# Development and Control of an Innovative Underwater Vehicle Manipulator System

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## Abstract

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## 1. Introduction

- A novel concept of a dual-arm UVMS with manipulators as its core is proposed, the mechanical structure is designed in detail based on the modular design approach, and the control architecture is constructed based on the Robot Operating System (ROS).
- The dynamic model of FAUVMS that considers dynamic coupling is developed, and the RNEM is used to evaluate the dynamic coupling effects in the system.
- A robust adaptive controller is designed based on CTC, EKF and chattering-free SMC, and the closed-loop stability is guaranteed by Lyapunov theory.
- The simulation platform for FAUVMS is proposed based on Gazebo and the unmanned underwater vehicle simulator (UUVSimulator), and simulations are carried out to verify the effectiveness of the proposed control method.

## 2. Design of FAUVMS

#### 2.1. Mechanical Structure

#### 2.2. Control Architecture

#### 2.2.1. Ground Control Station

#### 2.2.2. Mission Layer

#### 2.2.3. Execution Layer

#### 2.2.4. Perception Layer

## 3. Dynamic Modeling of FAUVMS

#### 3.1. General Model of FAUVMS

#### 3.2. Coupling Force Estimation

## 4. Robust Adaptive Control of FAUVMS

#### 4.1. EKF Disturbance Observer Design

#### 4.2. Chattering-Free Sliding Mode Controller Design

**Theorem**

**1.**

- (i)
- In the absence of uncompensated disturbances, i.e., $d=0$, the system error $\tilde{q}$ will converge to zero in finite time.
- (ii)
- In the presence of uncompensated disturbances, i.e., $d\ne 0$, the system error will converge to the region$$\begin{array}{cc}\hfill \phantom{\rule{1.em}{0ex}}& \hfill ||s||\le \mathsf{\Delta}=min\{\frac{{\left|\right|M\left(q\right)}^{-1}\left|\right|d}{\overline{{k}_{s1}}},{\left(\frac{{\left|\right|M\left(q\right)}^{-1}\left|\right|d}{\overline{{k}_{s2}}}\right)}^{1/\varrho}\}\hfill \end{array}$$$$\begin{array}{c}\hfill |\tilde{{q}_{i}}|\le 2\mathsf{\Delta},|\tilde{\dot{{q}_{i}}}|\le {\left(\frac{\mathsf{\Delta}}{{\alpha}_{i}}\right)}^{1/{\gamma}_{i}},\end{array}$$

**Proof.**

## 5. Simulation and Analysis

#### 5.1. Description of the Simulation Platform

#### 5.2. Description of the Scenarios

#### 5.3. Results and Discussion

#### 5.3.1. Scenario 1

#### 5.3.2. Scenario 2

#### 5.3.3. Scenario 3

## 6. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Mechanical structure of FAUVMS. (

**a**) CAD drawing of FAUVMS. (

**b**) Thruster layout of FAUVMS. (

**c**) The control warehouse of FAUVMS. (

**d**) CAD drawing of the manipulator. (

**i**) Perspective drawing of the four DOF manipulator. (

**ii**) Prototype of the four DOF manipulator. (

**iii**) Prototype of the joint module. (

**iv**) CAD drawing of the joint and gripper.

**Figure 7.**Tracking history of positions and attitudes of the vehicle with different controllers in Scenario 1. (

**a**–

**c**) Tracking errors of the surge, sway and heave displacements. (

**d**–

**f**) Tracking errors of the roll, pitch and yaw angles.

**Figure 8.**Tracking history of the positions of each end-effector with different controllers in Scenario 1. (

**a**–

**c**) Tracking errors of the left end-effector in the X, Y and Z directions. (

**d**–

**f**) Tracking errors of the right end-effector in the X, Y and Z directions.

**Figure 9.**Tracking history of positions and attitudes of the vehicle with different controllers in Scenario 2. (

**a**–

**c**) Tracking errors of the surge, sway and heave displacements. (

**d**–

**f**) Tracking errors of the roll, pitch and yaw angles.

**Figure 10.**Tracking history of the positions of each end-effector with different controllers in Scenario 2. (

**a**–

**c**) Tracking errors of the left end-effector in the X, Y and Z directions. (

**d**–

**f**) Tracking errors of the right end-effector in the X, Y and Z directions.

**Figure 11.**Tracking history of positions and attitudes of the vehicle with different controllers in Scenario 3. (

**a**–

**c**) Tracking errors of the surge, sway and heave displacements. (

**d**–

**f**) Tracking errors of the roll, pitch and yaw angles.

**Figure 12.**Tracking history of the positions of each end-effector with different controllers in Scenario 3. (

**a**–

**c**) Tracking errors of the left end-effector in the X, Y and Z directions. (

**d**–

**f**) Tracking errors of the right end-effector in the X, Y and Z directions.

Parameters | Values | Parameters | Values |
---|---|---|---|

Vehicle mass | 63 kg | Metacentric height | <5 mm |

Vehicle length | 640 mm | Vehicle width | 450 mm |

Vehicle height | 450 mm | Maximum depth | 1000 m |

Max/Min thrust | 5 kg/−4 kg | Number of thrusters | 6 |

Payload of arm | 5 kg | Number of joints | 4 |

Link mass | 1.5/2.5/2.5/2.5 kg | Link length | 220/330/250/50 mm |

Link radius | 60/60/60/50 mm | IMU&Compass | Pixhawk |

Altimeter | Ping30 | Velocity logger | Waterlinked A50 |

Parameters | Values | Parameters | Values |
---|---|---|---|

Inertia of vehicle | $diag\left[11.5\phantom{\rule{3.33333pt}{0ex}}7.1\phantom{\rule{3.33333pt}{0ex}}11.5\right]$ ${\mathrm{kgm}}^{2}$ | COM of vehicle | ${\left[0\phantom{\rule{3.33333pt}{0ex}}0\phantom{\rule{3.33333pt}{0ex}}0\right]}^{T}$ mm |

