Time-Optimal Planning for Long-Range Quadrotor Flights: An Automatic Optimal Synthesis Approach

TL;DR

This paper introduces an automatic optimal synthesis method for long-range quadrotor flights that achieves near-optimal timing with low computational cost, enabling efficient planning for large operation areas.

Contribution

The paper presents a polynomial-based approach that efficiently generates time-optimal trajectories for long-range quadrotor flights, reducing computational complexity compared to existing methods.

Findings

Faster than state-of-the-art by orders of magnitude

Achieves aggressive time-optimal maneuvers with peak velocity of 8.86 m/s

Maintains low computational cost across different flight ranges

Abstract

Time-critical tasks such as drone racing typically cover large operation areas. However, it is difficult and computationally intensive for current time-optimal motion planners to accommodate long flight distances since a large yet unknown number of knot points is required to represent the trajectory. We present a polynomial-based automatic optimal synthesis (AOS) approach that can address this challenge. Our method not only achieves superior time optimality but also maintains a consistently low computational cost across different ranges while considering the full quadrotor dynamics. First, we analyze the properties of time-optimal quadrotor maneuvers to determine the minimal number of polynomial pieces required to capture the dominant structure of time-optimal trajectories. This enables us to represent substantially long minimum-time trajectories with a minimal set of variables. Then, a robust optimization scheme is developed to handle arbitrary start and end conditions as well as intermediate waypoints. Extensive comparisons show that our approach is faster than the state-of-the-art approach by orders of magnitude with comparable time optimality. Real-world experiments further validate the quality of the resulting trajectories, demonstrating aggressive time-optimal maneuvers with a peak velocity of 8.86 m/s.