Deep Neural Network with A* Based on Floyd Search for Quadrupedal Robot Navigation

Robust quadrupedal navigation in unstructured environments necessitates the simultaneous exploitation of geometric precision and semantic awareness within the search domain. To address this challenge, we introduce a hybridized framework that integrates a deep neural network with an$\mathrm{A}^{\star}$architecture augmented through Floyd's all-pairs search strategy. The neural module encodes latent geometric descriptors as weighted transitions while embedding semantic regularities of terrain and obstacle configurations as structured priors. In addition to this enriched representation, the Floyd-enhanced$\mathrm{A}^{\star}$algorithm computes globally consistent path estimates, ensuring both the locality of feasible transitions and the coherence of longhorizon connectivity. We establish the theoretical soundness of the method by proving convergence under bounded uncertainty and show that its search trajectories exhibit improved resilience to topological perturbations compared with conventional$\mathrm{A}^{\star}$formulations. Extensive validation on quadrupedal robotic platforms across 2D terrain navigation, 3D kinematic constraints, and high-dimensional locomotion manifolds demonstrates that the proposed framework consistently prioritizes stable, lowuncertainty trajectories. Comparative analysis against baseline$\mathrm{A}^{\star}$and deep-RL planners reveals that our approach yields superior path optimality and uncertainty attenuation, thereby enabling reliable autonomy for legged robots in complex, partially observable environments.