# Mechanism Design and Experiment of a Bionic Turtle Dredging Robot

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Mechanism Analysis and Solution Method

#### 2.1. The Overall Bionic Design of the Dredging Robot

#### 2.2. Outrigger Mechanism Modeling and Positive Kinematics Analysis Method

_{F}is the angle between the ground and horizontal plane.

_{N}of the dredging robot is established, and the direction of each coordinate axis of the dredging robot O

_{N}is exactly the same as that of the geodetic coordinate system O

_{G}. The coordinate origin O

_{N}is the center of the upper layer of the dredging robot body, the x

_{0}direction is the same as the forward direction of the dredging robot, the z

_{0}direction is perpendicular to the plane of the body upward, and the y

_{0}direction is determined to point to the paper surface according to the right-hand rule. O

_{0}is the coordinate system where O

_{N}is translated from the upper center of the body to the hip joint, which is exactly the same as the direction of each axis of O

_{N}. O

_{0}rotates θ

_{1}around the y

_{0}axis to obtain the coordinate system O

_{1}. The origins of the two coordinates coincide. At this time, the x

_{1}axis of O

_{1}points downward along the supporting leg. O

_{1}first rotates θ

_{2}around the y

_{1}axis and then translates s

_{1}along the x

_{1}axis to obtain the ankle joint coordinate system O

_{2}. The x

_{2}axis of O

_{2}is perpendicular to the ground and downward. O

_{2}is translated l

_{1}along the x

_{2}axis to obtain O

_{F}, and the directions of each axis of O

_{F}and O

_{2}are exactly the same.

_{1}is (−0.75π, −0.25π). The angle of θ

_{2}is determined by β

_{F}and θ

_{1}together, θ

_{2}= 90° + β

_{F}− θ

_{1}.

_{N}, O

_{0}, O

_{1}, O

_{2}, and O

_{F}can be obtained, and then the transformation matrix between O

_{N}and O

_{F}can be obtained as shown in Equation (1).

^{N}X

_{F},

^{N}Y

_{F},

^{N}Z

_{F}representing the upper center of the body in the geodetic coordinate system, which are, respectively, equal to the three elements in the fourth column of the change matrix. Bring the above constants and variables into Equation (1) to obtain the foot’s motion range, as shown in Figure 4.

#### 2.3. Inverse Kinematics of Outrigger Mechanism and Method of Solving Body Pose

_{F}value will be obtained after landing on foot, it is replaced with the β

_{F}on the same side of the foot.

_{1}and variable s

_{2}can be obtained as shown in Equation (4).

_{1}and s

_{2}, as shown in Equations (5) and (6), respectively.

^{N}X

_{F}and

^{N}Z

_{F}, the coordinate range of the foot tip in the forward direction is (−0.95, −1.95), and the coordinate range in the vertical direction is (−0.9, −1.2). Substituting these values into Equations (5) and (6), the change diagrams of s

_{1}and s

_{2}corresponding to the coordinates of the foot in the advancing direction and the vertical direction can be obtained, as shown in Figure 6 and Figure 7, respectively.

_{1}is between 0.9 m and 1.3 m, that is, the change range of the length of the supporting telescopic mechanism is greater than 0.4 m. When the hip joint angle of the outrigger is not 90°, s

_{1}will increase to compensate for the z-axis coordinate change caused by the tilt of the outrigger, and the larger the s

_{1}, the greater the absolute value of the z-axis coordinate.

_{2}is between 1.4 m and 1.8 m, that is, the swing telescopic mechanism and the supporting telescopic mechanism have the same length, and the change range must be greater than 0.4 m. The size of s

_{2}in the figure is mainly related to the x-axis coordinate and the closer the foot is to the center of the body on the x-axis, the longer the length of the swing mechanism.

_{f}and z

_{h}, respectively. When the two feet are parallel to the horizontal plane, according to the geometric relationship in Figure 3, z

_{f}and z

_{h}can be obtained by Equation (7).

