This paper presents a novel approach to efficiently parameterize and estimate the state of a hanging tether for path and trajectory planning of a UGV tied to a UAV in a marsupial configuration. Most implementations in the state of the art assume a taut tether or make use of the catenary curve to model the shape of the hanging tether. The catenary model is complex to compute and must be instantiated thousands of times during the planning process, becoming a time-consuming task, while the taut tether assumption simplifies the problem, but might overly restrict the movement of the platforms. In order to accelerate the planning process, this paper proposes defining an analytical model to efficiently compute the hanging tether state, and a method to get a tether state parameterization free of collisions. We exploit the existing similarity between the catenary and parabola curves to derive analytical expressions of the tether state.

翻译：本文提出了一种新颖方法，用于高效参数化并估计悬垂缆绳状态，以支持无人机牵引地面无人车（UGV）在母子配置下的路径与轨迹规划。现有技术中的多数实现方案要么假设缆绳处于张紧状态，要么采用悬链线模型来模拟悬垂缆绳的形态。悬链线模型计算复杂，在规划过程中需实例化数千次，成为耗时任务；而张紧假设虽简化了问题，却可能过度限制平台的移动自由度。为加速规划过程，本文提出通过定义解析模型来高效计算悬垂缆绳状态，并开发了一种获得无碰撞缆绳状态参数化的方法。我们利用悬链线与抛物线曲线间的固有相似性，推导出缆绳状态的解析表达式。