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

Nishanth Bobbili, Pratyaksh Rao, Luca Morando, Luca Masci, Giuseppe Loianno

arXiv:2608.20655v1cs.RO

TL;DR

Fixed-wing UAV trajectory tracking is difficult under nonlinear aerodynamics and uncertain wind. The paper combines differential-flatness trajectory generation with constraint-aware NMPC and wind-aware sampling, achieving robust tracking in simulations and real-world experiments, including strong-wind conditions.

  • Problem

    Fixed-wing UAVs require reliable, safe, and computationally efficient planning and control despite nonlinear coupled dynamics, aerodynamic complexity, and uncertain time-varying winds.

  • Method

    The framework combines differential-flatness trajectory generation with full-model NMPC and wind-aware sampling that adapts reference velocities to maintain safe cruising airspeed.

  • Results

    The proposed formulation achieves robust trajectory tracking in simulations, PX4 SITL, and real-world flight experiments, including under strong wind disturbances.

  • Takeaways & Limitations

    Wind-aware sampling helps maintain safer, more consistent airspeeds and reduces stall-risking behavior under wind disturbances.

Abstract

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Planning and control of fixed-wing Unmanned Aerial Vehicles (UAVs) are challenging due to nonlinear dynamics, aerodynamic limits, and environmental disturbances. Differential flatness offers a principled way to generate fast, feasible trajectories, but its use has largely been confined to model-free controllers, which lack predictive capabilities and demand tuning. In this paper, we propose a unified framework that integrates differential flatness-based trajectory generation with Nonlinear Model Predictive Control (NMPC), combining computationally efficient planning with predictive, constraint-aware control. To further improve robustness, we introduce a wind-aware sampling strategy embedded within the NMPC framework, enabling the generation of dynamically feasible reference trajectories that proactively account for wind disturbances while strictly enforcing aerodynamic and control input constraints. We validate the proposed framework through extensive simulations and real-world flight experiments, demonstrating improved tracking accuracy and robustness for complex trajectories, particularly when using the proposed wind-aware sampling strategy under strong wind conditions.

SUPPLEMENTARY MATERIAL · I. INTRODUCTION

Fixed-wing UAV planning and control is difficult because strongly coupled nonlinear aerodynamics and uncertain, time-varying wind disturbances challenge safe, efficient trajectory tracking. The paper addresses these issues with a full-model NMPC framework and wind-aware reference generation, validated in simulation and real-world flight experiments.

  • I. INTRODUCTION: Fixed-wing UAVs are widely used because their superior endurance, extended operational range, and high cruise efficiency support many missions.Applications include environmental monitoring, disaster response, agriculture, and logistics,, while fixed-wing platforms are preferred for these mission characteristics.
  • I. INTRODUCTION: Planning and control are challenging because fixed-wing dynamics are highly nonlinear and coupled, aerodynamic effects are difficult to model, and wind disturbances are uncertain and time-varying.Together, these factors create a need for reliable, safe, and computationally efficient methods.
  • I. INTRODUCTION: Traditional architectures use geometric guidance, total-energy control, and cascaded PID stabilization to follow simple reference paths.Typical paths consist of sequential straight-line segments and circular arcs.
  • I. INTRODUCTION: These conventional methods create curvature discontinuities, restrict maneuver flexibility, lack predictive capability, and degrade under aggressive flight or near aerodynamic and actuation limits.PID implementations are also difficult to tune in highly dynamic regimes.
  • I. INTRODUCTION: NMPC is motivated by its ability to optimize tracking over a receding horizon while explicitly enforcing dynamic feasibility and input constraints.Its adoption for fixed-wing UAVs has been comparatively recent because of nonlinear aerodynamic modeling complexity, wind sensitivity, and state-estimation uncertainty.
  • I. INTRODUCTION: The proposed framework develops NMPC for differentially flat fixed-wing aerial systems using a full 6-DOF nonlinear model with aerodynamic forces, moments, and wind effects.This formulation explicitly incorporates the aircraft’s nonlinear dynamics and environmental disturbances at the dynamics level.
  • I. INTRODUCTION: Wind-aware reference generation adapts trajectory sampling velocity to guarantee safe cruising airspeed under external disturbances.The strategy embeds wind effects into reference generation rather than treating them only as a downstream tracking disturbance.
  • I. INTRODUCTION: Simulation and real-world flight experiments show improved tracking accuracy and robustness for complex trajectories, especially with wind-aware sampling under strong winds.The validation covers both simulated and physical flight conditions.

II. RELATED WORKS

FW-UAV navigation has commonly used lightweight guidance and cascaded PID controllers, while NMPC offers constraint-aware dynamic control. Differential-flatness trajectory generation provides efficient, dynamically consistent references, but its integration with fully coupled 6-DOF NMPC and wind-aware reference generation is presented as an unaddressed direction.

