Ground-Effect-Aware Modeling and Control for Multicopters (2506.19424v1)

Abstract: The ground effect on multicopters introduces several challenges, such as control errors caused by additional lift, oscillations that may occur during near-ground flight due to external torques, and the influence of ground airflow on models such as the rotor drag and the mixing matrix. This article collects and analyzes the dynamics data of near-ground multicopter flight through various methods, including force measurement platforms and real-world flights. For the first time, we summarize the mathematical model of the external torque of multicopters under ground effect. The influence of ground airflow on rotor drag and the mixing matrix is also verified through adequate experimentation and analysis. Through simplification and derivation, the differential flatness of the multicopter's dynamic model under ground effect is confirmed. To mitigate the influence of these disturbance models on control, we propose a control method that combines dynamic inverse and disturbance models, ensuring consistent control effectiveness at both high and low altitudes. In this method, the additional thrust and variations in rotor drag under ground effect are both considered and compensated through feedforward models. The leveling torque of ground effect can be equivalently represented as variations in the center of gravity and the moment of inertia. In this way, the leveling torque does not explicitly appear in the dynamic model. The final experimental results show that the method proposed in this paper reduces the control error (RMSE) by \textbf{45.3\%}. Please check the supplementary material at: https://github.com/ZJU-FAST-Lab/Ground-effect-controller.

• The paper presents a comprehensive experimental identification that quantifies rotor disturbances, including leveling torque and altitude-dependent lift, near ground.
• It introduces a closed-form analytical model for ground effect disturbances and validates it with flight tests on single-rotor and quadrotor platforms.
• The integrated controller uses dynamic inversion and feedforward compensation to achieve a 45.3% reduction in tracking error during near-ground operations.

Ground-Effect-Aware Modeling and Control for Multicopters

This work provides a comprehensive investigation into the aerodynamic ground effect on multicopter unmanned aerial vehicles (UAVs), focusing on establishing accurate dynamic models and corresponding control methods that compensate for induced disturbances in near-ground operations. The paper combines extensive experimental system identification, theoretical modeling, and practical control design, with a particular emphasis on ground effect phenomena such as additional lift, leveling torque, and rotor drag modification.

Problem Motivation and Background

Multicopters are regularly required to perform maneuvers near the ground in applications including delivery, manipulation, automated landing, and aggressive low-altitude flight. Proximity to surfaces gives rise to complex aerodynamic phenomena collectively termed the ground effect, which alters rotor thrust, introduces attitude-dependent torques, and modifies aerodynamic drag. Historically, control solutions have compensated for ground-effect-induced lift but have mostly neglected the associated torques (leveling torque) and changes to drag and mixing matrix parameters, which results in degraded performance or instabilities during aggressive, near-ground trajectories.

Main Contributions

The paper's contributions are articulated in three primary dimensions:

1. Comprehensive Experimental System Identification: The work employs both single-rotor and quadrotor platforms with high-precision force and torque sensing to empirically map the relationship between rotor speed, tilt angle, altitude, and resulting aerodynamic disturbances. Real-world flight data further substantiates these models under operational conditions.
2. Modeling of Ground Effect Disturbances: The paper introduces, for the first time, a closed-form analytical model for the leveling torque induced by ground effect. This formulation connects the tilt angle, altitude, and net thrust to the magnitude and direction of the disturbance torque, which behaves to return the multicopter to level flight. Additionally, it quantitatively assesses the variation of rotor drag and verifies that, while the primary lift coefficient changes substantially near the ground, mixing torque coefficients remain essentially invariant.
3. Integrated Control Design: The controller leverages disturbance feedforward using the newly identified models while employing dynamic inversion (and optionally, incremental nonlinear dynamic inversion, INDI) for disturbance rejection, thus ensuring trajectory tracking precision both near and far from surfaces. Critically, the leveling torque is treated via model equivalence to a shifted center of gravity (payload model), preserving the differential flatness property and enabling flatness-based planning and control. Experimental validation on custom UAV hardware demonstrates a 45.3% reduction in RMSE error compared to conventional controllers.

