Efficient Social Navigation: Leveraging Discrete Morse Theory for Dynamic Agent Interaction^*

Robotic navigation in dynamic environments presents significant challenges, particularly in managing interactions with moving agents while ensuring efficient path planning. We introduce a novel integration of social navigation strategies with topological path planning, leveraging Discrete Morse Theory, Vietoris-Rips complex, and a homotopical framework to enhance adaptability. Our method dynamically assesses path feasibility and optimizes trajectory selection through three key strategies: waiting, deflection, and diverse path selection. By incorporating Morse values into a sampling-based roadmap, our approach prioritizes critical configurations for efficient motion planning. Unlike existing methods that rely on static heuristics or extensive learning-based predictions, our framework offers a real-time, adaptive mechanism for congestion-aware navigation. Experimental evaluations demonstrate an efficient solution(< 100s in computation) with improved path adaptability, resulting in 30–60% increase in traversal time in environments containing 3–9 degrees of freedom robot and 15–60 dynamic agents.