A Fluid-Mechanism-and-Differential-Evolution-Enhanced Particle Swarm Optimizer for Robot Path Planning

Path planning of mobile robots on grid maps is a complex optimization problem, and applying standard particle swarm optimization (PSO) to this task often leads to stagnation and premature convergence. To address these issues, a particle swarm optimizer enhanced by fluid mechanics and differential evolution (FMDEPSO) is proposed. The method integrates fluid-inspired neighborhood feedback with a differential evolution recombination mechanism to construct a semi-discrete population evolution framework. Specifically, FMDEPSO introduces a pressure repulsion term and a viscous diffusion term to mitigate early population collapse and suppress oscillations caused by abrupt velocity variations. Meanwhile, a gas–liquid phased adaptive scheduling strategy is adopted to dynamically adjust the learning factors, thereby balancing exploration and exploitation. In addition, the mutation–crossover–greedy selection operator of differential evolution (DE) is embedded into the update process to preserve population diversity and enhance the capability of escaping local optima. On the CEC2017 benchmark suite, FMDEPSO achieved the best mean results on 17, 19, and 17 functions under 30-, 50-, and 100-dimensional settings, respectively, compared with eight representative PSO variants. It maintained a top-three ranking on the majority of functions and obtained the overall best average rank according to the Friedman test. The Wilcoxon rank-sum test further confirmed its statistical advantage on most benchmark functions. In grid-based path-planning experiments on multi-scale environments (20×20, 40×40, and 60×60), FMDEPSO generates smooth and goal-directed feasible trajectories in successful runs and achieves the best overall performance among PSO-based methods while maintaining a favorable balance among path quality, success rate, and runtime across different complexity levels. Overall, the proposed method exhibits stable convergence behavior and competitive solution quality in both numerical benchmark optimization and mobile robot path-planning tasks.