_{f}

_{1}and s

_{h}

_{1}are the lengths of the hip joint of the LF and RH of the dredging robot from the bare joint, respectively; l

_{f}

_{1}and l

_{h}

_{1}are the vertical distance between the ankle joint of the LF and the RH and the supporting plane of the foot; θ

_{f}

_{1}and θ

_{h}

_{1}are the swing angles of the hip joints of the LF and the RH, respectively; and θ

_{f}

_{2}and θ

_{h}

_{2}are the swing angles of the ankle joints of the LF and the RH, respectively. When l

_{f}

_{1}and l

_{h}

_{1}are equal, the value of the pitch angle β of the fuselage is calculated as shown in Equation (8).

## 3. Gait Analysis and Trajectory Planning of the Bionic Turtle Robot

#### 3.1. Turtle Crawling Mechanism

#### 3.2. Gait Analysis of the Bionic Turtle Robot

#### 3.2.1. Gait Sequence Design

#### 3.2.2. Three Kinds of Movement Gait of Dredging Robot

#### 3.3. Motion Track Design

_{0}, the forward direction of the foot should satisfy the position of 0 and E, respectively, and T

_{0}is the time of the single-leg swing. At the same time, in order to make the speed and acceleration of the piston rod of the electric cylinder more stable, the initial speed and the end speed of the foot in the forward direction are set to 0.

_{0}/2, and t = T

_{0}. Then, the displacement equation of the foot tip in the vertical direction is shown in Equation (11).

_{0}and T

_{0}—2T

_{0}are all in a supporting state. At this time, the foot trajectory equation of the RH and the LF is shown in Equation (12). After 2T

_{0}, the LF is lifted, and the RF and the LH in 3T

_{0}—4T

_{0}are all in a supporting state. At this time, the foot trajectory equation of the RF and the LH is shown in Equation (13).

_{1}and the abscissa of the foot can be obtained, and the relationship between θ

_{2}and θ

_{1}can be used to obtain the relationship between θ

_{2}and the coordinate of the foot, as shown in Equation (14).

_{0}and 2T

_{0}-4T

_{0}are different, two fixed support legs need to be determined before 2T

_{0}and after 2T

_{0}. In this way, the center trajectories of the front and hind ends of the body can be merged according to the coordinate relationship of the two fixed legs. In 0-2T

_{0}, select the foot of the RH as the reference coordinate origin of the body center coordinates and select the foot of the RF in 2T

_{0}-4T

_{0}.

_{0}can be obtained, and then substituting the obtained equation into Equation (9) calculates the center of the RH to obtain Equation (15).

_{0}-4T

_{0}time period, take the LF as a reference. According to the above method, the trajectory of the body center coordinate relative to the foot of the RF is obtained, and the trajectory of the body center in 0-4T

_{0}can be obtained by combining the coordinate of the RH relative to the LF before lifting.

_{1}and s

_{2}, and the time change of the RH leg s

_{1}and s

_{2}; the curves are shown in Figure 13a,b.

