Table A1.

List of main symbols.

Symbol	Description
$x$, $y$, $z$	Position in surge, sway, heave
$\theta$, $\psi$	Pitch, yaw
$u$, $v$, $w$	Linear velocity in surge, sway, heave
$q$, $r$	Pitch velocity, yaw velocity
$\mathit{x}={[x,y,z,\theta ,\psi ]}^T$	Position and orientation vector of UUV
$\mathit{v}={[u,v,w,q,r]}^T$	Linear and angular velocity vector of UUV
$\mathrm{W}$	Gravity
$\mathrm{B}$	Buoyancy
$r_B^W=[0,0,0]$	The coordinates of gravity center in body-fixed frame
$r_B^B=[x_B^B,y_B^B,z_B^B]$	The coordinates of buoyancy center in body-fixed frame
$X_{prop},Y_{prop},Z_{prop}$	Thrusts
${\delta }_r,{\delta }_s$	Steering angles
$m$	Weight of the UUV
$n$	Total number of follower uuvs
${\mathit{x}}_i^{}(t)$	The ith follower’s position and orientation vector, $i=1,2,\dots n$
${\mathit{v}}_i^{}(t)$	The ith follower’s velocity vector, $i=1,2,\dots n$
${\mathit{\epsilon }}_i(t)={[\begin{array}{cc}{\mathit{x}}_i^T(t)& {\mathit{v}}_i^T(t)\end{array}]}^T$	The ith follower’s state vector, $i=1,2,\dots n$
${\mathit{x}}_l^{}(t)$	The leader’s position and orientation vector
${\mathit{v}}_l^{}(t)$	The leader’s velocity vector
${\mathit{\epsilon }}_l(t)={[\begin{array}{cc}{\mathit{x}}_l^T(t)& {\mathit{v}}_l^T(t)\end{array}]}^T$	The leader’s state vector
$\mathit{\epsilon }(t)={[\begin{array}{cccc}{\mathit{\epsilon }}_1^T(t)& {\mathit{\epsilon }}_2^T(t)& \cdots & {\mathit{\epsilon }}_n^T(t)\end{array}]}^T$	State vectors of all followers
${\mathit{\xi }}_i(t)={\mathit{\epsilon }}_i(t)-{\mathit{\epsilon }}_l(t)$	The ith follower’s state error vector
$\mathit{\xi }(t)={[{\mathit{\xi }}_1^T(t),\dots ,{\mathit{\xi }}_n^T(t)]}^T$	The formation system’s state error vector
${\mathit{U}}_E=(u_e,v_e,w_e)$	Ocean current velocities in earth reference frame
${\mathit{U}}_B=(u_b,v_b,w_b)$	Ocean current velocities in body-fixed frame
$\vartheta (t)$	Bernoulli’s distribution function
$N$	The quantity of the topological set
${\overline{G}}_{pi}({\overline{V}}_{pi},{\overline{\epsilon }}_{pi},{\overline{A}}_{pi})$	The ith position topological unit in position topology set, $i=1,2,\dots N$
${\overline{G}}_{vi}({\overline{V}}_{vi},{\overline{\epsilon }}_{vi},{\overline{A}}_{vi})$	The ith velocity topological unit in velocity topology set, $i=1,2,\dots N$
${\overline{G}}_p^u\triangleq {\overline{G}}_{p1}\cup \dots \cup {\overline{G}}_{pN}$	Joint topology of position topology set
${\overline{G}}_v^u\triangleq {\overline{G}}_{v1}\cup \dots \cup {\overline{G}}_{vN}$	Joint topology of velocity topology set
${\gamma }_{ij}$	The switching probability from topology $i$ to topology $j$, $i,j=1,2,\dots N$
${\mathit{K}}_p$, ${\mathit{K}}_v$	Control gains for the position and velocity communication topologies