## 2 Improving the Accuracy of Determination of Work Object's Shape and Location  
As noted in the Introduction, the high-accuracy determination of the shape and location of an object relative to UUV is carried out in the stabilized hovering mode [11; 12; 13; 14]. The undersea surroundings are scanned by the MVS units [16; 17] to form clouds of points distributed over the bottom and object surfaces. The point clouds are set in a rectangular coordinate system (CS) _Oxyz_ rigidly fixed to the UUV hull, with the origin located at the center of buoyancy of the vehicle, the _Ox_ axis coincides with the horizontal, longitudinal axis of the UUV, the _Oz_ axis coincides with its vertical axis and is directed downward, and the _Oy_ axis complements the other two axes to form the right-hand CS. To identify a certain known object in the point cloud obtained from MVS, the work [18] suggests using a 3D model of this object, preprocessed and transformed into a point cloud set in the CS _Oxyz_. This cloud, consisting of \(m\) points \(K_{q}\in R^{3}\left(q=\overline{1,m}\right)\), first, is virtually approximated to the cloud of points belonging to the actual object through the linear transfer in the direction of the vector \(\overset{\rightarrow}{p}_{1}\in R^{3}\), whose magnitude and direction are determined by the systems of detection of underwater objects that stand out from the surrounding [9; 10]. Then the displaced cloud, defined by the points \(P_{q}=\left(K_{q}+\overset{\rightarrow}{p}_{1}\right)\), is aligned with the point cloud of the object using the iterative closest point (ICP) algorithm [29] implemented in the open-access Point Cloud Library (PCL) [30]. In the case the point clouds are aligned by the standard PCL tools (see Figure 2), the vector \(\overset{\rightarrow}{p}_{2}\in R^{3}\) and the matrix \(M_{r1}\in R^{3\times 3}\) are calculated. These are required for the cloud alignment as they describe, respectively, the linear displacement and rotation of the model point cloud relative to the axes of the CS _Oxyz_. Consequently, for any point \(P_{q}\) belonging to the point cloud of the object model, a point \(G_{q}\) can be obtained that defines the position of the point \(P_{q}\) after the two clouds are aligned [18]:  
\[G_{q}=H_{P}+M_{r1}\overset{\rightarrow}{l}_{q}+\overset{\rightarrow}{p}_{2} \tag{1}\]  
where \(H_{P}=\frac{1}{m}\sum_{q=1}^{m}P_{q}\) is the midpoint (center of mass) of the point cloud of the object model, and \(\overset{\rightarrow}{l}_{q}=\left(P_{q}-H_{P}\right)\) is the vector that defines the position of any point \(P_{q}\) relative to the point \(H_{p}\) of this cloud. Accuracy of cloud alignment is evaluated by the method of least squares for the nearest points of these clouds at each iteration of the ICP algorithm. Therefore, the presence of \"excess\" points in the displaced object model (which are absent from the scan of the actual  
Figure 2: Preliminary alignment of point clouds. object due to the unidirectional scanning by MVS) often causes errors in alignment of the centers of mass of the two clouds. Nevertheless, studies have shown that correct spatial orientation of the object model's cloud is usually achieved even in such cases (Figure 2). To increase accuracy of the point clouds alignment, some of the points \(G_{q}\) of the object model lying on the surface of this model and invisible to MVS should be discarded. Thus, we assume that a preliminary alignment of clouds allows setting a spatial orientation of the object model that would match quite precisely the orientation of the actual object.