More Stable Payload Transportation with Three-Loop Control: AMOVLAB Scholarship Paper Spotlight

In aerial transportation, cable-suspended payloads are widely used because they are flexible and suitable for many scenarios. However, they also introduce a difficult problem: once the load starts swinging, wind disturbance or waypoint switching can amplify the motion. At best, precision decreases; at worst, system stability is affected.

To address this challenge, Zheng Zhiyuan and collaborators from Southwest Jiaotong University published a paper in IEEE Transactions on Intelligent Transportation Systems. Starting from the real engineering problem of actuation constraints, they proposed a control framework better suited for real flight and verified its effectiveness under strong disturbances and trajectory switching.

With this research, Zheng Zhiyuan received the AMOVLAB Campus Scholarship Second Prize of RMB 5,000. The 2026 scholarship program is also being prepared, and details will be announced soon.

01. Research Background

Anti-swing control often requires fast maneuvering. In real systems, however, the classical double-loop cascaded control framework for quadrotors (outer-loop position/anti-swing control plus inner-loop attitude control) may not execute those commands effectively. The key reason is that the inner-loop actuation bandwidth is limited.

To solve this, the paper proposes a backstepping hierarchical framework that combines an uncertainty and disturbance estimator (UDE) with robust dynamic compensation.

The framework consists of three control loops. The outer loop handles trajectory tracking and anti-swing control, while the inner attitude controller keeps the conventional design. The most important change is the introduction of an intermediate control loop. Based on an experimentally validated actuator model, a robust dynamic compensator (RDC) is designed to expand the effective actuation bandwidth of the quadrotor, allowing the system to better satisfy the bandwidth requirements of the outer loop.

The paper further proves closed-loop stability using Lyapunov methods, analyzes system performance through singular perturbation theory, and verifies feasibility and effectiveness through comparative simulations and real-flight experiments.

02. Technical Highlights

Three-Loop Control Structure

A new RDC module is introduced between the outer and inner loops of the classical quadrotor cascaded control framework, forming a new three-loop control structure. Without redesigning the inner-loop controller, this structure systematically improves the effective inner-loop bandwidth and helps preserve outer-loop performance.

First-Order Identification and UDE Backstepping

Instead of modeling the entire inner-loop control system, the research identifies a simplified first-order inner-loop model from data. Based on this model, a UDE-based backstepping control method is proposed to address mismatched disturbances commonly found in multi-loop control systems.

Elastic Degrees of Freedom

Cable elasticity introduces extra degrees of freedom and makes the design of virtual anti-swing acceleration commands more difficult. The paper uses singular perturbation theory to prove that when the elastic coefficient is sufficiently large, a control law designed under the inextensible-cable assumption remains feasible for elastic cable systems.

03. Simulation and Flight Tests

Simulation Case 1: Hovering with an Initial Swing Angle

In this scenario, the quadrotor must hover while the payload starts with an initial swing angle. The proposed controller shows the best decay performance in both position tracking error and payload swing angle. In particular, during the initial stage when the quadrotor maneuvers to reduce payload swing, the proposed method suppresses swing effectively even though position error is temporarily larger.

Compared with two baseline controllers, the proposed method performs better in both trajectory tracking and anti-swing control. The proposed controller designs anti-swing control only on the x and y axes, preserving altitude stability. In contrast, finite-time convergence control introduces anti-swing control along all axes, causing the quadrotor to adjust altitude while damping swing and harming altitude-hold performance.

Simulation Case 2: Waypoint Flight

In this scenario, the quadrotor switches between two waypoints every 30 seconds. The reference position switch causes aggressive maneuvers, and payload swing inevitably increases. The proposed controller shows superior transient response, quickly converging to steady state while suppressing the growing swing angle.

Compared with the two baseline methods, the proposed method converges to steady state with the smallest swing amplitude, achieving the best trajectory tracking and anti-swing performance.

Simulation Case 3: Trajectory Flight

The quadrotor tracks a continuous circular trajectory in the horizontal plane while maintaining a fixed altitude reference. The proposed method minimizes trajectory tracking error, while the controller without RDC shows reduced tracking performance. In terms of swing angle, the proposed method achieves the smallest swing amplitude and fastest decay.

It should be noted that because the quadrotor must continuously change acceleration to track a circular path, the payload swing angle cannot strictly converge to zero, which is consistent with physical behavior.

Flight Test 1: Hovering and Impulse Disturbance

The payload is subjected to an impulse disturbance to verify swing suppression. The proposed method damps swing effectively within two seconds, while finite-time convergence control performs worse and cannot maintain comparable stability.

Flight Test 2: Waypoint Flight

The quadrotor tracks four waypoints with a switching period of four seconds. During waypoint changes, aggressive maneuvers cause the payload swing angle to increase rapidly. The proposed controller damps the swing quickly and maintains the best trajectory tracking performance.

Flight Test 3: Trajectory Flight

To verify continuous trajectory tracking, the quadrotor follows a circular path. In this smoother scenario, the proposed method and the method without RDC perform similarly, because the acceleration variation is relatively mild and the payload swing does not change significantly. As a result, the RDC effect is less obvious.

Conclusion

The proposed method achieves more accurate trajectory tracking and faster swing-angle decay in most cases, especially under large swing angles and waypoint switching.

After introducing the RDC module, the low-level control response is effectively improved. Under large swing disturbances, the proposed method clearly outperforms traditional double-loop control. In smooth circular trajectory tracking, the three methods show similar performance and the effect of RDC is less significant.

Resources

• Paper: Robust Dynamic Compensator-Based Hierarchical Control for Quadrotor-Suspended-Payload System With Actuation Constraints
• Journal: IEEE Transactions on Intelligent Transportation Systems
• DOI: 10.1109/TITS.2025.3594288
• Paper link: https://ieeexplore.ieee.org/document/11122372