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Autonomous underwater vehicles (AUVs) are important and useful tool platforms in exploring and utilizing ocean resource. However, the effect of control surfaces would decrease even invalid complete in this condition, and it is very hard for conventional AUVs to perform detailed missions at a low forward speed. Therefore, solving this problem of AUVs becomes particularly important to increase the application scope of AUVs. In this paper, we present a design scheme for the vectored thruster AUV based on 3RPS parallel manipulator, which is a kind of parallel manipulator and has advantages of compact structure and reliable performance. To study the performance and characteristics of the proposed thrust-vectoring mechanism, a series of works about corresponding kinematic and dynamic analysis have been performed through the theoretical analysis and numerical simulation. In the part of kinematics, the inverse, forward kinematics, and workspace analysis of the thrust-vectoring mechanism is presented, and the numerical simulations are accomplished to prove the feasibility and effectiveness of this design in AUVs. In order to further verify feasibility of the thrust-vectoring mechanism, based on the considerations of various affecting factors, a dynamic model of the designed thrust-vectoring mechanism is established according to theoretical analysis, and the driving forces of the linear actuator are presented through a series of numerical simulations. In addition, a control scheme based on PID algorithm is proposed for the designed vectored thruster with considering various affecting factors and the application environment. Meanwhile, the control scheme is also established and verified in MATLAB Simscape Mutibody. A series of numerical simulations of the thrust-vectoring mechanism prove the feasibility of the vectored thruster. According to equipping the designed vectored thruster, the AUVs can overcome the limit of weakening the control ability at zero or low forward speeds, and this improvement also expands the application of it, which has been scaled greatly.

Over the last few decades, due to exhausting of resources and energy, human beings are bearing with a series of survival predicaments and development challenges [

AUVs have become a main tool for surveying below the sea due to the great improvement in their performance and advancement in underwater research. Through equipping a large quantity of advanced instruments and equipment, AUVs are capable of accomplishing applications including scientific, commercial, and military tasks such as exploration of oceans [

Conventional AUVs are designed equipped with a main propeller and control surfaces at the tail cone for propulsion and control [

There are some approaches to solve this problem, such as installing additional thrusters to provide additional control forces for controlling AUVs [

Another more efficient and workable method to release this restriction is to use vectored thruster to replace the conventional propulsion types [

In the research areas of this field, some companies and research institutions have made progress in theory study and application of vectored thrusters [

On the contrary, compared with other commonly used mechanical structures, parallel manipulators have numerous advantages, such as small size, compact and reasonable structure, reliable performance, fast response, high positioning precision, high stability, high sensitivity, high stiffness, and better dynamic performance [

With comparing structure characteristics of different kinds of parallel manipulators and considering actors of application environment, 3RPS is chosen from various parallel manipulators as the thrust-vectoring mechanism mainly various advantages, including its compact structure, high position tracking precision, and fast response speed. This parallel mechanism is a strong coupled nonlinear structure, so its motion control is too complex to use more widely [

On the basis of the above considerations, the design concept of vectored thruster which is made up of 3RPS parallel manipulators is introduced. The vectored thruster based on 3RPS parallel manipulators has terse structure, convenient operation, convenient installation, steady working system, and wide adjustable range. Using this method, the AUVs are able to provide the vectored thrust effectively and efficiently. More than anything, the AUVs equipped with vectored thruster are able to complete a variety of the complex tasks at a comparably low forward speed.

In this paper, the structural design of the vectored thruster based on 3RPS is introduced briefly. In order to satisfy the design requirements and study the motion characteristics of vectored thruster, the kinematics and dynamics model of the thrust-vectoring mechanism are established, and the related simulation is presented to verify feasibility of the scheme. Finally, a control scheme for the vectored thruster is designed and simulated in Matlab. The theoretical analysis and numerical simulations prove that the proposed vectored thruster based on a 3RPS parallel manipulator can effectively realize the function of providing the required vectored thrust for thrust-vectoring propulsion.

