The ability to dynamically manipulate interaction between cables, carried by pairs of aerial vehicles attached to the ends of each cable, can greatly improve the versatility and agility of cable-assisted aerial manipulation. Such interlacing cables create hitches by winding two or more cables around each other, which can enclose payloads or can further develop into knots. Dynamic modeling and control of such hitches is key to mastering the inter-cable manipulation in context of cable-suspended aerial manipulation. This paper introduces an ellipsoid-based kinematic model to connect the geometric nature of a hitch created by two cables and the dynamics of the hitch driven by four aerial vehicles, which reveals the control-affine form of the system. As the constraint for maintaining tension of a cable is also control-affine, we design a quadratic programming-based controller that combines Control Lyapunov and High-Order Control Barrier Functions (CLF-HOCBF-QP) to precisely track a desired hitch position and system shape while enforcing safety constraints like cable tautness. We convert desired geometric reference configurations into target robot positions and introduce a composite error into the Lyapunov function to ensure a relative degree of one to the input. Numerical simulations validate our approach, demonstrating stable, high-speed tracking of dynamic references.

翻译：动态操控由多架空中飞行器（每对飞行器连接一根缆绳末端）所携带缆绳间相互作用的能力，可极大提升缆绳辅助空中操作的灵活性与敏捷性。此类交织缆绳通过两根或多根缆绳相互缠绕形成绳结，可用于包裹负载或进一步发展为绳结。对此类绳结进行动态建模与控制，是掌握缆绳悬挂式空中操作中缆绳间操控的关键。本文提出一种基于椭球体的运动学模型，用以连接由两根缆绳构成绳结的几何特性与由四架空中飞行器驱动的绳结动力学特性，从而揭示该系统的控制仿射形式。由于维持缆绳张力的约束同样具有控制仿射特性，我们设计了一种基于二次规划的控制器，该控制器结合了控制李雅普诺夫函数与高阶控制屏障函数（CLF-HOCBF-QP），能够在精确跟踪期望绳结位置与系统形态的同时，强制执行如缆绳绷紧等安全约束。我们将期望的几何参考构型转换为目标机器人位置，并在李雅普诺夫函数中引入复合误差，以确保系统对输入的相对阶为一。数值仿真验证了所提方法的有效性，结果表明其能够稳定、高速地跟踪动态参考轨迹。