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Energy Efficient Foot Trajectory of Trot Motion for Hydraulic Quadruped Robot^{ †}

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^{†}

## Abstract

**:**

## 1. Introduction

## 2. Robot Modeling

#### 2.1. General Method

#### 2.2. Kinematics of the SCalf Robot

#### 2.3. Dynamics of the SCalf Robot

## 3. The Foot Force Distribution

## 4. The Energy Model of the SCalf

## 5. The Foot Trajectory Analyses

#### 5.1. Stance Phase

#### 5.2. Swing Phase

#### 5.2.1. Reference Foot Trajectory

#### 5.2.2. Energy Efficient Foot Trajectory

#### 5.3. Energy Efficient Trajectory Generating Method

## 6. Simulations and Experiments

#### 6.1. MATLAB Simulation

#### 6.2. Experiments on the SCalf Robot

#### 6.3. Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A Solutions of the Fourier Coefficients

## References

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Parameter (i = 1,2) | Thigh | Shank |
---|---|---|

Mass(${m}_{i}$/Kg) | 4.10 | 2.24 |

Length(${l}_{i}$/mm) | 450.99 | 404.87 |

COM position(${l}_{mi}$/mm) | 210.43 | 227.20 |

COM angle(${\epsilon}_{i}$/rad) | 0.037 | −0.083 |

Moment of inertia(${I}_{i}$/Kg·m${}^{2}$) | 0.178 | 0.057 |

**Table 2.**Mechanical parameters used in Figure 6.

Joint | ${\mathit{a}}_{\mathit{i}}$(mm) | ${\mathit{b}}_{\mathit{i}}$(mm) | Angles(°) | |
---|---|---|---|---|

Pitching hip joint | 289.26 | 56.87 | ${e}_{1}$ = 5.36 | ${e}_{2}$ = 54.90 |

Pitching knee joint | 289.26 | 56.89 | ${e}_{3}$ = 8.02 | ${e}_{4}$ = 2.35 |

Items(time) | x-Direction | z-Direction |
---|---|---|

position(0) | $\frac{S}{2}$ | $-{z}_{0}$ |

position($\frac{T}{2}$) | $-{\displaystyle \frac{S}{2}}$ | $-{z}_{0}$ |

velocity(0) | $-{\displaystyle \frac{2S}{T}}$ | 0 |

velocity($\frac{T}{2}$) | $-{\displaystyle \frac{2S}{T}}$ | 0 |

Leg | Pitching Hip Joint | Pitching Knee Joint |
---|---|---|

RF/LF leg | −2.032 to 0.047 rad | 0.491 to 2.570 rad |

LH/RH leg | −0.047 to 2.032 rad | −2.570 to −0.491 rad |

Leg | ${\mathit{C}}_{1}$ | ${\mathit{C}}_{2}$ | Iteration Number |
---|---|---|---|

RF leg | −33.76 | 15.30 | 108 |

LH leg | −29.58 | −2.28 | 155 |

Trajectory | Leg | Stance Phase | Swing Phase | Total Energy |
---|---|---|---|---|

Reference | RF leg | 56.86 J | 28.18 J | 85.04 J |

LH leg | 55.03 J | 27.81 J | 82.84 J | |

Proposed | RF leg | 56.98 J | 20.78 J | 77.76 J |

LH leg | 55.24 J | 21.42 J | 76.66 J |

Trajectory | Leg | Stance Phase | Swing Phase | Total Energy |
---|---|---|---|---|

Reference | RF leg | 42.50 J | 29.46 J | 71.96 J |

LH leg | 39.46 J | 28.57 J | 68.03 J | |

Proposed | RF leg | 39.48 J | 26.86 J | 66.34 J |

LH leg | 38.17 J | 24.91 J | 63.08 J |

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**MDPI and ACS Style**

Yang, K.; Li, Y.; Zhou, L.; Rong, X.
Energy Efficient Foot Trajectory of Trot Motion for Hydraulic Quadruped Robot. *Energies* **2019**, *12*, 2514.
https://doi.org/10.3390/en12132514

**AMA Style**

Yang K, Li Y, Zhou L, Rong X.
Energy Efficient Foot Trajectory of Trot Motion for Hydraulic Quadruped Robot. *Energies*. 2019; 12(13):2514.
https://doi.org/10.3390/en12132514

**Chicago/Turabian Style**

Yang, Kun, Yibin Li, Lelai Zhou, and Xuewen Rong.
2019. "Energy Efficient Foot Trajectory of Trot Motion for Hydraulic Quadruped Robot" *Energies* 12, no. 13: 2514.
https://doi.org/10.3390/en12132514