COB of vehicle | ${\left[0\phantom{\rule{3.33333pt}{0ex}}0\phantom{\rule{3.33333pt}{0ex}}3\right]}^{T}$ mm | Ellipsoid parameters A | 280 mm |

Ellipsoid parameters B | 350 mm | Ellipsoid parameters C | 280 mm |

Inertia of link1 | $diag\left[7.6\phantom{\rule{3.33333pt}{0ex}}7.3\phantom{\rule{3.33333pt}{0ex}}4.5\right]$ ${\mathrm{gm}}^{2}$ | Inertia of link2 | $diag\left[5.8\phantom{\rule{3.33333pt}{0ex}}19.1\phantom{\rule{3.33333pt}{0ex}}17.2\right]$ ${\mathrm{gm}}^{2}$ |

Inertia of link3 | $diag\left[7.5\phantom{\rule{3.33333pt}{0ex}}20.6\phantom{\rule{3.33333pt}{0ex}}19.7\right]$ ${\mathrm{gm}}^{2}$ | Inertia of link4 | $diag\left[7.6\phantom{\rule{3.33333pt}{0ex}}7.3\phantom{\rule{3.33333pt}{0ex}}4.5\right]$ ${\mathrm{gm}}^{2}$ |

COM of link1 | ${\left[0\phantom{\rule{3.33333pt}{0ex}}17.8\phantom{\rule{3.33333pt}{0ex}}147.6\right]}^{T}$ mm | COM of link1 | ${\left[124.9\phantom{\rule{3.33333pt}{0ex}}4.7\phantom{\rule{3.33333pt}{0ex}}30.7\right]}^{T}$ mm |

COM of link3 | ${\left[108.9\phantom{\rule{3.33333pt}{0ex}}2.1\phantom{\rule{3.33333pt}{0ex}}9.6\right]}^{T}$ mm | COM of link4 | ${\left[0\phantom{\rule{3.33333pt}{0ex}}0\phantom{\rule{3.33333pt}{0ex}}238.6\right]}^{T}$ mm |

Volume of Link1 | $2.13\times {10}^{-3}$ ${\mathrm{m}}^{3}$ | Volume of Link2 | $1.64\times {10}^{-3}$ ${\mathrm{m}}^{3}$ |

Volume of Link3 | $1.64\times {10}^{-3}$ ${\mathrm{m}}^{3}$ | Volume of Link4 | $1.21\times {10}^{-3}$ ${\mathrm{m}}^{3}$ |

**Table 3.**Mean square errors (MSEs) of positions of each end-effector with different controllers in Scenario 1.

MSE/cm | PID | Mohan | Dai | Proposed |
---|---|---|---|---|

Left X | 1.89 | 1.23 | 3.36 | 1.31 |

Left Y | 2.19 | 1.39 | 3.98 | 1.65 |

Left Z | 1.78 | 2.31 | 1.45 | 0.29 |

Right X | 1.96 | 0.99 | 3.17 | 1.74 |

Right Y | 2.04 | 1.24 | 3.59 | 1.69 |

Right Z | 1.93 | 2.74 | 1.85 | 0.21 |

MSE/cm | PID | Mohan | Dai | Proposed |
---|---|---|---|---|

Left X | 1.74 | 1.92 | 1.49 | 0.93 |

Left Y | 1.95 | 2.33 | 1.35 | 1.23 |

Left Z | 4.99 | 4.15 | 3.89 | 1.02 |

Right X | 1.08 | 1.31 | 1.61 | 1.72 |

Right Y | 1.59 | 2.69 | 1.13 | 1.15 |

Right Z | 5.17 | 6.22 | 6.27 | 0.61 |

MSE/cm | PID | Mohan | Dai | Proposed |
---|---|---|---|---|

Left X | 9.28 | 9.24 | 9.71 | 1.63 |

Left Y | 1.88 | 3.37 | 4.33 | 1.59 |

Left Z | 5.23 | 3.95 | 3.82 | 1.92 |

Right X | 6.24 | 9.55 | 10.59 | 1.86 |

Right Y | 0.78 | 2.05 | 2.57 | 1.34 |

Right Z | 5.99 | 6.38 | 6.72 | 1.83 |

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## Share and Cite

**MDPI and ACS Style**

Zheng, X.; Tian, Q.; Zhang, Q.
Development and Control of an Innovative Underwater Vehicle Manipulator System. *J. Mar. Sci. Eng.* **2023**, *11*, 548.
https://doi.org/10.3390/jmse11030548

**AMA Style**

Zheng X, Tian Q, Zhang Q.
Development and Control of an Innovative Underwater Vehicle Manipulator System. *Journal of Marine Science and Engineering*. 2023; 11(3):548.
https://doi.org/10.3390/jmse11030548

**Chicago/Turabian Style**

Zheng, Xinhui, Qiyan Tian, and Qifeng Zhang.
2023. "Development and Control of an Innovative Underwater Vehicle Manipulator System" *Journal of Marine Science and Engineering* 11, no. 3: 548.
https://doi.org/10.3390/jmse11030548