In the field of UAV air transportation, cable-suspended heavy objects are widely used because they can maintain maneuverability. However, they are susceptible to swings and wind disturbances during flight, making it extremely difficult to control.

In response to this challenge, Zheng Zhiyuan and others from Southwest Jiaotong University proposed in the paper "Modeling, Robust Control Design, and Experimental Verification for Quadrotor Carrying Cable-Suspended Payload"Comprehensive air resistance modeling and improved UDE+TD robust control method, effectively improving the stability and accuracy of the quadcopter under wind disturbance and trajectory switching.

The research was published in the top international journal IEEE Transactions on Automation Science and Engineering (2025, Vol.22).

Research background

There are two main ways for UAV to transport heavy objects:

• Clamping type: Rigidly fixed heavy objects increase system inertia and reduce maneuverability.

• cable-suspended type: Suspended by a rope, it maintains maneuverability but is prone to swinging and wind interference.

The problem is

• The traditional air resistance model (linear/quadratic form) is difficult to accurately describe the shaking of heavy objects at small swing angles and low speeds;

• When the controller switches waypoints or encounters wind disturbance, it is easy to become unstable due to input saturation.

• how to Under multi-source interference Ensuring the stability and trajectory accuracy of UAV is a big problem.

Technical Highlights

More accurate modeling of heavy objects

The paper proposes a comprehensive air resistance model, which adds SPAD items(Airspeed depends on zero-order damping), used to reflect non-air resistance factors such as rope friction and elasticity. In the small swing angle experiment: the model error after adding SPAD is only 0.5%

Improved UDE robust controller

Based on the uncertainty and disturbance estimator (UDE), the researchers introduced the tracking differentiator (TD):

• Smooth the step signal when switching waypoints to avoid control input saturation;

• In the trajectory smoothing scenario, the TD parameter can be increased to keep the original reference signal unchanged.

Parameter tuning method

• Based on the singular perturbation theory, a clear relationship between UDE parameter T and trajectory tracking accuracy/robustness is revealed;

• A set of concise and efficient parameter adjustment guide is proposed to make the controller easier to apply in engineering.

Experimental testing

Simulation experiment

Circle trajectory tracking

On the horizontal plane, the UDE controller can closely follow the reference trajectory; on height control, due to the initial sinking caused by mounting heavy objects, the UDE controller can quickly compensate for gravity interference and make the trajectory converge quickly.

Waypoint flight

• Waypoint switching corresponds to a step signal, and the PID control signal is easily saturated, resulting in performance degradation.

• By smoothing the reference signal, the UDE+TD controller significantly reduces overshoot and can maintain high accuracy in the presence of wind disturbance.

Real aircraft flight

Experimental platform:

AMOVLABP230 quadcopter +Prometheus open-source framework, equipped with cable-suspended load, in Flying in calm, cross wind, strong wind and other scenarios.

1. Heavy object modeling and identification

The experiment compared Linear, quadratic, linear+SPAD, quadratic+SPAD、Comprehensive resistance model。

In the case of small swing angle:

• linear model error 21.8%

• Quadratic model error 51%

• The linear + SPAD model error is only 0.5%, which is close to the comprehensive model, verifying the importance of the SPAD term.

2. Controller performance comparison

circular trajectory flight

• The UDE controller maintains the highest tracking accuracy in both horizontal and vertical directions;

• There is phase lag in PID and obvious overshoot in NADRC;

• UDE compensates for the height phenomenon faster than NADRC in height control.

Waypoint flight (one-way wind disturbance)

• PID response is fast but steady-state accuracy is insufficient;

• NADRC converges slowly;

• The UDE controller can still maintain a tracking accuracy of approximately 0.1m under crosswind interference.

Waypoint flight (strong wind interference)

• PID height tracking is seriously deviated, and NADRC is oscillating;

• The performance of the UDE controller is close to the windless scene, and the anti-interference advantage is obvious.

The influence of different UDE parameters T

• When T decreases from 5 to 0.35, the trajectory error gradually decreases, consistent with theoretical analysis;

• Compared with adjusting feedback gain (kp, kd), adjusting T can improve performance more significantly, and the parameter adjustment process is more intuitive.

Comprehensive comparison

• Error index: The mean square error of the UDE controller in the four scenarios is significantly smaller than that of PID and NADRC.

• Difficulty of parameter adjustment: The UDE controller only needs to adjust 4 parameters, and T can be adjusted independently, making parameter adjustment simple and efficient; the coupling between PID and NADRC parameters is high and relies heavily on trial and error.

Experiment summary

• The UDE+TD controller is not only superior to other methods in a windless environment, but also maintains the highest accuracy and fastest convergence under the superimposed interference of strong wind and heavy object swings.

• Its core advantages are:

Even Accurate modeling (SPAD item improves damping characterization capabilities in small swing angle scenes);

Greater robustness(Effectively resist wind disturbance and input saturation);

Easier to adjust parameters(Parameter independent, quantifiable design).

Application scenarios

This research is not only applicable to UAV lifting, but can also be extended to other systems with disturbance suppression requirements:

• Emergency supplies airdrop

• Military transportation and delivery

• Agricultural spraying and material loading

• Water sampling and mapping

• Train/unmanned boat control

Resource Express

Paper link:

https://ieeexplore.ieee.org/abstract/document/10632105