The configuration of the whole AUV equipped with the designed vectored thruster based on 3RPS parallel manipulator is presented, as shown in Figure

Vectored thruster mounted at AUV.

In terms of structure design, considering the specific requirements of application environment and the stability of system, we adopted the modular design for vectored thruster AUV. The designed vectored thruster is mounted on the stern of an AUV as an integral and independent, which is adopted for convenient installation and maintenance. The designed vectored thrust duct propeller system mainly contains the duct propeller and the thrust-vectoring mechanism. A whole structure model of the vectored thruster AUV based on 3RPS parallel manipulator is built up, as shown in Figure

Vectored duct thrust propeller.

At present, the duct propeller is the most widely used form of propulsion device for underwater robots. A duct propeller is mainly composed of an annular wing and a propeller. There are many underwater vehicles equipped with duct propellers, for the extraordinary performance of improving the propulsive efficiency and avoiding cavitation conditions [

Furthermore, underwater environments are very complex and harsh; propellers are very easily destroyed by underwater animals and plants, waves, even currents, and other uncertainties. Hence, the existence of a duct can protect the propeller against damage from the underwater environment during all kinds of missions. Moreover, since the duct also can generate the thrust during the voyage, the duct is an important source of control force for AUV’s yaw and pitch motion.

In our design, the duct propeller is driven by a main electric motor installed in the rotating body, which is aligned with the holes of the duct’s inner shaft with fastening screws. In order to simplify the unnecessary transmission structure and reduce the redundant weight, the main motor has been bedded on the rotating body with a duct propeller. It is very clean and efficient to take direct connects with the propeller and the main motor. This installation mode of the main motor and rotating body can improve space utilization significantly and reduce the weight of vectored thruster effectively. And this modularity makes the duct propeller system easy to maintain and debug on the whole vectored thruster control system.

As the implementing actuator of the vectored thruster, the thrust-vectoring mechanism is fundamental to the overall system for its basic functions. There are many methods on how to realize thrust vectoring, and each method has its own advantages and disadvantages. Considering the limited space of AUVs’ tailcone and the harsh operation condition, it is central to choose an appropriate mechanism structure that can complete the design function of achieving vector control effectively for AUVs. Comparing to the serial mechanism, parallel manipulators have many inherent superiorities, such as small size, compact and reasonable structure, reliable performance, fast response, high positioning precision, high stability, high sensitivity, high stiffness, and better dynamic performance.

Integrating practical application environment of AUVs and based on the application background of various parallel manipulators, 3RPS parallel manipulator is chosen as the thrust-vectoring mechanism after analyzing various mechanical structures. In accordance with this notion, a novel thrust-vectoring mechanism based on the 3RPS parallel manipulator for AUVs is designed, as shown in Figure

Thrust-vectoring mechanism based on 3-RPS parallel manipulator.

The thrust-vectoring mechanism is designed based on 3-RPS manipulator, which has a top rotting platform, a fixed base, and three identical sets of driving limbs and joints. Each driving limb has an actuating prismatic joint (

The 3RPS parallel manipulator has two rotational and one translational degree of freedom (DOF). It is superfluous to have the translational DOF for the thrust-vectoring mechanism, the redundant DOF needs to be constrained by motion control, and the other two rotational DOFs are used to realize functions of the thrust-vectoring mechanism. In addition, the translational DOF of 3RPS parallel manipulator will make the top rotating body bump into the shell of the AUV. So, the importance of the study on redundant DOF of the 3RPS parallel manipulator is obvious for the actual application of the thrust-vectoring mechanism.

Since the vectored thruster could generate required control forces for controlling AUVs motion, there is no need to have extra rudders as conventional AUVs. The component of the thrust as control forces is dependent on the deflection angle and the thrust of the vectored thruster. Therefore, the research on deflection angle of the vectored thruster is essential for controlling the motions of AUVs. However, it is very difficult to measure the tilt angle of the vectored thruster directly because the limited space and underwater environment is not suitable for installing sensors to measure. Another common and efficient approach to get the rotation angles is using the kinematic analysis method, which can obtain the tilt angle by measuring the lengths of the three limbs. Based on this kinematic method, tilt angle information about the vectored thruster can be obtained via relative calculation with the lengths of three limbs, which can be measured directly by length sensors installed in actuators.