  • Guidance and PID-Based Control: FW-UAV navigation has largely relied on guidance controllers with cascaded PID loops, including pure pursuit, L1 guidance, and Lyapunov-based nonlinear controllers,.These approaches are described as lightweight, formally stable, and easy to deploy.
  • Nonlinear Model Predictive Control: NMPC has gained traction in aerial robotics because it incorporates actuator and sensor constraints while accounting for system dynamics, including FW-UAV attitude regulation, and actuator control.The supplied passage also notes data-driven and adaptive NMPC formulations, for multirotor platforms.
  • Differential-Flatness-Based Trajectory Generation: Differential-flatness trajectory generation, provides computationally efficient, dynamically consistent references, but its integration with fully coupled 6-DOF NMPC had not been explicitly addressed.The paper positions its framework as unifying flatness-based trajectory generation with fully coupled NMPC.
  • Wind-Aware Reference Generation: Wind-aware disturbance handling during reference generation is used to enhance robustness under strong wind conditions.This mechanism is part of the proposed trajectory-generation direction.

III. METHODOLOGY · A. Preliminaries

The methodology introduces an NMPC formulation that proceeds from notation and system modeling to optimization, trajectory generation, and wind sampling. Its preliminaries define the coordinate frames, air-relative velocity, airspeed, and angle of attack used to model the fixed-wing UAV.

  • III. METHODOLOGY: The NMPC formulation covers notation, system modeling, optimization, trajectory generation, and incorporation of wind sampling.The overall formulation is depicted in Fig. 2.
  • A. Preliminaries: The notation distinguishes bold lowercase vectors, non-bold scalar components with subscripts, bold uppercase matrices, and frame-specific superscripts.Examples include a, a_x, a_y, a_z, A, and frame-dependent vectors such as a^K and a^L.
  • A. Preliminaries: The system model uses an Earth-fixed North–East–Down inertial frame {I} centered at the home location and a body frame {B} attached to the UAV.These coordinate frames are illustrated in Fig. 3.
  • A. Preliminaries: Lift generation requires the airfoil to maintain a positive angle relative to the air-relative velocity vector.This orientation requirement connects the vehicle attitude to the aerodynamic relative velocity.
  • A. Preliminaries: The UAV’s relative velocity vector v_a describes its linear velocity with respect to the surrounding air mass.Its magnitude is the airspeed V_a.
  • A. Preliminaries: The angle of attack α is defined by a right-handed rotation about y_B that aligns the projected relative velocity with x_B.The rotation is applied in the x_B–z_B plane.

B. System Modeling

The system model represents fixed-wing motion through ground-relative velocity, wind-dependent airspeed, and body-to-inertial attitude, coupled with rigid-body force and moment dynamics. Aerodynamic forces and moments depend nonlinearly on flight state and control-surface inputs, while throttle scales available thrust.

  • B. System Modeling: Ground-relative velocity defines groundspeed, while the wind vector determines the corresponding airspeed used by the model.
  • B. System Modeling: The attitude R ∈ SO(3) maps body-frame quantities to the inertial frame, enabling velocity transformation and rigid-body motion modeling.
  • B. System Modeling: Rigid-body dynamics balance mass, gravity, angular velocity, inertia, aerodynamic forces, and aerodynamic moments expressed about the body axes.
  • B. System Modeling: Aerodynamic coefficients vary nonlinearly with angle of attack, sideslip, body angular velocity, and control-surface deflections, while throttle δt ∈ [0, 1] scales maximum thrust.

C. Finite-Horizon Optimal Control Problem

The paper formulates trajectory tracking as a finite-horizon optimal control problem using an RK4-discretized UAV model and direct multiple shooting. The formulation optimizes reference tracking while enforcing dynamics, actuator, and flight-envelope constraints, with reference velocity adjusted for wind.

  • Trajectory tracking is posed as a finite-horizon optimal control problem using fourth-order Runge–Kutta discretization with step size ∆t.
  • The finite-horizon problem uses direct multiple shooting with discrete dynamics xk+1 = ¯f(xk, uk) over prediction horizon N.
  • The objective penalizes state deviations along the horizon and at the terminal step, together with control-input deviations from the nominal reference.
  • State and input inequality constraints enforce limits such as actuator bounds and the aircraft flight envelope.
  • The reference velocity is adjusted according to wind to enforce a user-defined nominal cruise airspeed that preserves sufficient control authority.

D. Trajectory Generation and Wind-aware Sampling

The framework generates reference trajectories through differential-flatness-based planning parameterized by path length, then adapts horizon sampling to wind by decomposing wind relative to the reference direction. It assumes constant wind over the fast prediction horizon and bounds wind magnitude to preserve positive groundspeed.

  • Trajectory generation: Reference trajectories are generated with a differential-flatness-based planner parameterized by path length, exploiting a feedback-linearizable coordinated-flight model for the fixed-wing platform.Differential flatness expresses states and controls through flat outputs and finitely many derivatives.
  • Wind-aware sampling: Wind-aware sampling decomposes wind into parallel and perpendicular components relative to the reference-velocity direction, adding the parallel component to obtain the horizon’s progress velocity.The adjusted progress velocity is used to sample the reference horizon.
  • Wind-aware sampling: The wind vector is treated as constant over the prediction horizon because the optimizer runs at 100 Hz, substantially faster than typical wind variations.The assumption is motivated by wind changes occurring over several seconds or more, particularly at low altitudes.
  • Wind-aware sampling: Wind magnitude is constrained below the reference velocity to maintain positive groundspeed, lengthening velocity in tailwinds and shortening it in headwinds before distance-based sampling.Discrete samples use path increments defined by ∆d = V_sampling ∆t.

