💻 computer science

Nonlinear Model Predictive Control for Trajectory Tracking of Differentially Flat Fixed-Wing Aerial Systems

This paper proposes a unified framework that integrates differential flatness-based trajectory generation with Nonlinear Model Predictive Control (NMPC) and a novel wind-aware sampling strategy to achieve robust, constraint-aware trajectory tracking for fixed-wing UAVs under strong wind disturbances.

Original authors: Nishanth Bobbili, Pratyaksh Rao, Luca Morando, Luca Masci, Giuseppe Loianno

Published 2026-08-24

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Nishanth Bobbili, Pratyaksh Rao, Luca Morando, Luca Masci, Giuseppe Loianno

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Flying a fixed-wing aircraft is a delicate balancing act between speed, lift, and the invisible hand of the wind. Unlike helicopters or drones that can hover in place, these aircraft must keep moving forward to stay aloft, relying on air flowing over their wings to generate the lift that counteracts gravity. This requirement makes them incredibly efficient for long-distance travel, capable of covering vast distances with minimal energy, which is why they are the preferred choice for monitoring forests, surveying crops, or delivering supplies. However, this efficiency comes with a steep price in control. The physics governing a fixed-wing plane are complex and tightly interwoven; a change in speed affects the lift, which changes the turn radius, which in turn alters the speed. When you add the unpredictable push and pull of the wind, the task of guiding the aircraft along a precise path becomes a formidable challenge for computer algorithms.

For decades, engineers have managed this challenge by breaking the problem into smaller, simpler pieces. They would tell the aircraft to follow a simple geometric path, like a straight line or a circle, and use a standard control system to keep the plane on that line. While this approach works well in calm conditions, it struggles when the wind gets strong or when the aircraft needs to perform sharp, aggressive maneuvers. The old methods often react too slowly to sudden gusts and cannot predict how the wind will push the plane off course before it happens. They also lack the ability to explicitly respect the physical limits of the aircraft, such as the maximum angle at which the wings can tilt before the plane stalls and loses lift. To navigate the complex, real-world skies of the future, a smarter, more anticipatory approach is needed.

Researchers at the University of California, Berkeley, have developed a new control framework that allows fixed-wing drones to track complex trajectories with remarkable precision, even in strong winds. Their solution combines two powerful ideas: a method for planning smooth, physically possible paths and a predictive control system that constantly looks ahead to adjust for disturbances. The team created a system that does not just react to the wind but anticipates it. By using a mathematical property known as differential flatness, they can generate reference paths that are naturally consistent with the aircraft's physics, ensuring that the plane never attempts a turn that is too sharp or a speed that is too low. This planning step is then fed into a Nonlinear Model Predictive Control system, which acts like a highly skilled pilot who constantly simulates the next few seconds of flight in their mind. This system calculates the best possible control inputs—adjusting the throttle and the flaps on the wings—to keep the aircraft on track while strictly obeying all safety limits.

A key innovation in this work is a strategy that adapts how the aircraft samples its target path based on the wind. Imagine the aircraft is trying to follow a path marked by a series of points in space. If the wind is blowing from behind, the aircraft moves faster over the ground, so the system samples these points further apart to match the increased speed. If the wind is blowing against the aircraft, the system samples the points closer together to account for the slower ground speed. This simple but effective adjustment ensures that the aircraft always maintains a safe and steady speed relative to the air, which is critical for generating lift. Without this adjustment, the aircraft might try to follow the path too quickly in a tailwind or too slowly in a headwind, risking a loss of control or a stall.

The researchers tested their system through extensive computer simulations and real-world flight experiments using a custom-built fixed-wing drone equipped with an onboard computer. In the simulations, they subjected the aircraft to wind speeds ranging from gentle breezes to strong gusts of up to 10 meters per second. The results showed that the new system maintained a much tighter grip on the desired path compared to older methods. Specifically, when flying in winds of 10 meters per second, the system kept the aircraft's airspeed error to less than 1 meter per second on average, whereas the older approach without the wind-aware strategy allowed errors to grow significantly larger. More importantly, the new system kept the angle of attack—the angle at which the wing meets the air—well within safe limits, preventing the aircraft from coming dangerously close to stalling even in the most turbulent conditions.

In real-world flights conducted over a test area with wind speeds between 3 and 10 meters per second, the drone successfully tracked complex, three-dimensional paths, including spirals and ellipses. The aircraft was able to recover quickly from deviations caused by wind gusts, adjusting its throttle and control surfaces to stay on course. The system proved robust enough to handle not only natural wind variations but also intentionally injected errors in the reference path, such as sudden, physically impossible turns. Instead of crashing or failing, the controller recognized that the command was unfeasible and automatically adjusted the flight path to the closest possible safe trajectory that respected the laws of physics. This ability to gracefully handle impossible commands while staying safe is a significant step forward for autonomous flight.

The work demonstrates that by integrating advanced planning with predictive control, fixed-wing drones can operate with a level of agility and safety that was previously difficult to achieve. The researchers validated their approach using a high-fidelity model of the aircraft that included detailed aerodynamic forces and moments, ensuring that the computer's predictions matched the real-world behavior of the plane. While the current system relies on a pre-defined model of the aircraft's aerodynamics, the authors suggest that future work could incorporate data-driven learning to further refine these models and adapt to new aircraft designs more quickly. For now, the study confirms that a unified framework, which respects the full complexity of the aircraft's dynamics and the environment, can guide fixed-wing vehicles through the most challenging skies with confidence and precision.