In order to realize precision and stable positioning control of the proposed vectored thruster, the design of the automation control system is fundamental to achieve objectives. Hence, establishment of kinematic and dynamic models for the thrust-vectoring mechanism based on the 3RPS parallel manipulator is significant to achieving perfect control of the vectored thruster based on the above analysis.

The thrust-vectoring mechanism is designed based on the 3-RPS parallel manipulator, which is composed of a base plate, a rotating platform, and three uniformly distributed driving limbs, as shown in Figure

Schematic diagram of the 3-RPS parallel manipulator.

The moving sides of driving limbs (linear actuators) are connected to the upper rotating platform through three sphere joints that is fixed directly to the center of the top platform, while the other sides of the limbs are connected to the base with three revolute joints that are symmetrical about the center of base. _{1}, _{2}, and _{3} are the connected points between the fixed base and the driving legs (linear actuators), _{1}, _{2}, and _{3} denote the points of the revolute joints. It should be mentioned that _{1}_{1}, _{2}_{2}, and _{3}_{3} are perpendicular to the fixed base because _{1}_{1}, _{2}_{2}, and _{3}_{3} represent revolute joints with a certain height. A reference frame _{1}, _{2}, and _{3}, and this plane parallels with the fixed base _{1}, _{2}, and _{3}. The connected points between the moving parts and the rotating platform are expressed as _{1}, _{2}, and _{3}. The radius of the fixed base and the top platform are defined as _{1} and _{2}, _{1}, _{2}, and _{3} denote the lengths of three linear actuators between the top platform and the fixed base.

As we can see in Figure _{1}, _{2}, and _{3} is expressed as _{1} = _{2} = _{3} = _{1}. Hence, the location of _{i} in global reference frame

Similarly, _{1}, _{2}, and _{3} denote the axes of revolution of the revolute joints with a certain height _{r}, and this plane parallel is with the fixed base. Hence, the locations of point _{i} can be denoted as follows:

A local coordinate system _{1}, _{2}, and _{3}. So, the locations of connection point between the linear actuators and the top platform can be described as follows:

From Figure

The thrust-vectoring mechanism only needs two rotational DOFs to realize its functionality; the 3RPS parallel manipulator has one more translational DOF that is redundant. In order to present the condition of the top rotating platform of the thrust-vectoring mechanism, the rotation angles are also important parameters that need to be defined. According to the need of the thrust-vectoring mechanism, the displacement between centers of the base and the top platform are set as _{x}, _{y}, and _{x} and _{y} also can be written as follows:_{Px}, _{Py}, and _{Ly} denote the influence factor of _{x}, _{y}, and _{P}. According to the application needs to be designed in this design, the numerical simulations about _{Px}, _{Py}, and _{LP} and the angle of rotation of

Influence factor.

From Sections

In this design, inverse position analysis of the thrust-vectoring mechanism is carried out to establish the mapping relations between the position and orientation of top moving platform and the lengths of three driving linear actuators. Referring to Figure _{i} with respect to the fixed base reference frame _{i} (_{i}) denotes the vector from point _{i} (_{i}) in frame

The length change of the _{ave} is the initial length of the linear actuators at the tilt angle

According to (

Geometric Parameters of the thrust-vectoring mechanism.

Symbol | Value (unit) |
---|---|

_{1} | 100 (mm) |

_{2} | 60 (mm) |

330 (mm) | |

_{r} | 10 (mm) |

Length changes of linear actuators.

To further study the relationship between the tilt angles of the top rotating platform and the lengths of three linear actuators, the top moving platform moves according to _{s} = _{s} = _{s} and _{s}, based on the kinematic analysis of the thrust-vectoring mechanism above, the length of linear actuators is plotted in Figure

Length of linear actuators.

