Liquid neural network-based multi-UAV path planning in dynamic, obstacle-aware environments

Deploying multiple unmanned aerial vehicles (UAVs) for last-mile delivery in urban airspace requires decentralized path planning under dynamic constraints, including moving obstacles, intermittently active no-fly zones, variable wind, limited onboard energy, and multi-vehicle coordination. Classical planners provide strong routing performance in structured settings, but repeated replanning becomes increasingly burdensome in dynamic environments, whereas learned policies trained purely from demonstrations may suffer from covariate shift during closed-loop execution. We propose a decentralized planning framework in which each UAV is controlled by a compact Liquid Neural Network (LNN) trained via masked behavioral cloning from a coordinated A* oracle. The policy uses continuous-time recurrent dynamics with learnable per-neuron time constants, while legality masks enforce obstacle, airspace, and inter-agent safety constraints during both training and deployment. This design aims to combine reactive decentralized execution with a compact recurrent architecture that can smooth transient disturbances while remaining responsive to persistent environmental changes. The empirical study is conducted over a benchmark family that varies both grid size and fleet size, including compact 10× 10 scenarios with 3–5 UAVs and enlarged 20× 20 scenarios with 3–5 UAVs. This setup enables separate analysis of fleet scaling within a fixed environment and spatial scale-up at fixed team size. The results show that the proposed LNN policy performs strongly in compact-grid settings, where it consistently achieves the best non-oracle performance across the 10× 10 scenarios. In enlarged-grid settings, however, all methods experience substantial degradation, accompanied by sharply increased battery-failure rates. These results indicate that larger-scale deterioration is driven not only by routing complexity, but also by growing energy-feasibility pressure as travel distances increase. Overall, the study suggests that liquid recurrent policies are a promising fit for compact-to-moderate decentralized multi-UAV routing under dynamic constraints, while also clarifying the limitations of the current framework in enlarged environments. The findings therefore provide both a positive assessment of LNN-based control in controlled routing regimes and a more explicit account of the conditions under which performance begins to deteriorate.