H* Algorithm: Enhancing A* for Smoother and More Feasible Robot Navigation

This paper presents <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathrm{H}^{*}$</tex>, an enhanced <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathrm{A}^{*}$</tex> algorithm designed to improve the realism and efficiency of pathfinding for real-world agents, especially in robotics. <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H^{*}$</tex> uses hexagonal grid decomposition and an improved geometric heuristic to model traversable space more effectively. By incorporating the agent's velocity and turning radius, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{H}^{*}$</tex> generates smoother, more realistic paths and detects sharp turns tailored to kinematic constraints. These enhancements aim to reduce travel time while maintaining feasibility for physical agents. Experimental results demonstrate the algorithm's practical benefits in realistic scenarios.