## 4. Gait Experiment of Dredging Robot

#### 4.1. Coordinated Gait Experiment

#### 4.2. Intermittent Gait Experiment

#### 4.3. Mixed Gait Experiment

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Cao, H.Q.; Zhou, J.J. Development and prospect of dredging at water conservancy works in China. J. Sedim. Res.
**2011**, 5, 67–72. [Google Scholar] - Manap, N.; Voulvoulis, N. Environmental management for dredging sediments—The requirement of developing nations. J. Environ. Manag.
**2015**, 147, 338–348. [Google Scholar] [CrossRef] [PubMed] - Seagren, E.H. Latest Developments in Small Hydraulic Dredges for Contaminated Sediment Removal in the USA. In Proceedings of the Third Specialty Conference on Dredging and Dredged Material Disposal, Orlando, FL, USA, 5–8 May 2002. [Google Scholar]
- Wang, H.X.; Wang, C.L.; Wang, C.Z. The Development of Boat-loaded Flushing-winching Submarine Dredging Machine. Mod. Manuf. Technol. Equip.
**2009**, 6, 32–34. [Google Scholar] - Cha, Y.H.; Sun, S.M. The actuality and developing trend of clearing silt technology and machine for lake and pond in china. Chin. Agric. Mech.
**2005**, 2, 27–30. [Google Scholar] - Ren, Z.X. Discussion on Silt Clearing and Silt Treatment in Middle and Small River. China Water Transp.
**2020**, 20, 180–181. [Google Scholar] - Liao, W.Q.; Luo, Z.Y.; Xu, S.M. Research Status and Development Trend of Underwater Cleaning Robot. Mech. Electr. Eng. Technol.
**2016**, 45, 12–14. [Google Scholar] - Xie, B.; Chen, C.; Zhang, G.X. Research and Implementation of Underwater Dredging Equipment Control System. Ship Eng.
**2017**, 39, 180–182. [Google Scholar] - Zhao, L. On Selection and Configuration of Dredging Construction Machinery. Value Eng.
**2017**, 13, 141–143. [Google Scholar] - Bao, J.P.; Zhu, W.; Min, J.H. Technology of dredging and sludge treatment in small and medium-sized river regulation. Water Resour. Protect.
**2015**, 31, 56–62. [Google Scholar] - Bruzzone, P.; Quaglia, L. Review article: Locomotion systems for ground mobile robots in unstructured environments. Mech. Sci.
**2012**, 2, 49–62. [Google Scholar] [CrossRef] [Green Version] - Hijdra, R.M.J.; Harst, S.V.D. Design of an Autonomous Underwater Maintenance Dredger: A teaser to the maritime industry. J. Phys. Conf. Ser.
**2019**, 1357, 012001. [Google Scholar] [CrossRef] - Raibert, M.; Blankespoor, K.; Nelson, G. BigDog, the rough-terrain quadruped robot. In Proceedings of the 17th World Congress on the International Federation of Automatic Control, Seoul, Korea, 6 July 2008. [Google Scholar]
- Semini, C.; Barasuol, V.; Boaventura, T. Towards versatile legged robots through active impedance control. Int. J. Robot. Res.
**2015**, 34, 1003–1020. [Google Scholar] [CrossRef] - Meng, J.; Liu, J.C.; Rong, X.W. Development status and prospect of quadruped robots. Sci. Technol. Rev.
**2015**, 33, 59–63. [Google Scholar] - Gonzalez, D.S.; Pablo, G.; Elena, E. Quadrupedal Locomotion. An Introduction to the Control of Four-Legged Robots; Springer: London, UK, 2006; pp. 50–92. [Google Scholar]
- Zeng, N.; Hang, G.R.; Cao, G.H. Present State and Tendency of Bionic Underwater Robot. Mech. Eng.
**2006**, 04, 18–21. [Google Scholar] - Chen, Y.H.; Tan, Y.G.; Li, Z. Method of Gait Generating for Quadruped Robot Walking on Rough Terrain. Comput. Meas. Control
**2016**, 24, 262–267. [Google Scholar] - Boussema, C.; Powell, M.; Bledt, G. Online Gait Transitions and Disturbance Recovery for Legged Robots via the Feasible Impulse Set. IEEE Robot. Auto. Lett.
**2019**, 04, 1611–1618. [Google Scholar] [CrossRef] - Koray, K.A.; Adams, G.G. Modeling and simulation of an artificial muscle and its application to biomimetic robot posture control. Robot. Auto. Syst.
**2002**, 41, 225–243. [Google Scholar] - Kim, J.Y.; Jun, B.H. Design of six-legged walking robot, Little Crabster for underwater walking and operation. Adv. Robot.
**2014**, 28, 77–89. [Google Scholar] [CrossRef] - Mao, S.; Dong, E.; Zhou, L. Design and Gait Analysis of a Tortoise-Like Robot with Soft Limbs. In Proceedings of the 18th International Conference on CLAWAR, HangZhou, China, 6–9 September 2015; Assistive Robotics, Printed in Singapore. pp. 215–223. [Google Scholar]
- Wang, D.; Li, H.; Lin, X. Study on the motion design and control algorithm of the tortoise robot. J. Phys. Conf. Ser.
**2019**, 1345, 042066. [Google Scholar] [CrossRef]

**Figure 6.**The length of the supporting leg and swinging leg in the desired coordinates: (

**a**) foot coordinates corresponding to s

_{1}size and (

**b**) foot coordinates corresponding to s

_{2}size.

