Most existing path planning approaches rely on discrete expansions or localized heuristics that can lead to extended re-planning, inefficient detours, and limited adaptability to complex obstacle distributions. These issues are particularly pronounced when navigating cluttered or large-scale environments that demand both global coverage and smooth trajectory generation. To address these challenges, this paper proposes a Wave Water Simulator (WWS) algorithm, leveraging a physically motivated wave equation to achieve inherently smooth, globally consistent path planning. In WWS, wavefront expansions naturally identify safe corridors while seamlessly avoiding local minima, and selective corridor focusing reduces computational overhead in large or dense maps. Comprehensive simulations and real-world validations—encompassing both indoor and outdoor scenarios—demonstrate that WWS reduces path length by 2%–13% compared to conventional methods, while preserving gentle curvature and robust obstacle clearance. Furthermore, WWS requires minimal parameter tuning across diverse domains, underscoring its broad applicability to warehouse robotics, field operations, and autonomous service vehicles. These findings confirm that the proposed wave-based framework not only bridges the gap between local heuristics and global coverage but also sets a promising direction for future extensions toward dynamic obstacle scenarios and multi-agent coordination.
Chen et al. (2026) studied this question.