Technical Summary

Experimental Modeling Framework

• Thrust Augmentation: The additional lift due to ground effect is parameterized as a function of rotor height above the ground, allowing calibration with respect to distance and rotor speed. Experiments confirm that the thrust increase is independent of tilt angle.
• Leveling Torque: The derivation shows that nonzero pitch or roll angles create an asymmetric ground effect on the rotors, generating a torque that opposes the attitude deviation—quantified and validated experimentally. The magnitude of this torque depends nonlinearly on height and linearly on tilt (for small angles), and peaks at a specific altitude relative to rotor radius.
• Rotor Drag: Contrary to prior assumptions, the rotor drag at low altitude is reduced substantially more than can be explained by decreased thrust alone, with empirical reductions of ~40%, necessitating altitude-dependent drag coefficients.
• Mixing Matrix Independence: Empirical analysis confirms that roll/pitch/yaw torque coefficients ($k_{TX}$, $k_{TY}$, $k_I$) are essentially independent of ground proximity, simplifying control design by obviating the need for state-dependent matrix adaptation.

Control and Implementation Architecture

The final controller is engineered as follows:

• Feedforward Compensation: The controller uses identified altitude-dependent models for both lift and drag as explicit feedforward terms within acceleration and attitude tracking loops.
• Leveling Torque Handling: The leveling torque is equivalently represented via an altitude-dependent shift in the moment of inertia, transforming the problem into one amenable to standard controller design by simply modifying $J$ as a function of $h$.
• Incremental Disturbance Mitigation: To address model discrepancies and unmodeled effects, dynamic inversion (or INDI) augments the model-based terms, relying on sensor feedback (e.g., IMU) to estimate and reject fast-varying external moments.
• Reference Generation via Flatness: The augmented model preserves differential flatness, allowing rapid reference generation for aggressive trajectories, with closed-form mappings from desired Cartesian/lateral-yaw trajectories to rotor thrust and attitude references.

Implementation Considerations

Code Integration and Real-Time Computation:

• The control framework is implemented within the APM firmware, with modifications for real-time rotor speed feedback and voltage compensation.
• Height-dependent parameters are either interpolated from precomputed lookup tables or directly computed with lightweight algebraic formulas, ensuring computational tractability at control rates of 100–200 Hz.

Sensor and Estimator Requirements:

• Accurate distance-to-ground sensing (e.g., multi-point LIDAR) is required for ground effect estimation.
• Sensor fusion (e.g., EKF with motion capture or GPS/IMU) provides the state feedback for position, velocity, and attitude estimation.

Computational Load and Hardware:

• The on-board compute platform is an Intel NUC, but the algorithms are lightweight enough for modern embedded ARM processors.
• Force/torque calibration is required for each airframe type; parameters can be stored in firmware flash.

Experimental Evaluation

Table 1 (in the text) illustrates a thorough controller benchmark on trajectory-following and hovering tasks at multiple altitudes and velocities. The proposed controller achieves:

• 45.3% RMSE reduction in challenging near-ground (12 cm altitude, 1 m/s) tracking compared to baselines.
• Substantial mitigation of altitude-dependent control degradation; error profiles remain nearly altitude-invariant with the combined model-based and incremental feedback design.
• Superior Z-axis control and comparable or better XOY-plane tracking compared to data-driven (Neural Lander) and INDI approaches.

Implications and Future Directions

Practical Implications:

• Reliable and precise tracking of aggressive low-altitude trajectories becomes feasible, enabling applications such as high-precision landing, near-ground manipulation, and tunnel/indoor navigation.
• The modeling procedure and paradigm—empirical torque and force identification, analytical fitting, and control-informed parameterization—provide a blueprint for extending this approach to other vehicles and aerodynamic configurations.

Theoretical Implications:

• Demonstrates that complex disturbance models, including those nonlinear in altitude and state, can be coherently integrated in a flatness-based geometric control framework by suitable model abstraction (payload model).
• Suggests that existing methods which treat ground effect as solely a force disturbance are incomplete; controllers require explicit modeling of all key aerodynamic couplings for optimal performance.

Limitations and Future Work:

• The paper does not address the decline of ground effect during high-speed forward flight, which may become relevant for velocities above rotor-induced flow speeds.
• The precise mechanism by which rotor drag decreases beyond thrust scaling near the ground remains an open area, inviting further paper via CFD or additional empirical campaigns.
• Extension to complex environments (e.g., interaction with irregular surfaces or walls) and adaptation to other multicopter topologies (e.g., hexacopters, morphing frames) are open practical pathways.

Conclusion

This paper delivers a meticulous and experimentally grounded methodology for modeling and actively compensating ground effect disturbances in multicopters. By extending system identification to torque effects and integrating these discoveries in a modern control structure, the work achieves both significant performance gains and valuable insights for future advances in aerial robotics operating near surfaces. The model abstraction and controller design strategies outlined herein constitute a robust reference for practitioners seeking to enhance multicopter reliability and precision in ground-proximate tasks.