Trajectory stabilization control for aerial recovery of cable-drogue-UAV assembly

Abstract

Unmanned aerial vehicles (UAVs) aerial recovery denotes the technology that UAVs are recovered in the air by the transport aircraft for reuse. During the recovery process, the multiple wind perturbations and fast-changing UAV’s engine shutdown will induce oscillations in the cable-drogue-UAV assembly (CDUA) with strong nonlinearities and tight coupling, which affects the safety and speed of the UAV aerial recovery. Aiming at this problem, this paper proposes a non-constraining force direction (NCFD)-based CDUA anti-disturbance trajectory control method for the first time. First, by transforming the CDUA trajectory control to the NCFD control, the coupling and nonlinear effects in the CDUA can be reduced, and the fast-changing disturbances caused by the engine shutdown can be compensated. Then, feed forward control is designed based on the relationship between the NCFD and cable shape, which is established based on the cable dynamics, to improve the response speed. Furthermore, a fixed-time anti-disturbance controller (FTADC) is designed for the flow angle of drogue-UAV assembly (DUA) given by the NCFD controller and compensates for the effects of wind and parameter perturbations. Finally, the stability of the proposed method is analyzed, and the effectiveness is demonstrated by abundant simulations.

Appendix

Aerodynamics model of drogue-UAV assembly (DUA):

$$ Q = \frac{1}{2}\rho V^{2} ,\rho = \rho_{0} {\text{e}}^{ - k\left| z \right|} $$

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$$ {\mathbf{F}}_{A} = \left[ \begin{gathered} L \hfill \\ D \hfill \\ C \hfill \\ \end{gathered} \right] = QS\left[ \begin{gathered} c_{L,0}^{{}} + c_{L}^{\alpha } \alpha + c_{L}^{{\alpha^{2} }} \alpha^{2} + c_{L}^{q} \overline{c}q/(2V) + c_{L}^{{\delta_{e} }} \delta_{e} \hfill \\ c_{D,0}^{{}} + c_{D}^{\alpha } \alpha + c_{D}^{{\alpha^{2} }} \alpha^{2} \hfill \\ c_{{C{,0}}}^{{}} + c_{C}^{\beta } \beta + c_{C}^{{\delta_{a} }} \delta_{a} + c_{C}^{{\delta_{r} }} \delta_{r} + c_{C}^{p} \overline{b}p/(2V) + c_{C}^{r} \overline{b}r/(2V) \hfill \\ \end{gathered} \right] $$

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$$ {\mathbf{M}} = \left[ \begin{gathered} {L} \hfill \\ {M} \hfill \\ {N} \hfill \\ \end{gathered} \right] = QS\left[ \begin{gathered} \overline{b}\left( {c_{{\mathcal{L}\ominus ,0}} + c_{\mathcal{L}}^{{\delta_{a} }} \delta_{a} + c_{\mathcal{L}}^{{\delta_{r} }} \delta_{r} + c_{\mathcal{L}}^{\beta } \beta + c_{\mathcal{L}}^{p} \overline{b}p/\left( {2V} \right) + c_{\mathcal{L}}^{r} \overline{b}r/\left( {2V} \right)} \right) \hfill \\ \overline{c}\left( {c_{{\mathcal{M}\ominus ,0}} + c_{\mathcal{M}}^{{\delta_{e} }} \delta_{e} + c_{\mathcal{M}}^{\alpha } \alpha + c_{\mathcal{M}}^{q} \overline{c}q/\left( {2V} \right)} \right) \hfill \\ \overline{b}\left( {c_{{\mathcal{N}\ominus ,0}} + c_{\mathcal{N}}^{{\delta_{a} }} \delta_{a} + c_{\mathcal{N}}^{{\delta_{r} }} \delta_{r} + c_{\mathcal{N}}^{\beta } \beta + c_{\mathcal{N}}^{p} \overline{b}p/\left( {2V} \right) + c_{\mathcal{N}}^{r} \overline{b}r/\left( {2V} \right)} \right) \hfill \\ \end{gathered} \right] $$

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where $L,D,C$ are lift, drag, and lateral force, respectively; ${L},{M},{N}$ are rolling, pitching, and yawing moment, respectively; $Q$ denotes the dynamic pressure; $\rho_{0}$ is the basic atmospheric density; $S$ denotes the reference area of DUA; $\overline{b}$ denotes the wind span and $\overline{c}$ denotes the wing mean chord; $c_{L} ,c_{D} ,c_{C}$ terms denote the lift, drag, lateral force coefficients, respectively; $c_{{\mathcal{L}\ominus }} ,c_{{\mathcal{M}\ominus }} ,c_{{\mathcal{N}\ominus }}$ terms denote the rolling, pitching, and yawing moment coefficients, respectively. These aerodynamic force and moment coefficients are the functions of angle of attack (AOA) $\alpha$, angle of sideslip (AOS) $\beta$ and airspeed $V$. And they are obtained using the computational fluid dynamics (CFD) method.