Study of Maneuverability the AUV flexibly Coupled to the Surface Repeater

The towed surface radio communication module (SRCM) allows the high-speed communication channel between the control station and an autonomous underwater vehicle (AUV) to be organized and significantly simplifies the navigation support. Herewith, disturbances by the communication cable acting on the SRCM and AUV are significantly affecting the whole system’s parameters. The paper aims to calculate the additional drag force acted on the vehicle by affecting the towed SRCM and communication cable on the AUV in steady conditions and along typical maneuvering trajectories. A model of an underwater tethered motion control system considers the AUV dynamics, and the communication cable is proposed. A kinematic model of the SRCM has been developed. This model determines the submerging of the communication module and hydrodynamic resistance during towing. The paper presents the results of modeling the tethered system’s movement along typical trajectories typical for survey-search AUV. The results allow the additional requirements to the vehicle’s propulsion system and the required additional buoyancy of the SRCM to be obtained.


Introduction
It is possible to increase the AUV work efficiency by providing high-speed communication with the operator's station in real-time. Simultaneously, it becomes possible to quickly obtain large amounts of information accumulated by vehicle equipment during the survey. The surface radio communication module solves this problem and allows refining the AUV global position [1][2][3][4][5][6] based on the satellite navigation system (SNS). This technical solution makes it possible to carry out underwater works in areas without a hydroacoustic navigation system. The errors in determining coordinates accumulated by the vehicle's onboard navigation system are proposed to periodically correct using the float GPS/GLONASS system installed on the SRCM. However, significant forces disturbing on the vehicle by the communication cable and SRCM are noticeable. It affects the maneuverability and movement accuracy along a given trajectory of the vehicle.
The research aims to evaluate the parameters of the AUV movement and disturbances by towing the SRCM. To achieve this goal, it is necessary to develop the tethered system's structure and simulate the tethered motion system along typical trajectories of the AUV survey based on the well-known dynamic models of the SRCM, the communication cable, and the AUV.  Figure 1 shows the structure of the control system aimed to simulate the tethered system.   The method for calculating the response at the ends of a cable connection is based on solving nonlinear differential equations of an elastic thread's dynamics with partial derivatives for independent variables -the arc coordinate and time [11,12]. In this case, the differential equations of motion of the thread are integrated, taking into account the initial and boundary conditions. The force effects of the SRCM due to its residual buoyancy п and hydrodynamic resistance п are the boundary conditions at the upper running end for the flexible coupling equation. The boundary conditions at the lower (root) end are the conditions for connecting the cable with the towing SRCM. The initial conditions should provide for the thread's configuration and the speed of its points at the initial moment. It can be obtained from a preliminary calculation of the statics of the cable line in a stationary flow, due to the flow rate and the absolute initial speed of movement of the AUV and SRCM. One of the approaches to constructing a mathematical model of cable dynamics is its representation in a discrete model, a system of concentrated masses connected by springs. The use of discrete models allows one to obtain dynamic equations in a system of nonlinear ordinary differential equations (ODE). This approach is the most popular in solving problems of tethered systems' dynamics with the determination of cable reactions , и кx кy кz F F F since the vehicle's dynamics are also described by the ODE system [11,12].

Model of the Tethered System Motion Control
As a prototype of the AUV for SRCM towing, a hybrid AUV "Chilim" developed by the Institute of Applied Mathematics and Mechanics of the Far East Branch of the Russian Academy of Sciences [13] was used.
In accordance with the functional purpose, the design of the SRCM was determined ( Figure 2). where:  xп C is coefficient of hydrodynamic resistance of SRCM;  ρ is density of water; Taking the assumption about the linear dependence of the additional buoyancy of the SRCM on its deepening, we obtain the following equation.
, at 0 , , at ; where п Q = 50 N, п h  = 0,4 m are buoyancy and SRCM draft to compensate for the vertical reaction of the cable, respectively. The SRCM immersion depth is dependent on the vertical response, which is preliminarily determined by the dynamic cable model [12]. Taking into account the fulfillment of the requirement of sufficiency of the SRCM buoyancy reserve

Simulation of the Movement of an Underwater Tethered System
Modeling of the robotic complex consisted of the hybrid AUV "Chilim", the communication cable, and the SRCM was carried out based on the equation of propulsion dynamics of the "Chilim" [13], the equations describing the movement of the SRCM obtained in Section 2 and the equations for vehicle movement in water [14]. The following constants were used in the simulation:  [13]. During the simulation, the "meander" trajectory of the vehicle survey was carried out. At the initial stage, both the AUV and the SRCM were located on the surface at 20 meters between each other. After that, the vehicle has submerged on 10 meters' depth and went forward 50 meters long with 1 m/s velocity and further went along the "meander" trajectory. Figure 4 illustrates the obtained simulation results. The blue line denotes the trajectory of the SRCM movement on the top plot in Figure 4, the red line indicates the trajectory of the AUV, and the dashed line shows the communication cable between them.