Unmanned aerial vehicles (UAVs) can be utilized as airborne base stations to deliver wireless communication and federated learning (FL) training services for ground vehicles. However, most existing studies assume that vehicles (clients) and UAVs (model owners) offer services voluntarily. In reality, participants (FL clients and model owners) are selfish and will not engage in training without compensation. Meanwhile, due to the heterogeneity of participants and the presence of free-riders and Byzantine behaviors, the quality of vehicles’ model updates can vary significantly. To incentivize participants to engage in model training and ensure reliable outcomes, this paper designs a reliable incentive mechanism (FedBeam) based on game theory. Specifically, we model the cooperation problem between model owners and clients as a two-layer Stackelberg game and prove the existence and uniqueness of the Stackelberg equilibrium (SE). For the cooperation among model owners, we formulate the problem as a coalition game and based on this, analyze and design a coalition formation algorithm to derive the Pareto optimal social utility. Additionally, to achieve reliable FL model updates, we design a weighted-beta (Wbeta) reputation update mechanism to incentivize FL clients to provide high-quality model updates. The experimental results show that compared to the baselines, the proposed incentive mechanism improves social welfare by 17.6% and test accuracy by 5.5% on simulated and real datasets, respectively.

Robots play a crucial role in experimental smart cities and are ubiquitous in daily life, especially in complex environments where multiple robots are often needed to solve problems collaboratively. Researchers have found that the swarm intelligence optimization algorithm has a better performance in planning robot paths, but the traditional swarm intelligence algorithm cannot be targeted to solve the robot path planning problem in difficult problem. Therefore, this paper aims to introduce a fuzzy controller, mutation factor, exponential noise, and other strategies on the basis of particle swarm optimization to solve this problem. By judging the moving speed of different particles at different periods of the algorithm, the individual learning factor and social learning factor of the particles are obtained by fuzzy controller, and using the leader particle and random particle, designing a new dynamic balance of mutation factor, with the iterative process of the adaptation value of continuous non-updating counter and continuous updating counter to control the proportion of the elite individuals and random individuals. Finally, using exponential noise to update the matrix of the population every 50 iterations is a way to balance the local search ability and global exploration ability of the algorithm. In order to test the proposed algorithm, the main method of this paper is simulated on simple scenarios, complex scenarios, and random maps consisting of different numbers of static obstacles and dynamic obstacles, and the algorithm proposed in this paper is compared with eight other algorithms. The average path deviation error of the planned paths is smaller; the average distance of untraveled target is shorter; the number of steps of the robot movements is smaller, and the path is shorter, which is superior to the other eight algorithms. This superiority in solving multi-robot cooperative path planning has good practicality in many fields such as logistics and distribution, industrial automation operation, and so on.