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Real-time Planning of Minimum-time Trajectories for Agile UAV Flight

Krystof Teissing, Matej Novosad, Robert Penicka, Martin Saska

TL;DR

This work tackles real-time planning of minimum-time UAV trajectories across multiple waypoints by employing a point-mass model with Limited Thrust Decomposition (LTD) to fully utilize collective thrust. It integrates gravity and drag into the planning process and uses a gradient-based optimization to determine waypoint velocities, achieving millisecond-scale computation suitable for onboard NMPC. Key contributions include closed-form solutions for time-optimal PMM segments, axis synchronization, an iterative LTD algorithm, and a gradient-based multi-waypoint velocity optimization, all validated in both simulation and real-world flights with accelerations up to $3.5g$ and speeds over $100\,\text{km/h}$. The approach yields trajectories with comparable or better tracking errors than full-dynamics time-optimal plans, while significantly reducing planning time, and is released as open-source for community use.

Abstract

We address the challenge of real-time planning of minimum-time trajectories over multiple waypoints, onboard multirotor UAVs. Previous works demonstrated that achieving a truly time-optimal trajectory is computationally too demanding to enable frequent replanning during agile flight, especially on less powerful flight computers. Our approach overcomes this stumbling block by utilizing a point-mass model with a novel iterative thrust decomposition algorithm, enabling the UAV to use all of its collective thrust, something previous point-mass approaches could not achieve. The approach enables gravity and drag modeling integration, significantly reducing tracking errors in high-speed trajectories, which is proven through an ablation study. When combined with a new multi-waypoint optimization algorithm, which uses a gradient-based method to converge to optimal velocities in waypoints, the proposed method generates minimum-time multi-waypoint trajectories within milliseconds. The proposed approach, which we provide as open-source package, is validated both in simulation and in real-world, using Nonlinear Model Predictive Control. With accelerations of up to 3.5g and speeds over 100 km/h, trajectories generated by the proposed method yield similar or even smaller tracking errors than the trajectories generated for a full multirotor model.

Real-time Planning of Minimum-time Trajectories for Agile UAV Flight

TL;DR

This work tackles real-time planning of minimum-time UAV trajectories across multiple waypoints by employing a point-mass model with Limited Thrust Decomposition (LTD) to fully utilize collective thrust. It integrates gravity and drag into the planning process and uses a gradient-based optimization to determine waypoint velocities, achieving millisecond-scale computation suitable for onboard NMPC. Key contributions include closed-form solutions for time-optimal PMM segments, axis synchronization, an iterative LTD algorithm, and a gradient-based multi-waypoint velocity optimization, all validated in both simulation and real-world flights with accelerations up to and speeds over . The approach yields trajectories with comparable or better tracking errors than full-dynamics time-optimal plans, while significantly reducing planning time, and is released as open-source for community use.

Abstract

We address the challenge of real-time planning of minimum-time trajectories over multiple waypoints, onboard multirotor UAVs. Previous works demonstrated that achieving a truly time-optimal trajectory is computationally too demanding to enable frequent replanning during agile flight, especially on less powerful flight computers. Our approach overcomes this stumbling block by utilizing a point-mass model with a novel iterative thrust decomposition algorithm, enabling the UAV to use all of its collective thrust, something previous point-mass approaches could not achieve. The approach enables gravity and drag modeling integration, significantly reducing tracking errors in high-speed trajectories, which is proven through an ablation study. When combined with a new multi-waypoint optimization algorithm, which uses a gradient-based method to converge to optimal velocities in waypoints, the proposed method generates minimum-time multi-waypoint trajectories within milliseconds. The proposed approach, which we provide as open-source package, is validated both in simulation and in real-world, using Nonlinear Model Predictive Control. With accelerations of up to 3.5g and speeds over 100 km/h, trajectories generated by the proposed method yield similar or even smaller tracking errors than the trajectories generated for a full multirotor model.
Paper Structure (14 sections, 22 equations, 4 figures, 3 tables, 2 algorithms)

This paper contains 14 sections, 22 equations, 4 figures, 3 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Methodology
  4. Time-Optimal Point-Mass Model Trajectory Planning
  5. Trajectory Axis Synchronization
  6. Limited Thrust Decomposition (LTD)
  7. Velocity Optimization
  8. Results
  9. Trajectory planning evaluation
  10. Single-segment trajectory
  11. Multi-waypoint trajectory
  12. Ablation study
  13. Real-world evaluation
  14. Conclusions

Figures (4)

  • Figure 1: Long exposure shot of real-world flight (left) and used UAV together with the visualization of trajectory optimization process (right).
  • Figure 2: PMM trajectory generation scheme (a) and the visualization of a two-segment single-axis trajectory velocity profile (b).
  • Figure 3: Improvement of LTD compared to PMM$_{equal}$ and TOP-UAV$^{\text{++}}$.
  • Figure 4: Tested maps defined by their respective start (green point), end (red point), and via (purple crosses) waypoints. The computed trajectory (multi-color line) and the recorded UAV positions from the real-world flight (red dashed line) tracking the trajectories are displayed.