Technical Summary: Nonlinear Model Predictive Control for Trajectory Tracking of Differentially Flat Fixed-Wing Aerial Systems

Problem Statement
Fixed-wing Unmanned Aerial Vehicles (FW-UAVs) offer superior endurance and efficiency compared to multirotors but present significant challenges for planning and control due to highly nonlinear, coupled dynamics, complex aerodynamics, and sensitivity to environmental disturbances like wind. Traditional flight control architectures typically decouple lateral and longitudinal dynamics, relying on geometric guidance laws (e.g., pure pursuit, L1 guidance) combined with cascaded PID controllers. While effective for simple paths, these methods introduce curvature discontinuities, lack predictive capabilities, and struggle to enforce aerodynamic and actuator constraints, particularly during aggressive maneuvers or in strong wind conditions. Although Nonlinear Model Predictive Control (NMPC) offers a principled approach to handle constraints and dynamics, its application to FW-UAVs has been limited by computational complexity and the difficulty of generating full-state, dynamically consistent trajectories.

Methodology
The authors propose a unified framework that integrates differential flatness-based trajectory generation with a full 6-DOF Nonlinear Model Predictive Control (NMPC) formulation.

System Modeling: The control framework utilizes a complete 6-DOF nonlinear rigid-body dynamics model. This model explicitly incorporates aerodynamic forces and moments (lift, drag, side force, and moments) as functions of angle of attack, sideslip, angular velocities, and control surface deflections. Wind effects are modeled as an external vector affecting the airspeed calculation.
Differential Flatness for Trajectory Generation: To address the computational burden of generating full-state trajectories, the authors leverage the differential flatness property of the fixed-wing system. The flat outputs are the position components in the inertial frame. Smooth reference trajectories are generated in this flat-output space using convex Quadratic Programming (QP) with Bernstein polynomials. These trajectories are then mapped back to the full state space via dynamic inversion to serve as references and warm starts for the NMPC.
Wind-Aware Sampling Strategy: A key innovation is a wind-aware sampling strategy embedded within the reference generation process. The reference ground-relative velocity is adjusted based on the estimated wind vector. Specifically, the wind vector is decomposed into parallel and perpendicular components relative to the reference trajectory direction. The parallel component is added to the reference velocity to determine a sampling velocity ( $V_{sampling}$ ). This ensures that the trajectory is sampled at intervals that guarantee a safe, positive airspeed under both headwind and tailwind conditions, preventing the generation of dynamically infeasible references.
NMPC Formulation: The trajectory tracking problem is formulated as a finite-horizon optimal control problem. The cost function minimizes deviations from the reference state and control inputs, subject to the discretized 6-DOF dynamics (solved via Runge-Kutta integration) and inequality constraints (actuator limits, flight envelope). The optimization is solved using the acados framework with the HPIPM interior-point method. The controller operates at approximately 100 Hz, solving the nonlinear program to convergence at each step.

Key Contributions

Unified NMPC Framework: Development of an NMPC controller for differentially flat fixed-wing systems that utilizes a full 6-DOF nonlinear model, explicitly accounting for aerodynamic forces, moments, and wind effects at the dynamics level.
Wind-Aware Reference Generation: Introduction of a sampling strategy that adapts trajectory sampling velocity based on wind conditions to ensure the generation of dynamically feasible reference trajectories that maintain safe cruising airspeeds.
Experimental Validation: Comprehensive validation through Software-in-the-Loop (SITL) simulations and real-world flight experiments, demonstrating the framework's ability to track complex trajectories under strong wind disturbances.

Results
The proposed framework was evaluated in both simulation (using PX4 and Gazebo) and real-world flight tests with a custom Strix Stratosurfer UAV.

Wind Robustness: In simulations with wind speeds up to 10 m/s, the NMPC with the wind-aware sampling strategy significantly outperformed a baseline NMPC without this strategy. The proposed method maintained mean airspeed errors around 0.3–0.9 m/s, whereas the baseline exhibited errors up to 5.4 m/s.
Safety and Feasibility: The wind-aware strategy prevented the aircraft from entering unsafe operating regimes (e.g., stall conditions) by keeping the Angle of Attack (AoA) within safe bounds. Without the strategy, the baseline controller allowed AoA deviations that brought the aircraft close to stall, particularly in high wind conditions.
Handling Infeasible References: The system demonstrated robustness when presented with physically infeasible reference trajectories (e.g., discontinuities violating curvature constraints). The NMPC naturally projected these references into the space of physically realizable solutions, adhering to dynamic constraints rather than attempting to follow impossible commands.
Real-World Performance: Flight experiments in wind conditions ranging from 3 to 10 m/s showed bounded position errors (RMSE within 3–5 m) and effective throttle regulation to compensate for wind disturbances, maintaining stable airspeed tracking.

Significance and Claims
The paper claims that the proposed framework successfully bridges the gap between computationally efficient trajectory generation (via differential flatness) and high-fidelity, constraint-aware control (via NMPC). By integrating a wind-aware sampling strategy, the authors demonstrate that it is possible to generate dynamically consistent references that proactively account for environmental disturbances. The work highlights that this approach improves tracking accuracy and robustness for complex trajectories, particularly under strong wind conditions where traditional PID-based or geometric guidance methods often degrade. The authors position this as a step toward reliable, safe, and computationally efficient control for fixed-wing UAVs operating in challenging environments, while noting that future work will explore neural dynamics models and data-driven system identification to further enhance accuracy and adaptability.

Technical Summary: Nonlinear Model Predictive Control for Trajectory Tracking of Differentially Flat Fixed-Wing Aerial Systems

More like this