GeoPF: Infusing Geometry into Potential Fields for Reactive Planning in Non-trivial Environments

Reactive intelligence remains one of the cornerstones of versatile robotics operating in cluttered, dynamic, and human-centred environments. Among reactive approaches, potential fields (PF) continue to be widely adopted due to their simplicity and real-time applicability. However, existing PF methods typically oversimplify environmental representations by relying on isotropic, point- or sphere-based obstacle approximations. In human-centred settings, this simplification results in overly conservative paths, cumbersome tuning, and computational overhead -- even breaking real-time requirements. In response, we propose the Geometric Potential Field (GeoPF), a reactive motion-planning framework that explicitly infuses geometric primitives -- points, lines, planes, cubes, and cylinders -- their structure and spatial relationship in modulating the real-time repulsive response. Extensive quantitative analyses consistently show GeoPF's higher success rates, reduced tuning complexity (a single parameter set across experiments), and substantially lower computational costs (up to 2 orders of magnitude) compared to traditional PF methods. Real-world experiments further validate GeoPF reliability, robustness, and practical ease of deployment, as well as its scalability to whole-body avoidance. GeoPF provides a fresh perspective on reactive planning problems driving geometric-aware temporal motion generation, enabling flexible and low-latency motion planning suitable for modern robotic applications.