## 2 The Problem Statement
Precisely in area \(\Phi\), a group of gliders should try to maintain the preassigned formation \(H_{group}\), performing reconfiguration and maneuvering. Thus, it is mandatory to satisfy the following condition (2):  
\[H_{group}(UG_{1},UG_{2},WG)\in\Phi \tag{2}\]  
In the case of a real application of the group, it is important to take into account the presence of stratification of the marine environment and external disturbing influences \(F_{d}\), (for example, currents) that can introduce significant deviations into the trajectory of the underwater glider. Under this assumption, we take the conditions for the group functioning within the Baltic Sea, where the stratification of the marine environment in relation to gliders can be neglected [38], and the average speed of steady currents in the straits ranges from 0.5 to 2 knots. As a result, with a minimum direct lateral impact at 0.5 knots on a vehicle moving at a longitudinal velocity at 0.8 knots, its lateral deviation from the target trajectory in the direction of the resulting velocity vector will be \(\sim\)1.3 km per 1 h of movement. Considering the submerged state of the underwater glider and the operating range of acoustic communication of 1.5--1.7 km (inclined range), such a flow practically takes the vehicle out of the \(\Phi\) group area. In order to keep vehicles within the \(\Phi\) area, it is important to ensure sufficient glider maneuverability, namely, the minimum allowable glider turning radius \(R^{\prime}\), which satisfies the condition (2). Figure 2: Statement of the problem of gliders’ group motion. A closer look at motion models of the underwater glider in a group is presented in the Section 3. SHADOW Underwater Glider Model  
A steady motion model of an underwater glider with independence assumption of the glider immersion depth function in general form is presented in the expression (3) [39; 40; 41]. \[\dot{Y}=\sum(\theta,x)=\left( \begin{array}{c}\Sigma_{p}(\theta,x)\\ \Sigma_{\theta}(\theta,x)\end{array} \right) \tag{3}\] \[r_{p}^{\prime}=(1/m_{p})P_{p}-V-W-r_{p}\] \[\dot{P}_{p}=(\overline{u})\] \[\dot{m}_{b}=u_{b}\]  
where \(x\)--m-vector of internal coordinates; \(\dot{Y}\)--n-vector of position and orientation vector of the associated reference frame relative to the base one, \(n\leq 6\); \(\sum(\theta,x)\)--n-vector of kinematic relations; \(\Sigma_{p}(\theta,x)\)--vector of linear velocities of the associated reference frame relative to the base one; \(\Sigma_{\theta}(\theta,x)\)--vector of angular velocities of the associated reference frame relative to the base one; \(M\)--mxm-matrix of mass-inertial parameters: its elements are mass, moments of inertia, and added masses of the glider; \(F(x,Y,r_{p},P_{p},u,l,R)\)--m-vector of external and internal forces and moments; herein \(l\)--design parameter vector, R--vector of hydrodynamic forces and moments; \((\overline{u})=P_{p}*W+F_{p}+u\), where \(u\)--(m-1) vector of control actions (internal forces affecting the movable load); W--glider angular velocity vector; \(r_{p}\)--movable load position vector; \(P_{p}\)--momentum vector of the movable load; \(m_{p}\)--changing glider mass (ballast load); \(F_{p}\)--gravity vector acting on a movable load in associated reference frame. The direction of orientation angles and velocity vectors of the underwater glider is shown in the Figure 3[42], where \(XYZ\) is the glider-related reference frame; it should be noted that point \(O\) is the vehicle's center of mass coordinate, which coincides with the reference frame center origin and is located at a distance of 1.4 m from the bow of the glider; \(\gamma\)--pitch angle of the glider; \(\theta\)--heading angle of the glider; \(\theta\)--roll angle of the glider; \(w_{x},w_{y},w_{z}\)--angular velocities of the glider corresponding to the axes. It is necessary to note that the depth sensor is located in the bow of the glider. The glider rotation matrix is presented in the expression (4), where \(C(\theta)\) and \(S(\theta)\) are \(cos(\theta)\) and \(sin(\theta)\) accordingly. \[R_{m}=\left(