# Fast Time-optimal Avoidance of Moving Obstacles for High-Speed MAV Flight

## TL;DR

This paper introduces a fast, efficient method for computing smooth, time-optimal trajectories for high-speed MAVs to avoid moving obstacles, enabling real-time obstacle evasion during rapid flight.

## Contribution

The paper presents a novel approach that quickly computes dynamically feasible, collision-free, time-optimal trajectories with online re-planning capabilities for MAV obstacle avoidance.

## Key findings

- Computational demands are minimal, enabling obstacle avoidance within milliseconds.
- The method maintains time-optimality even with obstacle circumvention.
- It supports frequent online re-planning from various initial conditions.

## Abstract

In this work, we propose a method to efficiently compute smooth, time-optimal trajectories for micro aerial vehicles (MAVs) evading a moving obstacle. Our approach first computes an n-dimensional trajectory from the start- to an arbitrary target state including position, velocity and acceleration. It respects input- and state-constraints and is thus dynamically feasible. The trajectory is then efficiently checked for collisions, exploiting the piecewise polynomial formulation. If collisions occur, viastates are inserted into the trajectory to circumvent the obstacle and still maintain time-optimality. These viastates are described by position, velocity, and acceleration. The evaluation shows that the computational demands of the proposed method are minimal such that obstacle avoidance can begin within few milliseconds. Optimality of generated trajectories, combined with the ability for frequent online re-planning from non-hover initial conditions, make the approach well suited for evasion of suddenly perceived obstacles during fast flight.