Payload trajectory tracking control for aerial transportation systems with cable length online optimization

TL;DR

The paper tackles payload trajectory tracking for aerial transport using variable-length cables by coupling a backstepping controller with an online cable-length generator. It develops a four-module cascaded control scheme—payload position, cable length, cable direction, and multirotor attitude—and proves asymptotic stability via Lyapunov analysis and growth-restriction conditions, without requiring predefined cable trajectories. A model-based cable-length generator optimizes $L_d^{(5)}$ in real time under state constraints, ensuring smooth control inputs and coordinated motion. Simulation results, including robustness tests and comparisons with alternative methods, demonstrate effective trajectory tracking, safe cable-length evolution, and practical feasibility at 100 Hz. The work advances flexible, safe, and controllable aerial transportation with actively varying cable length, with potential impact on operations in narrow environments and dynamic tasks.

Abstract

Cable-suspended aerial transportation systems are employed extensively across various industries. The capability to flexibly adjust the relative position between the multirotor and the payload has spurred growing interest in the system equipped with variable-length cable, promising broader application potential. Compared to systems with fixed-length cables, introducing the variable-length cable adds a new degree of freedom. However, it also results in increased nonlinearity and more complex dynamic coupling among the multirotor, the cable and the payload, posing significant challenges in control design. This paper introduces a backstepping control strategy tailored for aerial transportation systems with variable-length cable, designed to precisely track the payload trajectory while dynamically adjusting cable length. Then, a cable length generator has been developed that achieves online optimization of the cable length while satisfying state constraints, thus balancing the multirotor's motion and cable length changes without the need for manual trajectory planning. The asymptotic stability of the closed-loop system is guaranteed through Lyapunov techniques and the growth restriction condition. Finally, simulation results confirm the efficacy of the proposed method in managing trajectory tracking and cable length adjustments effectively.

Figures (8)

• Figure 1: Schematic of the aerial transportation system with variable-length cable.
• Figure 2: Block diagram of the designed payload trajectory tracking algorithm.
• Figure 3: Geometric illustration of $\bm q$, $\bm q_d$, and $(\bm q_d^{\top}\bm q) \bm q-\bm q_d$.
• Figure 4: Results for Simulation 1. (The first column presents the two-dimensional trajectories of the payload and the multirotor, while the second column displays their three-dimensional trajectories. The third column depicts the tracking errors for the payload's position, cable direction and length, and multirotor attitude, as well as the generated desired and actual cable length curves. The fourth column shows the multirotor's thrust force and torque, the payload's hoisting/lowering force, and the velocities of both the multirotor and the cable length.)
• Figure 5: Results for Simulation 2 Test 1.

Theorems & Definitions (8)

• Theorem 1
• Proof 1
• Theorem 2
• Proof 2
• Remark 1
• Theorem 3
• Proof 3
• Remark 2