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Guan et al. Intell Robot 2024;4(1):61-73 I http://dx.doi.org/10.20517/ir.2024.04 Page 71

Figure 9. Rastrigin function comparison curves. PIO: Pigeon-inspired optimization; GA: genetic algorithm.

Figure 10. Multi-UAVs three-dimensional trajectories. UAVs: Unmanned aerial vehicles.

Figure 10 depicts the detailed results of six UAVs in formation light in a three-dimensional environment.

4. DISCUSSION
This paper proposes an IMCPIO algorithm that introduces the Metropolis criterion based on the basic PIO al-
gorithm and combines it with the PID algorithm to optimize controller parameters. Simulation results demon-
strate that the IMCPIO algorithm significantly improves the convergence speed and the ability to escape local
optima compared to the basic PIO algorithm and the GA, ultimately enhancing the optimization effect.

Currently, this algorithm only introduces the IMC in the map and compass operator stage of the base PIO
algorithm. Looking forward, there is potential for introducing more advanced optimization strategies into
IMCPIO to further refine both the map and compass operator stage and the landmark operator stage. This
would further enhance the ability of the IMCPIO algorithm to escape local optima and its convergence. More-
over, the integration of the IMCPIO algorithm with the PID algorithm opens up new avenues for optimization.
The balance between global and local search in the IMCPIO algorithm can be used to adaptively adjust the pa-
rameters of the PID controller, enhancing its performance. This combination could also improve the handling
of non-linear systems and uncertainties, which are common in practical applications.

Inthefuture, thisalgorithmwillbefurtherrefinedtoenhanceitsoptimizationcapability, suchasescapingfrom