# Stability Control and Turning Algorithm of an Alpine Skiing Robot

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## Abstract

**:**

## 1. Introduction

## 2. System Modeling Consideration

#### 2.1. Robot Kinematics

#### 2.2. Turn Radius of a Carving Turn

#### 2.3. Modeling the Forces Applied to the Ski Plate

## 3. Navigation Using a LiDAR Sensor

#### 3.1. LiDAR Sensor

#### 3.2. Navigation Algorithm

## 4. Stability Control

## 5. Simulation Results

## 6. Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**(

**a**) Turn radius ${r}_{d}$; (

**b**) Parameters characterizing of ski geometry; (

**c**) Edging angle $\theta $ and penetration depth $e$.

**Figure 3.**(

**a**) $\phi $ is the lean angle between ${y}_{CoM}$ and middle of the vertical line, $\theta $ is an edging angle, ${z}_{c}$ is a constant CoM height normal to the snow surface; (

**b**) Approximation of $\phi $ and $\theta $.

**Figure 5.**${\theta}_{ref}$ is the direction of the skiing robot and ${\theta}_{target}$ is the angle from the skiing robot to the middle of the gate.

**Figure 6.**(

**a**) Robot’s feet with force-sensing resistor (FSR) sensors; (

**b**) Stable region of the zero-moment point (ZMP).

**Figure 9.**The skiing robot’s turn radius (

**a**) ${r}_{d}=6$ [m] is inputted; (

**b**) ${r}_{d}=3$ [m] is inputted.

**Figure 13.**The results of the ZMP control in long interval gates (

**a**) ${\mu}_{slope}=0.09$, $\alpha ={8}^{\xb0}$; (

**b**) ${\mu}_{slope}=0.12,\text{}\alpha ={10}^{\xb0}$.

**Figure 14.**The trajectory of the skiing robot in long interval gates (

**a**) ${\mu}_{slope}=0.09$, $\alpha ={8}^{\xb0}$; (

**b**) ${\mu}_{slope}=0.12,\text{}\alpha ={10}^{\xb0}$.

**Figure 15.**The linear velocity of the skiing robot (

**a**) ${\mu}_{slope}=0.09$, $\alpha ={8}^{\xb0}$; (

**b**) ${\mu}_{slope}=0.12,$ $\alpha ={10}^{\xb0}$.

**Figure 16.**Algorithm performance according to friction coefficient and slope angle in long interval gates (

**a**) with stability control; (

**b**) without stability control.

Gate Number | Short Interval (m) | Long Interval (m) | ||
---|---|---|---|---|

Front | Horizon | Front | Horizon | |

1 | 13 | 1 | 13 | 2 |

2 | 21 | 5 | 23 | 12 |

3 | 29 | 4 | 33 | 3 |

4 | 37 | 8 | 43 | 14 |

5 | 49 | 6 | 58 | 2 |

6 | 61 | 9 | 70 | 11 |

7 | 73 | 11 | 85 | 4 |

8 | 85 | 7 | - | - |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Kim, S.-H.; Lee, B.; Hong, Y.-D. Stability Control and Turning Algorithm of an Alpine Skiing Robot. *Sensors* **2019**, *19*, 3664.
https://doi.org/10.3390/s19173664

**AMA Style**

Kim S-H, Lee B, Hong Y-D. Stability Control and Turning Algorithm of an Alpine Skiing Robot. *Sensors*. 2019; 19(17):3664.
https://doi.org/10.3390/s19173664

**Chicago/Turabian Style**

Kim, Si-Hyun, Bumjoo Lee, and Young-Dae Hong. 2019. "Stability Control and Turning Algorithm of an Alpine Skiing Robot" *Sensors* 19, no. 17: 3664.
https://doi.org/10.3390/s19173664