# Time-Optimal Planning for Quadrotor Waypoint Flight

arXiv: https://arxiv.org/abs/2108.04537 · HTML: https://mlsanity.com/paper/2108.04537/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 42 references that are in the map.
- First posted on arXiv 10 Aug 2021.

## Builds on (most cited first, 12 of 12)

- [AirSim: High-Fidelity Visual and Physical Simulation for Autonomous Vehicles](https://mlsanity.com/paper/1705.05065/) (2017)
- [Deep Drone Racing: From Simulation to Reality with Domain Randomization](https://mlsanity.com/paper/1905.09727/) (2019)
- [Robust and Efficient Quadrotor Trajectory Generation for Fast Autonomous Flight](https://mlsanity.com/paper/1907.01531/) (2019)
- [Differential Flatness of Quadrotor Dynamics Subject to Rotor Drag for Accurate Tracking of High-Speed Trajectories](https://mlsanity.com/paper/1712.02402/) (2017)
- [AlphaPilot: Autonomous Drone Racing](https://mlsanity.com/paper/2005.12813/) (2020)
- [PAMPC: Perception-Aware Model Predictive Control for Quadrotors](https://mlsanity.com/paper/1804.04811/) (2018)
- [AirSim Drone Racing Lab](https://mlsanity.com/paper/2003.05654/) (2020)
- [Search-based Motion Planning for Aggressive Flight in SE(3)](https://mlsanity.com/paper/1710.02748/) (2017)
- [Human-Piloted Drone Racing: Visual Processing and Control](https://mlsanity.com/paper/2103.04672/) (2021)
- [Minimum-time trajectory generation for quadrotors in constrained environments](https://mlsanity.com/paper/1706.06478/) (2017)
- [Multi-Fidelity Black-Box Optimization for Time-Optimal Quadrotor Maneuvers](https://mlsanity.com/paper/2006.02513/) (2020)
- [Trajectory Generation for Quadrotor Based Systems using Numerical Optimal Control](https://mlsanity.com/paper/1602.01949/) (2016)

## Built on by (most cited first, 23 of 23)

- [Reaching the Limit in Autonomous Racing: Optimal Control versus Reinforcement Learning](https://mlsanity.com/paper/2310.10943/) (2023)
- [Neural-Fly Enables Rapid Learning for Agile Flight in Strong Winds](https://mlsanity.com/paper/2205.06908/) (2022)
- [Multi-agent Embodied AI: Advances and Future Directions](https://mlsanity.com/paper/2505.05108/) (2025)
- [Machine Learning-Aided Operations and Communications of Unmanned Aerial Vehicles: A Contemporary Survey](https://mlsanity.com/paper/2211.04324/) (2022)
- [Learning Perception-Aware Agile Flight in Cluttered Environments](https://mlsanity.com/paper/2210.01841/) (2022)
- [Policy Search for Model Predictive Control with Application to Agile Drone Flight](https://mlsanity.com/paper/2112.03850/) (2021)
- [Learning Deep Sensorimotor Policies for Vision-based Autonomous Drone Racing](https://mlsanity.com/paper/2210.14985/) (2022)
- [Dream to Fly: Model-Based Reinforcement Learning for Vision-Based Drone Flight](https://mlsanity.com/paper/2501.14377/) (2025)
- [Visual Attention Prediction Improves Performance of Autonomous Drone Racing Agents](https://mlsanity.com/paper/2201.02569/) (2022)
- [Dashing for the Golden Snitch: Multi-Drone Time-Optimal Motion Planning with Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2409.16720/) (2024)
- [Multi-Fidelity Reinforcement Learning for Time-Optimal Quadrotor Re-planning](https://mlsanity.com/paper/2403.08152/) (2024)
- [Agile Flight Emerges from Multi-Agent Competitive Racing](https://mlsanity.com/paper/2512.11781/) (2025)
- [Mastering Diverse, Unknown, and Cluttered Tracks for Robust Vision-Based Drone Racing](https://mlsanity.com/paper/2512.09571/) (2025)
- [Time-optimal Flight in Cluttered Environments via Safe Reinforcement Learning](https://mlsanity.com/paper/2406.19646/) (2024)
- [Factored Diffusion Policies:Compositionally Generalized Robot Control with a Single Score Network](https://mlsanity.com/paper/2605.22596/) (2026)
- [Non-Equilibrium MAV-Capture-MAV via Time-Optimal Planning and Reinforcement Learning](https://mlsanity.com/paper/2503.06578/) (2025)
- [Motion Planning in Compressed Representation Spaces](https://mlsanity.com/paper/2606.30940/) (2026)
- [Dynamic Q-planning for Online UAV Path Planning in Unknown and Complex Environments](https://mlsanity.com/paper/2402.06297/) (2024)
- [Agile Robotics: Optimal Control, Reinforcement Learning, and Differentiable Simulation](https://mlsanity.com/paper/2407.01568/) (2024)
- [Drag-Aware Aerodynamic Manipulability for Torque-Limited Redundant Multirotors: Aerodynamic Promptness based on the Symmetric Acceleration Capacity](https://mlsanity.com/paper/2603.07998/) (2026)
- [MAVEN: A Meta-Reinforcement Learning Framework for Varying-Dynamics Expertise in Agile Quadrotor Maneuvers](https://mlsanity.com/paper/2603.10714/) (2026)
- [Bridging Performance and Generalization in Reinforcement Learning for Agile Flight](https://mlsanity.com/paper/2606.27348/) (2026)
- [Conditional Invertible Neural Networks for Data-Driven UAV Control: A 2-D Proof of Concept](https://mlsanity.com/paper/2607.13703/) (2026)

## Abstract (arXiv)

Quadrotors are among the most agile flying robots. However, planning time-optimal trajectories at the actuation limit through multiple waypoints remains an open problem. This is crucial for applications such as inspection, delivery, search and rescue, and drone racing. Early works used polynomial trajectory formulations, which do not exploit the full actuator potential because of their inherent smoothness. Recent works resorted to numerical optimization but require waypoints to be allocated as costs or constraints at specific discrete times. However, this time allocation is a priori unknown and renders previous works incapable of producing truly time-optimal trajectories. To generate truly time-optimal trajectories, we propose a solution to the time allocation problem while exploiting the full quadrotor's actuator potential. We achieve this by introducing a formulation of progress along the trajectory, which enables the simultaneous optimization of the time allocation and the trajectory itself. We compare our method against related approaches and validate it in real-world flights in one of the world's largest motion-capture systems, where we outperform human expert drone pilots in a drone-racing task.