3D Euler-Angle Orientation Control for Two-Ray Fading Mitigation in Maritime Air-to-Sea Communications

System Model

We consider a UAV communicating with a ship through an A2S two-ray channel (see Fig. 1 ). We adopt an inertial world frame $\mathcal{F}_{W}$ whose $z$-axis is vertical and whose origin is set at the UAV flight altitude, so that points below it have negative $z$-coordinates; in particular, the sea surface is at $z=-20\penalty\ \mathrm{m}$.

Closed-Form 3D Orientation Optimization

The exact problem ( 6 ) is non-convex. We derive a tractable closed-form approximation by exploiting two regularities of long-range maritime A2S links: the attitude corrections of interest are small, and the link distance is large compared to the antenna offset. Section III-A states these assumptions and linearizes the two-ray phase.

Section III-B uses the linearized model to obtain a closed-form family of minimum-norm attitude candidates that enforce constructive interference at leading order.

Optimal Control Problem

The UAV is modeled as a fully actuated Generalized Tilting Multirotor ( GTMR ) [ 16 , 15 ] , whose continuous-time rigid-body dynamics admit the standard Newton–Euler form $\dot{\mathbf{x}}=\mathbf{h}(\mathbf{x},\mathbf{u})$, with state $\mathbf{x}=[\mathbf{p}^{\top},\bm{\eta}^{\top},\mathbf{v}^{\top},\bm{\omega}^{\top}]^{\top}\in\mathbb{R}^{12}$ collecting position, Euler angles $\bm{\eta}=[\phi,\vartheta,\psi]^{\top}$, translational velocity, and body-frame angular velocity, and control input $\mathbf{u}=\bm{\Omega}\in\mathbb{R}^{N_{p}}$ give...

Numerical Results

We evaluate the proposed controller in a maritime A2S scenario governed by the two-ray model.

To exercise the 3D orientation law across a time-varying relative bearing, the UAV tracks a horizontal circular trajectory of radius $R$ centered at $(x_{0}-R,y_{0},z_{0})$, parameterized as $\mathbf{p}_{d}(t)=(x_{0}-R+R\cos(2\pi s(t)),\,y_{0}+R\sin(2\pi s(t)),\,z_{0})$ with the smooth time-warp $s(t)=\tfrac{1}{2}\bigl[1-\cos(\pi t/T)\bigr]$, $t\in[0,T]$, ensuring jerk-free start/stop kinematics.

Sources and Demonstrations

Figures are reproduced from Bajja et al. See the full paper for experimental details and the project page, when the paper links one, for demonstrations and videos.