IV. EXPERIMENTAL SETUP

The real-world NMPC implementation runs onboard a custom Strix Stratosurfer UAV using an NVIDIA Orin NX, ROS1, and an STM32H757-based flight controller. The system uses acados-generated code with a 10-step, 2-second horizon and sends optimized collective-thrust and angular-rate setpoints to PX4 for low-level stabilization.

  • IV. EXPERIMENTAL SETUP: The experiments use a custom Strix Stratosurfer UAV equipped with an NVIDIA Orin NX running Ubuntu 22.04 and ROS1, connected via UART to an STM32H757-based flight controller.The flight controller also provides airspeed and inertial-frame horizontal wind-velocity estimates.
  • IV. EXPERIMENTAL SETUP: acados generates efficient C code for onboard real-time implementation using N = 10 shooting steps over a 2-second system horizon.Dynamically feasible full-state references improve optimizer convergence and solution quality, while the nonlinear program is solved to convergence at each control step instead of using SQP-RTI.
  • IV. EXPERIMENTAL SETUP: The NMPC optimization produces collective-thrust and angular-rate setpoints, while PX4 performs inner-loop attitude and thrust regulation through onboard PID stabilization.This interface reflects practical limitations of low-level flight controllers that restrict direct actuator-deflection control.

V. RESULTS

The results evaluate the feasibility of trajectory tracking for fixed-wing UAVs through software-in-the-loop simulations and real-world flight experiments.

  • The study evaluates the feasibility of solving the trajectory-tracking problem for fixed-wing UAVs.
  • The first evaluation scenario uses software-in-the-loop simulations with PX4 and Gazebo as the physics engine.
  • The second evaluation scenario consists of real-world flight experiments.

A. Robustness to Wind in SITL Simulation

In SITL simulations, wind-aware sampling improves NMPC trajectory tracking and airspeed safety under wind, while the controller also handles physically infeasible references by predicting feasible trajectories.

  • Spiral trajectory tracking: Despite coordinated roll, pitch, and velocity changes in a spiral maneuver, wind-aware NMPC keeps the predicted state close to the reference trajectory.The result demonstrates trajectory fidelity for a complex maneuver under wind.
  • Wind-aware sampling comparison: Wind-aware sampling substantially improves NMPC airspeed tracking and reduces unsafe operating behavior compared with NMPC without sampling under identical wind conditions.The proposed method achieves approximately 1 m/s average airspeed error, while the baseline permits larger angle-of-attack deviations and can drive the aircraft into unsafe airspeeds.
  • Recovery from infeasible references: When discontinuities make a prescribed reference physically infeasible, the controller is tested for its ability to predict feasible trajectories despite curvature and actuator constraints.The failure-mode test injects discontinuities into selected motion regions to violate fixed-wing vehicle constraints.

B. Real-world Validation

Real-world flight experiments evaluated NMPC robustness over a 0.15 km2 test area in winds from 3 to 10 ms−1. The controller tracked an elliptical trajectory while regulating airspeed and throttle against wind disturbances.

  • B. Real-world Validation: Real-world experiments evaluated NMPC robustness in a 0.15 km2 test area under wind conditions ranging from 3 to 10 ms−1.The experiments used flight tests to assess controller robustness.
  • B. Real-world Validation: Fig. 9(a) shows closed-loop tracking of an elliptical x–y path with predicted and reference trajectories compared in horizontal and vertical directions.The figure covers both x–y-plane motion and the vertical z direction.
  • B. Real-world Validation: Airspeed deviations remained small, while throttle increased under headwind and decreased under tailwind as wind affected ground speed.Errors rose during tailwind phases as Vg increased, and the UAV quickly recovered and stabilized Va when errors exceeded 2ms−1.

VI. CONCLUSION

The paper presents an NMPC framework combining differential-flatness trajectory generation, predictive constraint-aware control, aerodynamic modeling, and wind-aware sampling for fixed-wing UAV tracking. Future work targets improved modeling accuracy, flight efficiency, and rapid dynamics estimation for new aircraft.

  • Conclusion: The proposed NMPC framework combines differential-flatness trajectory generation with predictive, constraint-aware control and aerodynamic force-and-moment modeling, while wind-aware sampling proactively accounts for disturbances.The framework was validated in simulation, PX4 SITL, and real-world flight experiments.
  • Future Work: Future work will investigate neural dynamics models, energy-aware predictive control, and data-driven system identification to improve modeling accuracy, flight efficiency, and rapid estimation for new aircraft.These directions address the increased model complexity and broader operating regimes of fixed-wing UAVs compared with multirotors.
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