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Onboard Wind-Preview Model Predictive Control Using Pitot-Static Sensing for Multirotor UAVs
Bas Meere, Eline Wisse, Laurens Vousten, Sander Doodeman, Elena Torta, Paula Chanfreut, Duarte Antunes
TL;DR
Reactive gust rejection waits until wind has begun to affect the drone, limiting compensation. This paper uses a boom-mounted pitot-static sensor to feed wind preview to onboard nonlinear MPC and studies the boom-length trade-off. Indoor and outdoor experiments report improved hover performance, including a 54 percent reduction in wind-direction error outdoors versus baseline.
Problem
Existing gust-rejection methods infer wind from drone motion or measure it at the airframe, so compensation begins only after the disturbance has started acting.
Source: §I · p. 1Method
A boom-mounted pitot-static sensor measures wind ahead of the drone, and onboard nonlinear MPC uses the preview to anticipate gust disturbances.
Source: §I · pp. 1–2Results
Indoor hover RMSE fell 66 percent versus PX4 and 60 percent versus wind-unaware MPC; outdoors, wind-direction RMSE fell 54 percent versus baseline.
Source: §VI · p. 8Takeaways & Limitations
A simple pitot sensor can provide preview at low added hardware cost and mass, leaving room for the mission payload.
Source: D. Discussion · p. 8
Abstract
from arXiv · showhide
Effective wind gust rejection and stable hovering are critical for the outdoor operation of autonomous drones. However, existing gust rejection methods are primarily reactive, inferring the disturbance from the resulting motion or measuring it at the airframe. Either way, the wind has already begun to act before it can be compensated. In this work, we anticipate the gust instead by measuring the wind ahead of the drone with a low-cost, low-weight pitot-static sensor mounted on a boom. The resulting wind preview is incorporated into a nonlinear model predictive controller (MPC), which optimizes the drone motion while anticipating wind disturbances. A longer boom offers more preview time but adds inertia and degrades flight performance. We characterize this trade-off in simulation and show that the optimal preview distance is not a fixed property of the platform, but shifts with the wind speed and with how quickly the drone can respond. Indoor hardware experiments confirm the trend and show that the proposed controller substantially improves hover performance against a PX4 baseline and an otherwise identical wind-unaware MPC. Outdoor experiments show that the error along the wind direction is reduced by 54 percent with respect to the baseline, demonstrating that a single wind-aligned sensor can significantly improve hovering performance.
I. INTRODUCTION
Wind gust rejection is often reactive, so compensation begins only after the disturbance has started acting on the drone. This work combines a boom-mounted pitot-static sensor with onboard MPC to anticipate gusts and examines how boom length affects the trade-off between preview and flight performance.
I. INTRODUCTION
- Reactive methods infer wind from drone motion or measure it at the airframe, so compensation starts after the disturbance has begun acting.That delay becomes more limiting for larger, slower platforms.Source: §I · p. 1
- A boom-mounted pitot-static sensor supplies onboard wind preview to nonlinear MPC, which incorporates incoming disturbances into its prediction horizon for preemptive action.The approach is presented as combining onboard wind preview sensing with MPC on a multirotor.Source: §I · pp. 1–2
- Longer booms provide more time to mitigate gusts, but added inertia degrades flight performance and farther-ahead wind can decorrelate from the flow reaching the drone.The work studies how this balance depends on wind conditions and drone maneuverability.Source: §I · p. 2
- Hover experiments in simulation and indoors and outdoors on hardware demonstrate the benefit of onboard wind preview and validate the boom-length trade-off analysis.Source: §I · p. 2
II. RELATED WORKS
The related work motivates a lightweight boom-mounted pitot tube for onboard preview, while the wind-sensing section describes its directional correction, filtering, and measurement performance.
II. RELATED WORKS
- Pitot tubes weigh roughly 5 g and update at several hundred hertz, making them lighter and faster than the lightest 2D ultrasonic units at 50 g or more and tens of hertz.The pitot’s inline form causes little flow interference, and the boom-axis wind component is especially relevant when previewing into the wind.Source: §II · p. 2
- Prior UAV wind-preview MPC used ground-based LiDAR or repeat-pass measurements; the authors identify no prior multirotor work combining onboard preview sensing with MPC and real-world deployment.Ground-based sensing also has limited spatial coverage and can face local obstructions.Source: §II · p. 2
III. WIND SENSING
- The single-hole pitot probe measures along-axis airspeed and is directionally sensitive; attitude-based inversion of Cp(α) corrects the estimate when drone tilt moves the boom off-axis.Cp remains essentially flat within a ±20° acceptance cone; the boom should face the main wind direction, with minimum offset needed to avoid rotor downwash.Source: §III · pp. 2–3
- A three-stage filter uses an exponential moving average, a short rolling maximum, and a sigmoid down-weighting below roughly 1 m/s to address vibration noise, off-axis turbulence dips, and low-pressure uncertainty.Source: §III · p. 3
- The filtered pitot estimate tracks a stationary ultrasonic reference while hovering with 0.72 m/s RMSE over the shown interval, capturing low-speed gust dynamics for control despite lower accuracy than typical LiDAR or ultrasonic sensing.The probe weighs only a few grams and requires no external infrastructure.Source: §III · p. 3, Figure 3 · p. 3
IV. WIND PREVIEW CONTROL
The section presents an MPC formulation that uses wind preview in its horizon to generate anticipatory actions, with the control architecture summarized in Fig. 4.