Similarly, the forward position analysis of the thrust-vectoring mechanism is established to study the mapping relations between the lengths, three linear actuators, and the position and orientation of top moving platform. The position and orientation of the top moving platform is obtained according to the given length of the

Referring to Figure _{i} on the top rotating platform in global frame _{i}_{i} denotes the vector of the _{1i} is the angle between the actuator and the fixed base. Since points _{1}, _{2}, and _{3} form an equilateral triangle in the top rotating platform, based on the theory in geometry, the relationship of _{1}_{2}_{3} can be determined by

Hence, the position of points _{i} in reference frame

Because _{1}_{2}_{3} in the top moving platform, the position of center point _{x}, _{y}, _{z}).

The position vector _{i} of points _{i} is regarded as a known parameter when the length of linear actuator is given; thus, the three equations about the point of

To further investigate the relationship between the lengths of linear actuators with the position and orientation of the top platform, different lengths of the linear actuator are used for the forward kinematic analysis. In this simulation, the linear actuator _{1}_{2} ∈ [310 340] mm and _{3} = 310, 325, 340 mm. According to equations (

The position and orientation of the top rotating platform with certain actuator lengths.

Due to the available space of AUV is limited, it is important to analyze the workspace of the thrust-vectoring mechanism for optimizing structure design and improving performance. According to the kinematic analysis mentioned above, all the positions and orientations of the top rotating platform can be obtained by changing the lengths of actuators. Considering the motion characteristics of the thrust-vectoring mechanism and constraint on available space, the workspace analysis is mainly referring to study the tilt angle and angle change of the revolute joint and spherical joint of the thrust-vectoring mechanism in this paper.

In this section, _{r} and _{t} denote, respectively, the rotational angles of the revolute joint and spherical joint. The schematic diagram of revolute joint and spherical joint is presented, as shown in Figure

Schematic diagram of revolute joint and spherical joint.

The tilt angle _{ri} and angle change ∆_{ri} of the revolute joint at point _{i} can be defined by_{1} is the direction vector of the

The tilt angle _{ti} and angle change _{ti} of the spherical joint at point _{i} can be expressed as_{1} is the direction vector of the _{t-avg} is the initial angle between the linear actuators with the rotating platform at the tilt angle

Similarly, to study the relations between the tilt angles of revolute and spherical joints and the lengths of linear actuators, the tilt angles of revolute joint _{ri} and spherical joint _{ti} by forward kinematic analysis are performed with linear actuator length _{1}_{2} _{3} = 310, 325, 340 mm. The simulation results are plotted in Figure

Tilt angle of revolute and spherical joint of the actuator by forward kinematic analysis.

The tilt angle of the three linear actuators and the top rotating platform has close relation, the platform moves according to _{s} and _{s} mentioned above. When the top rotating platform moves according to _{s} and _{s} (_{s} = _{s} =

The tilt angle and angle change. (a) _{ri}. (b) _{ri}. (c) _{ti}. (d) _{ti}.

For improving the dynamic performance and control accuracy of the designed vectored thruster, it is greatly important to analyze the dynamics model. Since the thrust-vectoring mechanism is designed based on the 3RPS parallel manipulator, which includes three closed-loops kinematic chains, it is very complicated to perform the dynamic analysis of the thrust-vectoring mechanism.

According to the theoretical analysis and practical needs, the dynamic model of the thrust-vectoring mechanism based on the 3RPS parallel manipulator is established. The schematic diagram of the dynamic analysis model of the 3RPS parallel manipulator is represented graphically, as shown in Figure

Schematic diagram of the dynamic model of the thrust-vectoring mechanism.

