Three-Dimensional Flight Trajectories of Tethered UAV for Optimal Energy Generation

Hironori A. Fujii Professor

TMIT (Tokyo Metropolitan Institute of Technology) Research centre Tokyo Metropolitan University

2-27-13, Asakusa, Taitoh, Tokyo 111-0032,

Japan

tmit@pa2.so-net.ne.jp www013.upp.so-net.ne.jp/tmit/

Three-Dimensional Flight Trajectories of

Tethered UAV for Optimal Energy Generation

1_{TMIT and Tokyo Metropolitan University,}2_{Tokyo Metropolitan University,} 3_{Tokyo Metropolitan College of Industrial Technology}

Three-dimensional trajectories of the tethered Un-manned Aerial Vehicles (TUAV) is studied for periodic mo-tion connected through deployable tether. The momo-tion is not constrained to a spherical surface formed by tether in constant length.Two types of AWE are investigated for the optimal energy generation where 1) UAV affords power through tether (Ampyx type), and 2) UAV contains wind turbine on UAV (Makani type). Performance indices for the optimal trajectories are selected as the time integral of 1) the work done by the traction by tether, and 2) veloc-ity of UAV. The lift power production of the airborne wind energy generation employs commonly many turns of tra-jectories traced on a gradually growing sphere [1]. The three-dimensional trajectories are sought to utilize the gradient of wind-speed in the ‘wind window’ distributed different wind strength all over the windows. Results of the analysis is shown in Figs.1 and 2 [2]. Figure 1 shows the optimal power extraction through tether in one cy-cle of orbit. The tension is seen to reduce to the lowest level at the retrieval as shown. The increase of flight ve-locity of UAV with wind turbine is shown in Fig.2. The trajectory can be switched between right and left turns to avoid entangling of the tether. The control is simple free from many turns of gradual deployment flight tra-jectory. These results are necessary to be confirmed by experimental study.

Fig.1 From top to bottom; Time responses of 1) Deployment/retrieval velocity of tether,2.) Tension, and 3) obtained energy.

0 5 time (s) 10 15 25 30 35 vel o c ity (m/ s ) velocity 0 5 time 10 15 100 120 140 teth er l en g th (m) tether length 0 5 10 15 time (s) 0 50 100 Ten sio n (N) Tension

Fig.2 From top to bottom; Time responses of 1) velocity of UAV, 2) Tether length, and 3) Tension.

References:

[1] J. Lago Garcia. Periodic Optimal Control and Model Predictive Control of a Tethered Kite for Airborne Wind Energy. Master’s thesis, Delft University of Technology, Kluyverweg 1, 2629 HSDelft, Nether-lands, 7 (2016).

[2] Matthew Kelly, An Introduction to Trajectory Optimization, How to Do You Own Direct Collocation,SIAM REVIEW Society for Industrial and Applied Mathematics Vol. 59, No. 4, pp. 849ś904.(2017).