Fast and Efficient Drone Path Planning Using Riemannian Manifold in Indoor Environment

Abstract

This paper introduces an innovative dual-path planning algorithm rooted in a topological three-dimensional Riemannian manifold (T3DRM) to optimize drone navigation in complex environments. It seamlessly integrates strategies for both discrete and continuous obstacles, employing spherical navigation for the former and hyperbolic paths for the latter. Serving as a transformative tool, the T3DRM facilitates efficient path planning by transitioning between discrete and continuous domains. In uncertain environments with unpredictable obstacle positions, our methodology categorizes these positions as discrete or continuous based on their distribution patterns. Discrete obstacles exhibit random distributions, while continuous obstacles display symmetrical patterns with continuity. Leveraging topological metrics, the T3DRM efficiently classifies these patterns for effective path planning. The findings of this research demonstrate the efficiency of path planning based on classified obstacle positions, enabling swift and efficient drone navigation. This research introduces a pioneering application of a T3DRM, accelerating drone navigation in uncertain environments through a dual approach that simultaneously transforms navigation in primal and dual domains. By enabling spherical and hyperbolic navigation concurrently, the T3DRM offers a comprehensive solution to discrete and continuous path planning challenges. The proposed approach can be used for various indoor applications, especially for warehouse management, surveillance and security, navigation in complex structures, indoor farming, site inspection, healthcare facilities, etc.