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.

翻译：缆索悬挂式空中运输系统在各行业中得到广泛应用。多旋翼飞行器与有效载荷之间相对位置的可灵活调节能力，激发了人们对配备可变长度缆索系统的日益关注，该系统展现出更广阔的应用潜力。与固定长度缆索系统相比，引入可变长度缆索增加了一个新的自由度，但也导致系统非线性增强，多旋翼、缆索及有效载荷之间的动态耦合更为复杂，为控制设计带来显著挑战。本文提出一种专为可变长度缆索空中运输系统设计的反步控制策略，旨在精确跟踪有效载荷轨迹的同时动态调节缆索长度。进而，开发了一种缆长生成器，可在满足状态约束条件下实现缆索长度的在线优化，从而平衡多旋翼运动与缆长变化，无需人工轨迹规划。通过李雅普诺夫方法与增长限制条件，保证了闭环系统的渐近稳定性。最后，仿真结果验证了所提方法在有效管理轨迹跟踪与缆长调节方面的优越性能。