According to different mission scenarios, the UAV swarm needs to form specific topology shapes to achieve more robust system capability. The topology shaping, which will guide the UAVs autonomously to form the desired topology shape, is considered one of the most basic procedures in the UAV swarm field operations. The traditional optimization model of UAV swarm topology shaping proposed in most studies roughly represents the energy consumption by the squared Euclidean distances from initial positions to target positions of nodes. However, in practice, UAVs flying in different directions (vertical or horizontal) usually exhibits different energy consumption even though under the same moving distance. This paper proposes a more precise energy consumption model for UAV swarm topology shaping while taking the energy consumption for a UAV flying vertically upward, vertically downward, and horizontally into account. Simulation results show that the global energy consumption of the topology shaping modeled by the proposed energy consumption model is reduced by more than $38\%$ on average compared with that using the traditional energy consumption model. Furthermore, to further reduce the global energy consumption, a translation vector is introduced in the optimization model to obtain the optimal topology shaping position of the UAV swarm system. Newton’s method is employed to derive the translation vector which exhibits good convergence. Simulation results show that the global energy consumption of optimal topology shaping position is reduced by $9.8\%$ on average compared with that without translation.

Functional topology shaping is crucial for unmanned aerial vehicles (UAVs) swarm applications, such as remote sensing, precision agriculture, and emergency wireless communication. However, the current research on topology shaping is mostly based on the assumption that the target positions of the nodes are known or have been pre-defined. Moreover, the computational complexity of existing shaping methods is still high. In this paper, a topology shaping method based on a relative coordinate system is proposed to solve the problem of UAV swarm topology shaping with no external source of localization information. Based on the relative coordinates of nodes and target topology shape of the swarm, the topology shaping is transformed into a problem of optimal coordinate mapping from initial relative coordinates to target relative coordinates of nodes with minimized global energy consumption. The Jonker–Volgenant algorithm is employed to solve the optimization problem. As verified by simulations, the proposed method can achieve UAV swarm topology shaping with no external localization information. Furthermore, simulation results show that the proposed method has an average reduction in computation time of $94\%$ in the case of 1000 nodes compared with existing methods with the same level of global energy consumption.