**Figure 7.**Turtle’s crawling posture. (

**a**) the coordinated gait of a tortoise, (

**b**) The four legs of the tortoise and their corresponding symbols, (

**c**) the step sequence relationship.

**Figure 8.**The eight crawling stages of a tortoise. (

**a**) Before the LF moves, (

**b**) the LF vacated, (

**c**) before the RH moves, (

**d**) the RH vacated, (

**e**) before the RF moves, (

**f**) the RF vacated, (

**g**) before the LH moves, and (

**h**) the LH vacated.

**Figure 9.**Gait diagrams in different sequences. (

**a**) the moving of LH and RF, (

**b**) the moving of LH, and RH, (

**c**) the moving of LF, and RF, (

**d**) the moving of LF and RH.

**Figure 10.**The relative position of the body and the ends of the four legs in the intermittent gait. (

**a**) the LF has moved to the limit position, (

**b**) the LF drops the ground, (

**c**) the moving of LF, (

**d**) the moving of RF, (

**e**) the moving of RH and RF, (

**f**) the moving of LF and LH.

**Figure 11.**The relative position of the body and the ends of the four legs in the intermittent gait. (

**a**) the LF has moved to the limit position, (

**b**) the LF drops the ground, (

**c**) the moving of RH, (

**d**) the RH drops the ground, (

**e**) the moving of LH, (

**f**) the LH drops the ground.

**Figure 13.**Changes in the length of the supporting leg and swinging leg in two cycles: (

**a**) foot coordinates corresponding to s

_{1}size and (

**b**) foot coordinates correspond to s

_{2}size.

**Figure 15.**The motion state of the experimental prototype in a cycle in the coordinated gait: (

**a**) the RH is about to lift, (

**b**) the RF is about to lift, (

**c**) the LH is about to lift, and (

**d**) the LF is about to lift.

**Figure 17.**The motion state of the experimental prototype in a cycle in the intermittent gait: (

**a**) the RH is about to lift, (

**b**) the RF is about to lift, (

**c**) adjust the center of gravity for the first time, (

**d**) the LH is about to lift, (

**e**) the LF is about to lift, and (

**f**) adjust the center of gravity for the second time.

**Figure 18.**The motion state of the experimental prototype in a cycle in the mixed gait: (

**a**) the RH is about to lift, (

**b**) the RF is about to lift, (

**c**) adjust the center of gravity for the first time, (

**d**) the LH is about to lift, (

**e**) the LF is about to lift, and (

**f**) adjust the center of gravity for the second time.

Parameter Symbol | Parameter Meaning | Value |
---|---|---|

l_{1} | Vertical distance between ankle joint and foot plane | 160 mm |

l_{2} | The distance between the hinge point of the swing leg and the support leg and the hip joint in the vertical support leg | 220 mm |

l_{3} | The distance between the hinge point of the swing leg and the supporting leg and the hip joint along the supporting leg | 510 mm |

h | The vertical distance between the hinge point of the swing leg and the body and the plane of the body | 450 mm |

c | The vertical distance between the hinge point of the swing leg and the body and the center cross section of the body | 100 mm |

a | The distance between the hip joint and the short side of the body | 250 mm |

b | The distance between the hip joint and the long side of the body | 130 mm |

m | Half of the body length | 1700 mm |

n | Half of the body width | 1200 mm |

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**MDPI and ACS Style**

Wang, T.; Wang, Z.; Zhang, B.
Mechanism Design and Experiment of a Bionic Turtle Dredging Robot. *Machines* **2021**, *9*, 86.
https://doi.org/10.3390/machines9050086

**AMA Style**

Wang T, Wang Z, Zhang B.
Mechanism Design and Experiment of a Bionic Turtle Dredging Robot. *Machines*. 2021; 9(5):86.
https://doi.org/10.3390/machines9050086

**Chicago/Turabian Style**

Wang, Tao, Zhuo Wang, and Bo Zhang.
2021. "Mechanism Design and Experiment of a Bionic Turtle Dredging Robot" *Machines* 9, no. 5: 86.
https://doi.org/10.3390/machines9050086