search (ITS) algorithm that we have developed is presented. This algorithm, which makes use of adaptive neighborhood operations, double-objective taboo lists, and elite solution crossover learning methods, optimizes the 0 - 1 position assignment variables and continuous capacity variables in two phases. We carried out simulations with LRP standard instances and made comparative verifications under different uncertainty budgets Γ (3, 6, 9, 12), and demand fluctuation ranges (from 30% to 80%), and also carried out sensitivity analysis at the same time. The results show that the uncertainty budget Γ has a rather significant impact on the number of take-off and landing points and load balancing: a high Γ can ensure a 100% service level, but the construction cost will be higher. There is a non - monotonic positive correlation between the demand fluctuation range and the total cost, and this model can balance costs and services by adaptively adjusting the scale of facilities. In this research, in the situation of uncertain demands, it offers the scientific decision-making basis for the layout of the take-off and landing points of logistics drones, and also enhances the network’s elastic and adaptive capabilities.