## 1 Introduction  
UAVs have the advantages of top maneuverability, robust battlefield adaptability, small size, and low cost and are extensively used in military and civilian missions, such as surveillance, reconnaissance operations, search and rescue, emergency communications, and agriculture. The secure path planning of UAVs is of excellent magnitude to the completion rate and efficiency of UAVs performing tasks. Path planning [1, 2] refers to calculating the optimal path between the beginning point and the goal point based on totally satisfying the constraints of the UAV itself and exterior threats. UAV secure path planning performs a key function in enhancing the autonomy and intelligence level of unmanned systems, so research on this topic has received greater and greater attention. For the path planning issue of UAVs or robots, domestic and international scholars have proposed many techniques [3, 4, 5, 6, 7], such as the A\({}^{\star}\) algorithm [8], the rapidly exploring random tree [9], the probabilistic roadmap algorithm [10], the Voronoi diagram algorithm [11], etc. However, these algorithms ignore the dynamics and kinematic constraints of UAVs, so they typically cannot be utilized in practical situations. The potential field methods, such as the artificial potential field method [12] and the interfeed fluid dynamical system algorithm are additional superb techniques for path planning [13]. However,when the goal and the obstacle are close, the algorithm can fall into the local optimum, and the optimal flyable path cannot be guaranteed. In recent years, the population-based evolutionary algorithm has made much progress. Compared with classical algorithms, metaheuristic algorithms [14; 15] can effectively solve complex combinatorial optimization problems and have been widely used in multi-UAV path planning research. Metaheuristic algorithms are improved algorithms based on heuristic algorithms., The most famous bio-inspired algorithms are the genetic algorithm (GA) [16] and the differential evolution algorithm (DE). The algorithms based on swarm intelligence include the ant colony optimization algorithm [17], the artificial bee colony (ABC) algorithm [18], the particle swarm optimization (PSO) [19], the moth flame optimization (MFO) [20], and the butterfly optimization algorithm (BOA) [21] etc. Bio-inspired algorithms have a sturdy capability to search for the optimal solution and are very bendy and efficient, so they are extensively used in the path planning of UAVs. The PSO algorithm has the disadvantages of having a slow convergence speed, being easy fall into local optimum, and having a path that is not smooth, but the PSO algorithm has two vital properties, cognitive consistency and social consistency. These properties allow each particle in the population to find a solution according to its own experience and swarm experience, rather than by using traditional evolution operations such as mutation and crossover. Therefore, in contrast with other bio-inspired algorithms, it can be used to find a global solution with convergence in a shorter time. Moreover, the particle swarm algorithm is not very sensitive to the modifications of initial conditions and objective functions and can adapt to a variety of environmental structures via a small number of parameters such as an acceleration coefficient and two weight factors. Based on these advantages, the PSO algorithm is widely used in path planning, and a variety of variants of the PSO algorithm have emerged. [PERSON] et al. [22] introduced an improved particle swarm algorithm to make UAV shape formations in a three-dimensional (3D) environment. This approach makes use of logistic chaotic mapping to enhance the preliminary distribution of particles and designs the acceleration coefficient and the maximum velocity as adaptive linearly altering coefficients to reap a better solution. A mutation method for replacing terrible particles with good ones is additionally proposed, which speeds up the convergence of the algorithm. [PERSON] et al.