Static and Dynamic Modeling and Simulation of the Umbilical Cable in A Tethered Unmanned Aerial System

The research at hand has been accomplished in collaboration with our industry partner, Rigid Robotics Inc. and aims to predict and suggest solutions for some of the known and unknown issues that might appear in operation of a tethered Unmanned Aerial System (to be referred to as UAS hereafter). In this work, the static and dynamic behaviour of the power cable connecting a hovering UAS to its base station is studied in different flight scenarios. The mathematical modelling of the cable is carried out using catenary equations for the static case and multi-body dynamics principles are employed for the dynamic condition. In the preliminary stages of the project, for the purpose of the cable and UAS design, a simple technique is used to estimate the maximum tension forces present in the static state of the cable as well as the cable shape function and other related parameters when UAS is in hovering mode. The derivation of the system’s equations of motion is done using Lagrange’s Equations by considering the cable as a discrete multi-body system. The equations of motion are derived for a system of finite segments and are solved numerically using MATLAB™ software package in order to simulate the cable’s motion. The effect of wind on the dynamics of the cable is also implemented using theoretical methods and simulations. The system’s dynamics is modeled in a planar motion as well as a 3D space in separate chapters.