We study the problem of dynamically controlling the shape of a cable that is fixed at one end and attached to an actuated robot at another end.This problem is relevant to unmanned aerial vehicles (UAVs) tethered to a base.While rotorcrafts,such as quadcopters,are agile and versatile in their applications and have been widely used in scientific,industrial,and military applications,one of the biggest challenges with such UAVs is their limited battery life that make the flight time for a typical UAVs limited to twenty to thirty minutes for most practical purposes.A solution to this problem lies in the use of cables that tether the UAV to a power outlet for constant power supply.However,the cable needs to be controlled effectively in order to avoid obstacles or other UAVs.In this paper,we develop methods for controlling the shape of a cable using actuation at one end.We propose a discrete model for the spatial cable and derive the equations governing the cable dynamics for both force controlled system and position controlled system.We design a controller to control the shape of the cable to attain the desired shape and perform simulations under different conditions.Finally,we propose a quasi-static model for the spatial cable and discuss the stability of this system and the proposed controller.
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