Referring to Figure _{Bi} and _{Bi} denote force and moment applied at point _{i}, and _{Ci} and _{Ci} denote force and moment at point _{i} accordingly. _{gi} and _{bi} are the gravity and buoyancy of the linear actuator, _{gi} and _{bi} denote the moments generated by gravity and buoyancy of the linear actuator, respectively. It should be noted that the buoyancy of the linear actuator _{bi} can be obtained by the diameters _{r} and _{t} of bottom section and the movable part and the length of bottom section _{r}. _{t} and _{i} represent the mass of the translating component and the inertia moment of the linear actuator. _{ti} denotes the vector from point _{i} to the mass center of linear actuator, and

Due to acting by an external force and moment, it is necessary to carrying out dynamic analysis of the top moving platform for establishing overall dynamics model for the thrust-vectoring mechanism. According to the forces and moments distributions analysis of the proposed thrust-vectoring mechanism, the stress conditions of the top platform can be represented as Figure

Schematic diagram of the dynamic analysis of the rotating platform.

As shown in Figure _{i} generated from many respects, such as the linear actuator, the top rotating platform, and duct propeller. Based on the definition of forces and moments at point _{i} above, the dynamical equations of the top rotating platform can be expressed as_{P} and _{Ci} denotes actuating force from the linear actuator along the direction of actuator. Because the top platform is an axisymmetric structure, _{b−P} are the gravity and buoyancy from the top platform, and _{1}_{2}_{3} to the center of mass and buoyancy of the top rotating platform, respectively. _{e} and _{e} are the external force and moment mainly generated from the propeller and the duct in our paper. Referring to Figure _{e} and external moment _{e} can be defined as_{prop} and _{duct} denote the force generated by the propeller and the duct of the thrust-vectoring mechanism and _{e} denotes the moment generated by the duct, respectively. The thrust vector _{prop} is produced by the propeller and can be expressed as_{p} denotes the thrust produced by propeller and based on standard propeller theory [_{p} = _{T}^{2}_{p}^{4}. _{T}, _{p}, and

In this AUV, the duct propeller has been widely adopted to protect from damage and improve the propulsive efficiency by being enclosed by a duct. To further investigate the dynamic model of the vectored thruster, it is clearly necessary to considerate the effect on lift and drag generated by the duct. The force generated by the duct applied to the platform can be expressed as

Because the duct rotates around the center of the duct in use, a transformation matrix _{d} is established to convert the duct frame into the body frame, and the matrix _{d} can be described as

Referring to equations (_{duct} and moment _{duct} generated by the duct that are applied on the platform of the thrust-vectoring mechanism can be calculated as

Finally, based on the above analysis and according to Figures _{i} denotes the force produced by the linear actuator to complete the key components of drive function and _{i} is the unit vector of the

In order to do a better research on the effect of motion on the vectored thruster, the numerical dynamic simulation on the thrust-vectoring mechanism has been developing. Some parameters used in the simulation, such as the dimension parameters of vectored thruster, are calculated through CAD software, and other parameters can be obtained by in [

Parameters of the thrust-vectoring mechanism.

Symbol | Value (unit) |
---|---|

_{r} | 50 (mm) |

_{t} | 10 (mm) |

_{r} | 250 (mm) |

35 (mm) | |

_{b−p} | 70 (mm) |

100 (N) | |

_{b−p} | 30 (N) |

_{gi} | 20 (N) |

_{p} | 200 (N) |

_{p} | diag (3.2 3.2 1.54) (kg · m^{2}) |

_{i} | diag (24.5 24.5 0.1) (kg · m^{2}) |

_{t} | 0.1 (kg) |

60000 | |

40000 | |

15000 |

Based on the abovementioned theory analysis and parameters, the analysis formulations in Section

When only considering the thrust produced by the duct propeller and the top platform moving according to

Length change of actuators at _{s} and

Driving forces of actuators at _{s} and

In the dynamic analysis above, the gravity, buoyancy, drag, and torque of the vectored thruster is ignored. When the weights of the rotating platform and the three actuators are taken into account only, the driving forces of the linear actuator can be calculated and plotted in Figure

Driving forces of actuators at _{s} and

In addition, the buoyancy of actuator depends on the length changes of actuators, and the buoyancy of linear actuator can be calculated by the length change. When the top platform moves according to the designed trajectory, the buoyancy is created with the movement of the vectored thruster and the result of buoyancy is shown in Figure

Buoyant forces of actuators at _{s} and

As we can see in Figure

Generally, the emphases of dynamic analysis of the parallel manipulator for research are mainly focused on the gravity, the external force, and torques. However, the buoyancy is also an important factor that affects the driving force of the actuators because the designed vectored thruster is used in underwater vehicles. In addition, the buoyancy of the other parts can be directly calculated by CAD software.

