Gate-Aware Online Planning for Two-Player Autonomous Drone Racing

TL;DR

PMPC addresses time-critical, collision-free racing of two autonomous drones through gates with varying orientations. It blends a time-optimal point-mass reference with yaw optimization and a MIL-based spatial curve to enforce vertical gate passage, then refines these references with a full 3D quadrotor MPC solved online at about $200$ Hz. Key contributions include a two-step velocity search for time-optimal references, the MIL-based gate traversal curve, and a high-frequency onboard solver validated in both simulation and real flights achieving a top speed of $6.1$ m/s on a $7$-gate track in a $5\times4\times2$ m arena. The results demonstrate real-time, collision-free operation and pave the way for scaling to larger swarms and dynamic MIL generation for changing gates.

Abstract

The flying speed of autonomous quadrotors has increased significantly over the past 5 years, particularly in the field of autonomous drone racing. However, most research primarily focuses on the aggressive flight of a single quadrotor, simplifying the racing gate traversal problem to a waypoint passing problem that neglects the orientations of the racing gates. In this paper, we propose a systematic method called Pairwise Model Predictive Control (PMPC) that can guide two quadrotors online to navigate racing gates with minimal time and without collisions. The flight task is initially simplified as a point-mass model waypoint passing problem to provide analytical time optimal reference through an efficient two-step velocity search method. Subsequently, we utilize the spatial configuration of the racing track to compute the optimal heading at each gate, maximizing the visibility of subsequent gates for the quadrotors. To address varying gate orientations, we introduce a novel Magnetic Induction Line-based spatial curve to guide the quadrotors through racing gates of different orientations. Furthermore, we formulate a nonlinear optimization problem that uses the point-mass trajectory as initial values and references to enhance solving efficiency, enabling the method to run onboard at a frequency of 200 Hz. The feasibility of the proposed method is validated through both simulation and real-world experiments. In real-world tests, the two quadrotors achieved a top speed of 6.1 m/s on a 7-waypoint racing track within a compact flying arena of 5 m * 4 m * 2 m.

Figures (8)

• Figure 1: Two quadrotors race in an $8$-shape track with two different gate orientations and achieve a top speed of $6.1m/s$.
• Figure 2: The pipeline of the proposed method. Step 1: A point-mass model is used to generate the global time-optimal trajectory which is used as initial values for the optimization. Step 2: An optimization problem is established to guide two quadrotors to fly through the waypoints without collision.
• Figure 3: Step 1: sample velocities in the direction of $\mathbf{v}_i$ but in different magnitudes. Find the best velocities $v_i^{\rm min}$. Step 2: resample the velocities around $v_i^{\rm min}$ in different directions. Find the optimal velocity $v_i^{*}$.
• Figure 4: We use the magnet model to find the optimal MIL (solid curve) which (a) connects two magnets/gates, (b) is perpendicular to the magnets/gates at both ends (c) is the closest MIL to the point-mass reference trajectory (dashed curve) among the infinite MILs.
• Figure 5: The MIL is used as a spatial reference to attract the quadrotor fly near the center and perpendicular to the gate.