IV. WIND PREVIEW CONTROL
- The section formulates an MPC that uses preview information in its horizon to generate anticipatory actions.Source: §IV · p. 3
- The controller architecture is shown in Fig. 4.Source: §IV · p. 3
- Wind preview is used within the MPC horizon as part of the control formulation.Source: §IV · p. 3
A. System dynamics
The model expresses quadrotor position and velocity in an inertial frame and attitude and angular rate relative to a body-fixed frame. It uses a cascaded control structure and includes aerodynamic force to couple wind into translational motion.
A. System dynamics
- The state combines inertial-frame position, velocity, and Euler attitude, while the input combines total thrust and body rates.The model places the body-fixed frame at the center of mass.Source: A. System dynamics · p. 3
- The prediction model treats body-rate tracking as instantaneous and omits rotational dynamics, the inertia tensor, and motor mixing.The MPC commands thrust and body rates while the faster PX4 inner loop tracks the rates.Source: A. System dynamics · p. 4
- Aerodynamic force couples wind into the translational dynamics, and the previewed wind is reconstructed in the inertial frame by a vertical-axis rotation.The sensor aligns with the body x-axis, and the drone heading coincides with the wind direction.Source: A. System dynamics · p. 4
B. Controller design
The controller discretizes the quadrotor dynamics and solves a constrained finite-horizon optimal control problem at each step. It maps spatial wind preview into a temporal prediction and supplies wind values along the horizon from a timestamped sensor buffer.
B. Controller design
- The continuous-time dynamics are discretized using fourth-order Runge-Kutta at sampling time Ts.Source: B. Controller design · p. 4
- At each controller step, the optimization penalizes predicted state error, control effort, and terminal state error subject to dynamics and state and input bounds.The predicted states and inputs span a finite horizon and depend on the discretized dynamics and current state.Source: B. Controller design · p. 4
- The Taylor Frozen Turbulence Hypothesis maps boom distance to preview time by assuming turbulent wind progresses downstream at constant mean velocity.The crossing time τ is based on boom length D and safe wind speed.Source: B. Controller design · p. 4
- The controller recovers preview airspeed by interpolating timestamped pitot readings at each predicted arrival time shifted by τ.When the horizon exceeds available preview, it holds the last measured value constant; a moving-average wind speed and lower bound Vth keep τ finite near zero wind.Source: B. Controller design · p. 4
V. RESULTS
The results section evaluates wind-preview MPC in simulation, indoors against two baseline controllers, and outdoors in real wind.
V. RESULTS
- Simulation assesses boom-length effects across wind conditions and platform response speeds.Source: §V · p. 4
- Indoor experiments compare two baseline controllers and assess the boom-length trend over the safely flyable range.Source: §V · p. 4
- Outdoor experiments demonstrate performance in real wind.Source: §V · p. 4
A. Experimental setup
The experiments use a Holybro S500 quadrotor with onboard control and a boom-mounted digital airspeed sensor. Table I lists parameters common to simulation and hardware experiments.
A. Experimental setup
- The experimental platform is a Holybro S500 quadrotor with a Pixhawk 6C flight controller.Source: A. Experimental setup · p. 4
- A Mateksys digital airspeed sensor is mounted on a rigid, low-mass carbon boom, with GPS and motion capture providing outdoor and indoor position feedback, respectively.Source: A. Experimental setup · p. 4
- The onboard MPC runs at 30 Hz, with a 1-meter boom used unless otherwise stated; Table I lists parameters common to simulation and hardware.The MPC solve time is on the order of 10 ms on hardware.Source: A. Experimental setup · p. 5, Table I · p. 5
B. Simulation results
Simulation shows that boom-length benefits depend on wind conditions and drone response speed: more preview helps until inertia or limited useful preview constrains performance.
