Geodesic Approach for the Control of Tethered Quadrotors

摘要

This Note proposes a control framework to study the stabilizationof tethered UAVs in three dimensions. In particular, the constraint onthe cable is modeled by a holonomic constraint and is conditioned bythe positiveness of the tension in the cable. Afterward, a cascadecontrol strategy is developed with the dual objective of controlling theUAV and guaranteeing the taut cable condition. To do so, a hierarchicalstrategy based on thrust vectoring has been proposed. Inparticular, the position of the UAV is stabilized using an outer loopthat follows the great-circle navigation path while imposing a positivecable tension. The attitude of theUAVis then stabilized using an innerloop, and small gain arguments are used to prove asymptotic stabilityof the interconnected inner/outer loops. The control lawis augmentedwith the RG to enforce constraints satisfaction at all times and toenlarge the domain of attraction of the points of equilibrium. Numericalresults demonstrate the stability of the control scheme even in thepresence of external disturbances such as wind gusts. The formalproof of robustness using ISS small gain arguments is left for futureworks. This Note shows also the advantage of using the ERG insteadof the classical discrete-time RG, as the ERG is less computationallyexpensive and moves more smoothly the reference to avoid spikes inthe cable tension. Finally, it is shown that the closed-loop systemaugmented with the ERG is able to handle time-varying set points.