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Page 62 Guan et al. Intell Robot 2024;4(1):61-73 I http://dx.doi.org/10.20517/ir.2024.04

the other hand, swarm intelligent systems are efficient and decentralized and can be controlled by a few simple
parameters, which enables a single operator to manipulate a large number of UAVs. Furthermore, multiple
UAVs can cooperate with each other, adopt dispersed flight paths, reduce the risk of detection and attack, and
enhance combat capabilities and task success.

One of the key issues in multi-UAVs systems is to maintain formation among the UAVs during flocking flight.
A common strategy for controlling UAV formations is the “Leader-Follower” approach, where one UAV is
designated as the Leader, and the rest become Followers. The Leader typically guides the movement of the
formation, while the Followers follow the Leader’s path and maintain the desired relative position and distance
to preserve the formation’s shape and collaborative work. In this approach, the trajectory of the ‘Leader’ is
clearly defined, along with the desired relative distance and movement direction between the “Leader” and
the “Follower”. Although the success of the Leader determines the flight outcome of the entire UAV swarm,
this method remains widely used in various fields due to its simplicity, modularity, high fault tolerance, and
[2]
scalability .

In the following section, we will introduce the proportional-integral-derivative (PID) control algorithm, a con-
trol strategy extensively employed in automation and control systems due to its simplicity and effectiveness in
diverse control situations. The PID algorithm is proficient in executing swift and robust command over the
formation of UAVs, ensuring the preservation of their relative positioning, system stability, and resilience to
potential faults. However, its linear control and parameter adjustment methods often fall into local optima.
The metaheuristic algorithm provides a solution to the above problems. Duan and Qiao proposed a novel
optimization algorithm, pigeon-inspired optimization (PIO), which draws inspiration from the behavior of
[3]
pigeons . This algorithm has found applications in solving optimization problems, including UAV path plan-
[5]
ning [4] and image recognition . It comprises two key components: the map and compass operator and the
[6]
landmark operator . However, the basic PIO algorithm also tends to get trapped in local optima and has a
slow convergence speed, which is not suitable for multi-UAVs formation scenarios.

Therefore, we propose an improved PIO algorithm, called improved Metropolis criterion PIO (IMCPIO), in-
spired by the simulated annealing (SA) algorithm [7] and the Iterative Modified PSO (IMPSO) algorithm. The
IMPIO algorithm has the following advantages over the basic PIO algorithm: (1) It allows inferior solutions
to be accepted with a certain probability, which enables the algorithm to escape local optima and enhances its
robustness; (2) It introduces a temperature parameter T, which decreases gradually. This implies that during
the initial phases of the algorithm, a greater likelihood of accepting suboptimal solutions aids in avoiding local
peaks. As the temperature decreases, the algorithm is more likely to accept solutions that are slightly worse
than the current solution, which helps the algorithm converge to the global optimum; (3) It adds a speed halv-
ing strategy, which controls the range of particle movement, improves search accuracy, and makes particles
more stable near the global optimum. This reduces unnecessary jumps and is conducive to fine-tuning the
solution; (4) It adopts a correction strategy from the IMPSO algorithm, proposed by Yang et al., which fixes
[8]
the defect that particles easily fall into local optima and hover near the optimal position .

The subsequent sections of this paper are structured in the following manner. The first part of Section 2
describes the mathematical model of a multi-UAV formation controller. The second part briefly reviews the
basic PIO algorithm, while the third part introduces the IMCPIO algorithm, which is an improved version of
the PIO algorithm. Comparative simulations are performed in Section 3. Section 4 summarizes the paper and
discusses future work.