# A Method for Supervisory Control of Manipulator of Underwater Vehicle
## 2 Specifics of the Method for Supervisory Control of MM  
Using this method (see Figure 2), the geometric shapes and positions of the objects in the work area are first determined using clouds of points obtained from the TVS. Then the operator targets the camera (with changeable spatial orientation of the optical axis) mounted on the UUV at the work object and uses it to set one or more working point on the selected object. These points are set by pressing a button on the control panel or the graphical interface. Depending on the manipulative task set, the spatial motion trajectories and orientation of the MM working tool are automatically set on the basis of the spatial coordinates of these points lying on the surfaces of the work object. Figure 3 shows a diagram of real-time supervisory control of MM 1 mounted on UUV 2 in the process of the sampling of a surface sediment layer using multibeam sonar 3. This sonar forms a point cloud to build a mathematical model of the seabed surface 4, which is used for the subsequent forming of the trajectory of the sediment sampler motion. The operator, moving the optical axis 5 of the camera, sets \(s\) target points  
Figure 2: The steps of the method. (\(i=\overline{1,\,s}\)), which are the points of intersection of this axis with the bottom surface at the most interesting places for sediment sampling. The motion trajectory 6 of the sediment sampler is built automatically by connecting the points \(A_{i}\). Its vector \(\overset{\rightarrow}{a}\) during movement along the trajectory (see Figure 3) should always be perpendicular to the bottom surface, and the vector \(\overset{\rightarrow}{n}\) of the normal line to \(\overset{\rightarrow}{a}\) should be directed to the next target point \(A_{i+1}\). Similarly, the proposed method of supervisory control can be used to perform more complex manipulative operations, according to operator's target indications. Building of Motion Trajectories for a MM Working Tool Performing Operations on a Flat Bottom Surface  
As numerous deep-sea studies [18; 32] have shown, sampling of sediment layers and geological rocks is frequently carried out on a relatively flat seabed surface. Such a surface can be represented by an averaged plane [32]. To do this, it is sufficient to use point clouds of points obtained with a Doppler velocity log (DVL). A DVL has at least three hydroacoustic antennas and allows measurement of the distance from their location on the UUV hull to the bottom, along all the axes of these antennas with a high accuracy. Therefore, in the coordinate system (CS) \(xyz\), rigidly fixed on the UUV hull, this plane can be described by the equation in the normal form [33]:  
\[ax+by+cz=d, \tag{1}\]  
where \(x\), \(y\), and \(z\) are the axes of the CS, with origin point \(O\) located at the UUV center of buoyancy; the \(x\) axis coincides with the horizontal, longitudinal axis of the UUV; the \(z\) axis coincides with its vertical axis; the \(y\) axis forms the right-hand triple with them; \(a\), \(b\), and \(c\) are the directional cosines of the unit vector \(\overset{\rightarrow}{m}=[a,\,b,\,c]\) of the normal line to the plane (Equation (1)), which coincides with the vector \(\overset{\rightarrow}{a}\); and \(d\) is the distance from the origin of the CS \(xyz\) to this plane. The elements \(\overset{\rightarrow}{m}\) and \(d\) are calculated using the cloud of points belonging to the bottom surface, formed by DVL, according to the method described in [32]. To form the motion trajectory of the MM working tool in the CS \(xyz\), it is necessary to calculate the coordinates of the target points \(A_{i}\) (see Figure 3). If the camera is targeted at point \(A_{i}\), the position of this camera in the CS \(xyz\) is determined by the preset point \(P_{i}=[P_{ix},P_{iy},P_{iz}]\) located on the optical axis, and its orientation is determined by the  
Figure 3: An operation performed in the supervisory mode. unit vector \(\overrightarrow{d}_{i}=[d_{ix},d_{iy},d_{iz}]\).