# Investigation of Snake Robot Locomotion Possibilities in a Pipe

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## Abstract

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## 1. Introduction

## 2. Review of Snake Robot Applications in a Pipe

## 3. Design and Analysis of Locomotion Pattern in a Pipe

## 4. Simulation of Locomotion

## 5. Development of Experimental Snake Robot

#### 5.1. Mechanical Design of Snake Robot

#### 5.2. Electrical and Control System of Snake Robot

## 6. Experiments with Snake Robot in a Pipe

#### 6.1. Locomotion Pattern in a Pipe

#### 6.2. Locomotion on Different Surfaces

#### 6.2.1. Friction Models

#### 6.2.2. Testing of Locomotion on Different Kinds of Surfaces

#### 6.3. Experimental Analysis of Stability

#### 6.3.1. Mathematical Background of Symmetrical Curves

**Triangular Curve**

**Cycloid Curve**

**Gaussian curve**

#### 6.3.2. Digital Image Correlation Method

#### 6.3.3. Measurement of Stability by DIC Method

## 7. Conclusions

- Design of concertina locomotion based on revolute and linear joints of snake robot module. Design of mathematical model and analysis of the influence of input parameters.
- Development of a unique experimental snake robot consisting of eight modules, each with one revolute and one linear joint.
- Simulation and experimental analysis of proposed concertina locomotion.
- Experimental analysis of snake robot locomotion on different types of surfaces: dry, with a layer of oil, and with a layer of lubricant. Measured friction in both directions for all cases led to almost symmetrical characteristics. The results showed that electrical current consumption for all cases was almost the same. The robot traveled its maximum possible distance with dry friction. However, with oil or lubricant on the surface, some modules slid backward, resulting in less traveled distance per three locomotion cycles.
- A new approach based on anchoring of snake robot modules during locomotion in a pipe by means of symmetrical curves. Experimental analysis of their stability with changing slope of the pipe by modern DIC methodology using Q-450 Dantec Dynamics high-speed correlation system. The best solution was the use of a triangular curve. The circular pipe offered better stability for snake robot locomotion in the pipe.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Corn snake concertina locomotion [13]

**Figure 6.**Snake robot locomotion in rectangular pipe using concertina and rectilinear locomotion patterns.

**Figure 15.**Friction models: (

**a**) Coulomb (without static friction), (

**b**) Coulomb + viscous friction (without static friction), (

**c**) stiction + Coulomb + viscous friction, (

**d**) Stribeck.

**Figure 30.**Typical reference images captured by Q-450 Dantec Dynamics high-speed digital image correlation system.

**Figure 32.**Pipe with rectangular cross-section and slope 0°: (

**a**) supply voltage 4V DC, (

**b**) supply voltage 8V DC.

**Figure 33.**Pipe with rectangular cross-section and slope 10°: (

**a**) supply voltage 4V DC, (

**b**) supply voltage 8V DC.

**Figure 34.**Pipe with rectangular cross-section and slope 20°: (

**a**) supply voltage 4V DC, (

**b**) supply voltage 8V DC.

**Figure 35.**Pipe with rectangular cross-section and slope 30°: triangle fixation curve, supply voltage 8V DC.

**Figure 36.**Pipe with circular cross-section and slope 0°: (

**a**) supply voltage 4V DC, (

**b**) supply voltage 8V DC.

**Figure 37.**Pipe with circular cross-section and slope 10°: (

**a**) supply voltage 4V DC, (

**b**) supply voltage 8V DC.

**Figure 38.**Pipe with circular cross-section and slope 20°: (

**a**) supply voltage 4V DC, (

**b**) supply voltage 8V DC.

**Figure 39.**Pipe with circular cross-section and supply voltage 8V DC with (

**a**) slope 30°, (

**b**) slope: 40°.

**Table 1.**Technical specifications of Q-450 Dantec Dynamics high-speed cameras used for experimental analysis.

Field of view | Adjustable from several mm^{2} to several m^{2}Typical size from 70 × 50 mm ^{2} to 400 × 300 mm^{2} |

Measuring range | Displacement: ≈10^{–5} of field of view (100 mm field corresponds to 1 μm) |

Exposure time | Adjustable from 300 ns |

Resolution | Max. 1280 × 800 px up to sampling frequency of 3140 fps |

Results form | 3D contour of analyzed object, 3D displacement |

Control electronics | Laptop with Windows 7 and Istra4D control software, 16-bit AD/DA converter (eight channels with voltage range from ±0.05 V to ±10 V) |

Illumination | High-power halogen lamp with natural light |

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## Share and Cite

**MDPI and ACS Style**

Virgala, I.; Kelemen, M.; Božek, P.; Bobovský, Z.; Hagara, M.; Prada, E.; Oščádal, P.; Varga, M.
Investigation of Snake Robot Locomotion Possibilities in a Pipe. *Symmetry* **2020**, *12*, 939.
https://doi.org/10.3390/sym12060939

**AMA Style**

Virgala I, Kelemen M, Božek P, Bobovský Z, Hagara M, Prada E, Oščádal P, Varga M.
Investigation of Snake Robot Locomotion Possibilities in a Pipe. *Symmetry*. 2020; 12(6):939.
https://doi.org/10.3390/sym12060939

**Chicago/Turabian Style**

Virgala, Ivan, Michal Kelemen, Pavol Božek, Zdenko Bobovský, Martin Hagara, Erik Prada, Petr Oščádal, and Martin Varga.
2020. "Investigation of Snake Robot Locomotion Possibilities in a Pipe" *Symmetry* 12, no. 6: 939.
https://doi.org/10.3390/sym12060939