# Path Planning of Hydraulic Support Pushing Mechanism Based on Extreme Learning Machine and Descartes Path Planning

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## Abstract

**:**

## 1. Introduction

## 2. Overall Framework

## 3. Trajectory Prediction of End-Effector in Equivalent Manipulator Model of Floating Connection Mechanism

#### 3.1. Establishment of the Dataset

#### 3.2. Extreme Learning Machines Model

#### 3.3. Model Evaluation Index

^{2}) are used as evaluation indexes of simulation deviation, which are used to reflect the difference between measured and simulated values and the fitting effect of the model.

#### 3.4. Comparison of Prediction Model Algorithms

^{2}are used as evaluation indexes. The data set of this section adopts the actual drum cutting height obtained from a coal mine in Shanxi, China, with a total of 17 × 39 sequences. This section uses the cutting height of the first 16 knives to predict the cutting height of the 17th knife.

^{2}value of the prediction results based on ELM prediction algorithm are the smallest and the largest respectively, which means that the error between the predicted value and the actual value is the smallest. Consequently, the ELM algorithm selected in this paper has a better prediction effect.

## 4. Path Planning of the End-Effector of The Equivalent Manipulator Model of Floating Connection Mechanism

#### 4.1. Establishment of Equivalent Manipulator Model of Floating Connection Mechanism

#### 4.2. Path Segmentation Technology

#### 4.3. Cartesian Path Planning

## 5. Motion Path Optimization Based on Gaussian Filter Correction

## 6. Establishment of Virtual Planning Space Based on Unity3D

#### 6.1. Construction of Virtual Coal Seam Floor Based on Reverse Reconstruction Technology

#### 6.2. Parameter Setting of Coal Mining Equipment

#### 6.3. Establishment of Virtual Contact Model

#### 6.4. Establishment of Virtual Control Model

## 7. Research on Virtual Simulation and Analysis

#### 7.1. Prediction and Application Results

^{2}value is between 0.98 and 0.99 and the MSE value is less than 0.01 respectively, which indicates that the trajectory predicted by ELM algorithm can be used as the basis of path planning.

#### 7.2. Experimental Results Based on Joint Action of Trajectory Planning and Correction

## 8. Conclusions and Prospect

- (1)
- A virtual simulation space equivalent to path planning of pushing mechanism is established. Based on actual geological conditions, the virtual coal seam is established, and virtual coal machine equipment is parameterized according to production requirements. After installing a physical engine for virtual equipment and coal seam, a visual and highly reliable virtual simulation space is established.
- (2)
- The proposed path planning model has a good planning effect. On the premise of obtaining the predicted trajectory, when Cartesian path planning method is used for planning, the coordinate curve of the planned equivalent end actuator fluctuates roughly around the true curve, and the planned trajectory is similar to Poisson distribution, with the maximum local error within 2 cm, the overall planning effect is better.
- (3)
- The modified model proposed in this paper has a better effect. The peak value of the planned curve is filtered to achieve local correction. The simulation test proves that the corrected curve error is within 0.1 cm, and the modified model proposed in this paper has a good correction effect.
- (4)
- After the path planning is applied to the virtual environment, the error between the actual path and the planned path is small, and the error is within 0.01 cm. Consequently, the path planning method proposed in this paper can be used to preliminarily realize the cooperation between hydraulic support and scraper conveyor.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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Algorithm Name | MSE | R^{2} |
---|---|---|

BP neural network | 0.005873 | 0.83075 |

SVM | 0.005966 | 0.783805 |

ELM | 0.0054874 | 0.97151 |

Symbol | Name | Meaning |
---|---|---|

${x}_{i}-{z}_{i}$ | Reference system | Local reference system assigned to each joint |

${\theta}_{i}$ | Articular angle | Angle of rotation of the ${x}_{i-1}$ axis around the xi axis |

${d}_{i}$ | Articular distance | Distance between ${x}_{i-1}$ axis and ${x}_{i}$ axis along ${z}_{i-1}$ axis |

${a}_{i}$ | Length of linkage | Distance between ${z}_{i-1}$ axis and ${z}_{i}$ axis along ${x}_{i}$ axis |

${\alpha}_{i}$ | Torsion angle of linkage | Rotation angle of ${z}_{i-1}$ axis around ${x}_{i}$ axis |

${l}_{1}$ | Length of the relay bar | |

${l}_{2}$ | Length of the joint |

Path Fragment | Polynomial | Range | Independent Variable | Boundary Conditions |
---|---|---|---|---|

