# Rapid Collision Detection for Multicopter Trajectories

## TL;DR

This paper introduces a fast continuous-time collision detection algorithm for polynomial multicopter trajectories interacting with convex obstacles, enabling rapid obstacle-aware motion planning in complex environments.

## Contribution

The paper presents a novel collision detection algorithm that efficiently integrates with trajectory generation for multicopters, handling static and dynamic convex obstacles in real-time.

## Key findings

- Algorithm detects collisions in milliseconds
- Benchmarked with Monte Carlo simulations showing high efficiency
- Experimental validation in real-world environments

## Abstract

We present a continuous-time collision detection algorithm for quickly detecting whether certain polynomial trajectories in time intersect with convex obstacles. The algorithm is used in conjunction with an existing multicopter trajectory generation method to achieve rapid, obstacle-aware motion planning in environments with both static convex obstacles and dynamic convex obstacles whose boundaries do not rotate. In general, this problem is difficult because the presence of convex obstacles makes the feasible space of trajectories nonconvex. The performance of the algorithm is benchmarked using Monte Carlo simulations, and experimental results are presented that demonstrate the use of the method to plan collision-free multicopter trajectories in milliseconds in environments with both static and dynamic obstacles.