Control of motion and internal stresses for a chain of two underactuated aerial robots

Given the tethered aerial robot problem, in this paper we investigate a multi-agent extension considering a chain of two underactuated flying robots. Our goal is to independently control the elevations (angles) of the two links (or, equivalently, the Cartesian position of the last robot) and their internal stress. For this purpose we theoretically prove the dynamic feedback linearizability of the system and we exploit this property to design a nonlinear controller that exactly linearizes the system. The controller is able to steer the outputs of interest along any trajectory s.t. the desired elevations and stresses are functions of time of class C³ and C¹, respectively. The controller is able to track independently both positive and negative stresses, i.e., both tension and compression. Resorting to an equivalence argument we then also show the differential flatness of the system. Finally we also demonstrate some of the abilities of the proposed method through numerical examples.