${q}_{1}(t)$ | $\begin{array}{l}{q}_{1}(t)={a}_{0}+{a}_{1}(t-{t}_{0})+\\ {a}_{2}{(t-{t}_{0})}^{2}+{a}_{3}{(t-{t}_{0})}^{3}\end{array}$ | $q({t}_{0})<q(t)<q({t}_{1})$ | ${t}_{0}<t<{t}_{1}$ | ${q}_{1}({t}_{0})={q}_{0}$ |

${q}_{1}({t}_{0})=0$ | ||||

$\ddot{q}({t}_{0})=0$ | ||||

${q}_{1}({t}_{1})={q}_{1}$ | ||||

${q}_{2}(t)$ | ${q}_{2}(t)={b}_{0}+{b}_{1}t+{b}_{2}{t}^{2}$ | $q({t}_{1})<{q}_{2}(t)<q({t}_{2})$ | ${t}_{1}<t<{t}_{2}$ | ${q}_{2}({t}_{1})={q}_{1}$ |

${\dot{q}}_{2}({t}_{1})={\dot{q}}_{1}({t}_{1})$ | ||||

${q}_{2}({t}_{2})={q}_{2}$ | ||||

${q}_{3}(t)$ | ${q}_{3}(t)={c}_{0}+{c}_{1}t+{c}_{2}{t}^{2}$ | $q({t}_{2})<{q}_{3}(t)<q({t}_{3})$ | ${t}_{2}<t<{t}_{3}$ | ${q}_{3}({t}_{2})={q}_{2}$ |

${\dot{q}}_{3}({t}_{2})={\dot{q}}_{2}({t}_{2})$ | ||||

${q}_{3}({t}_{3})={q}_{3}$ | ||||

${q}_{4}(t)$ | $\begin{array}{l}{q}_{4}(t)={d}_{0}+{d}_{1}t+{d}_{2}{t}^{2}\\ +{d}_{3}{t}^{3}+{d}_{4}{t}^{4}\end{array}$ | $q({t}_{3})<{q}_{4}(t)<q({t}_{4})$ | ${t}_{3}<t<{t}_{4}$ | ${q}_{4}({t}_{3})={q}_{3}$ |

${\dot{q}}_{4}({t}_{3})={\dot{q}}_{3}({t}_{3})$ | ||||

${q}_{4}({t}_{4})={q}_{4}$ | ||||

${\dot{q}}_{4}({t}_{4})=0$ | ||||

${\ddot{q}}_{4}({t}_{4})=0$ |

Name | Model | Research Object | Theoretical Value | Actual Value (In Unity3D) |
---|---|---|---|---|

Hydraulic support | ZY11000/18/38D | Base | About 7700 Kg | About 77 Kg |

Scraper conveyor | MG400/920-WD | Middle trough | 153 Kg | 1.53 Kg |

Middle trough spacing | — | Adjacent middle trough | $l=\frac{\alpha \pi r}{360}$ | 0.216 cm |

Name | Function | |
---|---|---|

Rigidbody | Make the virtual object move under the control of physical system, and make the virtual object accept external force and torque to ensure that the motion of the object is the same as that of the real world. | |

Colliders | Box Collider | Use with Rigidbody components to trigger a collision that causes virtual objects to collide with each other, and in physical simulation rigid bodies that do not have collisions pass through each other. |

Mesh Collider | ||

Capsule Collider | ||

Character Joint | Low Twist Limit | It is used to restrict the rotation angle of joints under different rotation axes. The values of Low Twist Limit and High Twist Limit are set to −4 and 4 respectively. |

High Twist Limit |

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**MDPI and ACS Style**

Li, S.; Xie, J.; Wang, X.; Ren, F.; Zhang, X.; Bao, Q.
Path Planning of Hydraulic Support Pushing Mechanism Based on Extreme Learning Machine and Descartes Path Planning. *Symmetry* **2021**, *13*, 97.
https://doi.org/10.3390/sym13010097

**AMA Style**

Li S, Xie J, Wang X, Ren F, Zhang X, Bao Q.
Path Planning of Hydraulic Support Pushing Mechanism Based on Extreme Learning Machine and Descartes Path Planning. *Symmetry*. 2021; 13(1):97.
https://doi.org/10.3390/sym13010097

**Chicago/Turabian Style**

Li, Suhua, Jiacheng Xie, Xuewen Wang, Fang Ren, Xin Zhang, and Qingbao Bao.
2021. "Path Planning of Hydraulic Support Pushing Mechanism Based on Extreme Learning Machine and Descartes Path Planning" *Symmetry* 13, no. 1: 97.
https://doi.org/10.3390/sym13010097