Flying through Moving Gates without Full State Estimation

TL;DR

The paper tackles autonomous drone racing through moving gates without a map or full state estimation. It develops a proportional navigation (PN) based vision-based controller that uses monocular line-of-sight to gates and IMU data, supported by a PN frame and a closed-form, constrained optimization for thrust and attitude, yielding a practical solution even when relative velocity is unknown. A Bayesian optimization pipeline tunes the PN constant $k_\text{PN}$ and field-of-view bound $\bar{\gamma}$, guided by rewards that balance time-to-gate and gate-centering accuracy, and the approach is validated across planar and knot gate motions in both simulation and real-world hardware. The results demonstrate robust, high-speed interception of moving gates with only LOS and IMU measurements, enabling agile flight in dynamic, uncharted environments without relying on maps or full state estimation.

Abstract

Autonomous drone racing requires powerful perception, planning, and control and has become a benchmark and test field for autonomous, agile flight. Existing work usually assumes static race tracks with known maps, which enables offline planning of time-optimal trajectories, performing localization to the gates to reduce the drift in visual-inertial odometry (VIO) for state estimation or training learning-based methods for the particular race track and operating environment. In contrast, many real-world tasks like disaster response or delivery need to be performed in unknown and dynamic environments. To make drone racing more robust against unseen environments and moving gates, we propose a control algorithm that operates without a race track map or VIO, relying solely on monocular measurements of the line of sight to the gates. For this purpose, we adopt the law of proportional navigation (PN) to accurately fly through the gates despite gate motions or wind. We formulate the PN-informed vision-based control problem for drone racing as a constrained optimization problem and derive a closed-form optimal solution. Through simulations and real-world experiments, we demonstrate that our algorithm can navigate through moving gates at high speeds while being robust to different gate movements, model errors, wind, and delays.

Figures (6)

• Figure 1: Quadrotor (colored) and gate (black) trajectories and the acceleration commanded by our control algorithm (green) for flying through a fast-moving gate ($7\,m/s$ top speed) solely based on line-of-sight (LOS) estimates. It can be seen that the normal acceleration, which is proportional to the LOS rate, increases as the quadrotor gets closer to the gate.
• Figure 2: Kinematics in the derivation of the PN law.
• Figure 3: Proposed control approach for flying through moving gates solely based on measuring the line-of-sight (LOS) angle $\gamma$ between the optical axis of the camera $\bm{o}_\text{cam}$ and the LOS $\bm{l}$. To ensure that the gate is not missed, we command a PN-informed acceleration $\bm{a}_n$ in the direction $\bm{n}$ normal to $\bm{l}$ and the LOS rotation axis $\bm{k_l}$ via \ref{['eq:meth_pn_guidance_law']}. Moreover, we maximize the acceleration towards the gate, i.e., in the direction $\bm{l}$, while enforcing an upper bound on $\gamma$ to ensure that the gate always stays within the field of view.
• Figure 4: Planar (2D) and knot (3D) gate motions used in our experiments.
• Figure 5: Impact of delays in the vision-based LOS estimation (e.g., due to camera latencies, inference times) on the success rate of passing the gates.