B. Simulation results
- Simulations used 70-second hovers at 2 m altitude, repeated ten times across 2, 4, 7, and 10 m/s wind conditions.The 7 m/s field shown is generated under IEC class A normal turbulence.Source: B. Simulation results · p. 5, Figure 5 · p. 5
- Short booms let the drone react late, while long booms add inertia and can produce oscillations; position-error standard deviation captures both effects.Source: B. Simulation results · p. 5, Figure 6 · p. 5
- At 2 m/s boom length has little effect, while at 10 m/s preview is too short to help and lengths beyond 1 m destabilize flight.Source: B. Simulation results · p. 5, Figure 7 · p. 6
- Slower response increases the value of preview; once required body rate falls below its limit, all tested rate limits converge to the same performance.The simulations artificially slowed the drone by tightening the MPC maximum-body-rate constraint at 4 m/s wind.Source: B. Simulation results · pp. 5–6, Figure 8 · p. 6
- At 4 and 7 m/s, position-error standard deviation reaches its sampled optimum at a 1.25 m boom as added inertia eventually outweighs preview.Boom lengths were tested on a 0.25 m grid, so 1.25 m is the best sampled length rather than a continuous minimum.Source: B. Simulation results · p. 5, Figure 7 · p. 6
C. Hardware experiments
Indoor hardware tests compare wind-aware MPC with PX4 and wind-unaware MPC, then assess boom lengths; outdoor tests evaluate a wind-aligned sensor in real wind.
C. Hardware experiments
- Indoor tests used a fan-generated gust, repeated each setting ten times, and compared PX4 position mode with otherwise identical MPC using zeroed versus live wind measurements.The fan was approximately 2.5 m from the hover position and operated at approximately 2 or 4 m/s.Source: C. Hardware experiments · p. 6
- Indoor boom-length tests found improved performance with length for 4 m/s gusts but no significant effect at 2 m/s; a 1.5 m boom was not considered safe to fly.At least 0.4 m of boom was needed to minimize propeller-downwash effects on sensor readings.Source: C. Hardware experiments · p. 6, Figure 11 · p. 7, Table II · p. 7
- 0.048 m RMSE with wind-aware MPC compares with 0.144 m for the PX4 baseline and 0.120 m for wind-unaware MPC, reductions of 66% and 60%.The wind-unaware MPC shares the same architecture and parameters, with its sensor measurement fixed to zero.Source: C. Hardware experiments · p. 6, Figure 10 · p. 7
- 54% lower x-direction RMSE was observed outdoors with wind-aware MPC, while y-direction error stayed similar to PX4.The mean wind was 4 m/s with gusts up to 7.5 m/s; the sensor was aligned with the prevailing wind direction.Source: Figure 12 · p. 7, C. Hardware experiments · p. 7
D. Discussion
Onboard wind-preview MPC reduces hover error across simulation and indoor and outdoor experiments. The best boom length balances additional preview against added inertia and depends on wind and platform responsiveness.
D. Discussion
- Wind-preview MPC substantially reduces hovering error in simulation and indoor and outdoor hardware experiments, while boom-length performance reflects competing preview and inertia effects.The optimum varies with wind speed and drone responsiveness; 1.25 m applies to the S500, while heavier or less agile platforms are expected to favor a longer boom.Source: D. Discussion · p. 7
- A single aligned boom assumes a stable dominant wind direction, limiting its fit for strongly obstructed environments with rapidly changing flow.Multiple booms, multiple sensors, or multi-hole probes could relax alignment requirements.Source: D. Discussion · p. 7
- Despite 0.72 m/s RMSE and unreliable readings below roughly 1 m/s, the controller improves hovering performance with the low-cost, 5 g probe.The authors report that preview is tolerant to measurement error, keeping added hardware cost and mass low enough to carry alongside mission payload.Source: D. Discussion · pp. 7–8
VI. CONCLUSION
The paper uses boom-mounted pitot-static wind preview with nonlinear MPC to improve hovering and characterizes the boom-length trade-off. Experiments report gains indoors and outdoors, while future work targets radiographic inspection.
VI. CONCLUSION
- Indoor hover RMSE fell 66 percent versus PX4 and 60 percent versus wind-unaware MPC; outdoors, wind-direction RMSE fell 54 percent versus baseline.Source: §VI · p. 8
- A longer boom provides more preview but adds inertia that degrades flight performance, and simulations show the optimum varies with wind conditions and drone responsiveness.Source: §VI · p. 8
- Future work will integrate the sensor on a radiographic inspection drone, using a gimbal to decouple the X-ray equipment from the airframe.The authors expect improved hover accuracy to translate into improved image quality while the equipment remains on target.Source: §VI · p. 8