With considering the buoyant forces of actuators as shown in Figure

Driving forces of actuators at _{s} and

Comparing the driving forces in Figures

In order to investigate the performance and characteristic of the vectored thruster more fully, some influential factors of the duct have been considered in the following simulations. Referring to (

Drag (a), lift (b), and pitch moment (c) with different angles of attack.

Based on the dynamics parameters of the duct, as shown in Figure

Force (a) and moment (b) generated by the duct at _{s} and

The calculation results show that the influential factors of the duct play a very important role in calculating the driving forces of actuators; hence, the influential factors of the duct should be considered in a calculation schedule.

To improve the performance of the vehicle motion control, the tilt angles

Control scheme of the thrust vector control system.

Control scheme of the thrust-vectoring mechanism.

Model of the the thrust-vectoring mechanism with Simscape Mutibody.

To further investigate the performance of proposed control model, related numerical simulations are carried out with top platform moves according to = _{s} and

The length response of the linear actuator.

The simulation results from Figures

Driving forces of linear actuator.

Comparing the driving force in Figures

In this paper, a design scheme for the vectored thruster based on a 3RPS parallel manipulator is proposed to solve the effect of the control surface weakening problems. Parallel manipulators have several advantages over the mechanical structure and are suitable for various application fields, such as compact and reasonable structure, fast response, and high positioning precision. Because of the merits of itself, this type mechanical structure is used to design the thrust-vectoring mechanism considering the limited space and hash environment. Additionally, a duct propeller is adopted as power source of the proposed vectored thruster, which is installed on the top rotating platform with a main motor as a whole structure, thereby this design ensures compact structure, reliable motion, and high propulsive efficiency. Because the control force is provided by the component force of thrust rather than common rudders, the proposed vectored thruster AUVs have the abilities to complete all kinds of certain tasks and operations at a low forward speed.

In order to make sure the designed vectored thruster can run efficiently and stably, studying and developing the control system is fundamental to implement the design function of the vectored thruster. Owing to the importance of control system, related theoretical research about kinematics and dynamics of the thrust-vectoring mechanism is carried out to establish the motion model. In the kinematic analysis, the inverse and forward kinematics of the thrust-vectoring mechanism is presented, and the numerical simulations are accomplished to prove the feasibility and effectiveness of this design. In the section of workspace analysis, the study of the tilt angles of revolute and spherical joints is also carried out to make sure the motion platform can implement its designed function in limited motion space. In order to further verify feasibility of the thrust-vectoring mechanism, based on the considerations of various affecting factors, a dynamics model of the designed thrust-vectoring mechanism is established according to theoretical analysis, and the driving forces of the linear actuator are presented though a series of numerical simulations. In addition, a control scheme based on PID algorithm is proposed for the thrust vector control system on the existing work basis, and a control model is established using Simsacpe Mutibody, and the simulation results proved the feasibility of the proposed control scheme, which can effectively realize the goal of controlling the thrust-vectoring mechanism.

According to the above, the designed vectored thruster is able to provide the vectored thrust effectively and efficiently, and the AUVs equipped with vectored thruster are able to complete a variety of the complex tasks at a comparably low forward speed.

In the future research, a series of numerical simulations and theoretical study are carried out to investigate hydrodynamic performance of this vectored thruster AUV. On this basis, a prototype of this designed vectored thruster will be developed and experimental test will be carried out to verify the principles design. Moreover, the corresponding control system of the vectored thruster as a part of the AUV will be developed and tested in pools or open water to check its performance.

The data used to support the findings of this study are included within the article.

The authors declare that they have no conflicts of interest.

This work was supported by the National Natural Science Foundation of China (Grant no. 51879220).