# RCS: a fast path planning algorithm for Unmanned Aerial Vehicles

## TL;DR

This paper introduces a fast path planning algorithm for UAVs in polygonal environments, considering UAV motion constraints, which efficiently finds near-optimal collision-free paths with preprocessing for rapid queries.

## Contribution

The paper presents a novel $O(n^2 \, \log n)$ algorithm for UAV path planning that incorporates turning and route length constraints, with a preprocessing method for quick path queries.

## Key findings

- Algorithm runs in $O(n^2 \log n)$ time.
- Preprocessing enables $O(n \log n)$ query time for path planning.
- Produces paths close to the shortest feasible paths under constraints.

## Abstract

Path planning is a major problem in autonomous vehicles. In recent years, with the increase in applications of Unmanned Aerial Vehicles (UAVs), one of the main challenges is path planning, particularly in adversarial environments. In this paper, we consider the problem of planning a collision-free path for a UAV in a polygonal domain from a source point to a target point. Based on the characteristics of UAVs, we assume two basic limitations on the generated paths: an upper bound on the turning angle at each turning point (maximum turning angle) and a lower bound on the distance between two consecutive turns (minimum route leg length). We describe an algorithm that runs in $O(n^2 \log n)$ time and finds a feasible path in accordance with the above limitations, where $n$ is the number of obstacle vertices. As shown by experiments, the output of the algorithm is much close to the shortest path with this requirements. We further demonstrate how to decompose the algorithm into two phases, a preprocessing and a query phase. In this way, given a fixed start point and a set of obstacles, we can preprocess a data structure of size $O(n^2)$ in $O(n^2 \log n)$ time, such that for any query target point we can find a path with the given requirements in $O(n \log n)$ time. Finally, we modify the algorithm to find a feasible (almost shortest) path that reach the target point within a given range of directions.