Multi-Scale Cell Decomposition for Path Planning using Restrictive Routing Potential Fields

TL;DR

This work introduces Larp (Last-mile restrictive path planning), a framework for safe routing in urban environments that uses restrictive routing potential fields as continuous cost maps. It decomposes a potential field into multi-scale quad-tree cells, assigns risk zones analytically, builds a routing network, and applies a modified A* to minimize distance while constraining accumulated potential, quantified by $R_A$, $R_d$, and $R_{avg}$. Safety validation relies on a defined trajectory metric with a practical threshold around $0.35$, and the approach is demonstrated on small-room scenarios and city-scale Austin routes, outperforming traditional and contemporary potential-field methods in safety while maintaining competitive path lengths. The authors provide an open-source implementation and show city-scale applicability, highlighting potential extensions to dynamic cell management and more accurate zone classification for real-time unmanned aircraft traffic management in urban air mobility.

Abstract

In burgeoning domains such as urban goods distribution, the advent of aerial transportation necessitates the development of routing solutions that prioritize safe navigation. This paper introduces Larp, a novel path planning and navigation framework that leverages the concept of repulsive potential fields as continuous cost maps to forge safe routes. The algorithm achieves it by segmenting the potential field into a hierarchy of cells, each with a designated risk zone determined by the proximity of obstacles. The meshing allows the airspace to be partitioned based on an area's potential for restriction violations, enabling navigation that is aware of these risks. While the primary impetus behind Larp is to enhance the safety of aerial pathways for Unmanned Aerial Vehicles (UAVs) in urban air mobility, its utility extends to a wide array of routing scenarios. Comparative analyses with both established and contemporary potential field-based methods reveal Larp's proficiency in maintaining a safe distance from restrictions and its adeptness in circumventing local minima. Additionally, large-scale aerial path planning of Austin, TX demonstrates Larp's capability to be implemented at a large scale.

Figures (9)

• Figure 1: Illustration of the repulsion vectors with respect to a location.
• Figure 2: Stages of Larp for a walled room scene
• Figure 3: Quad tree for a simple potential field.
• Figure 4: Estimating the maximum potential of an given area in the potential field.
• Figure 5: Comparison of routes in Scenario 1, featuring an unobstructed path. The red marker indicates the initial location of the agent.

Theorems & Definitions (4)

• Definition 1: Squared Distance to a Potential Field Unit
• Definition 2: Scaled Squared Distance to a Potential Field Unit
• Definition 3: Potential of an Unit
• Definition 4: Route in a Potential Field