# Simulation and Validation of an 8 × 8 Scaled Electric Combat Vehicle

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Literature Review

#### 1.2. Contributions

#### 1.3. Challenges

## 2. Hardware and Mathematical Model

#### 2.1. Mechanical Design and Sensors

_{t}, and θ

_{t}represent the change in the stroke position, the radius of the tire, and the steering wheel angle. Figure 2 describes the steering assembly including the linear actuator, steering rod, and steering housing.

_{t}θ

_{t}

#### 2.2. Vehicle Mathematical Model

_{ij}, and δ

_{oj}indicate yaw, each axle’s inner wheel angle, and each axle’s outer wheel angle. In addition, B and L indicate the track width and the wheelbase. Each axle’s inner and outer wheel velocity are described as V

_{ij}and V

_{oj}.

## 3. Results

#### 3.1. Stationary Evaluation

#### Wheel Rotational Speed and Radius of Vehicle Path

#### 3.2. Turn Radius Evaluation

#### Turn Radius Evaluation at Maximum Speed and Maximum Steering Angle

#### 3.3. Double Lane Change Evaluation

#### Double Lane Change at 5 km/h

^{st}axle left wheel angles in three different steering scenarios during the DLC evaluation are shown in Figure 21 to validate the simulated results with the experimentally obtained results. The 1

^{st}axle left wheel angles are selected in Figure 21 as they have the largest wheel angles during the left turn. Figure 21 shows quite similar positive and negative peak value times; however, some different amplitudes between the simulations and experiments are seen in negative values from 5 to 10 s. There are some difficulties for human drivers to maneuver the scaled vehicle like using a closed-loop driver model. In future research, the path following the closed-loop driver model will be implemented on the physically scaled vehicle to achieve the same trajectory of the simulation result. In both the experimental and simulation results of Figure 21, the all-wheel steering figure is the most shifted to the left compared to others between 5 and 15 s. This phenomenon indicates that all-wheel steering has the fastest response in three scenarios.

## 4. Discussion

#### Analysis of Turn Radius and Vehicle Sideslip in Double Lane Change Evaluation

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

R (m) | Turning radius |

L_{1} (m) | The shortest distance from point C to the first axle |

L_{2} (m) | The shortest distance from point C to the second axle |

L_{3} (m) | The shortest distance from point C to the third axle |

L_{4} (m) | The shortest distance from point C to the fourth axle |

B (m) | Track width |

r_{t} (m) | The radius of tire |

θ_{t} (rad) | The steering wheel angle |

$\dot{\theta}$ (rad/s) | Yaw |

δ_{oj} (rad) | Each axle’s outer wheel angle |

δ_{ij} (rad) | Each axle’s inner wheel angle |

V (m/s) | Longitudinal velocity |

${a}_{y}^{sensor}$ (g) | Lateral acceleration measured by IMU |

${\dot{v}}_{y}$ (g) | Lateral velocity change |

$\dot{\mathsf{\beta}}$ (rad/s) | Vehicle sideslip change |

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**Figure 1.**Closed-loop controller of linear actuator [14].

**Figure 4.**Mathematical model of traditional steering scenario [22].

**Figure 9.**Eight wheels’ velocities in a fixed 3

^{rd}axle scenario. (

**a**) Experimental result. (

**b**) Simulation result.

**Figure 10.**Eight wheels’ velocities in an all-wheel scenario. (

**a**) Experimental result. (

**b**) Simulation result.

**Figure 11.**Turn radius evaluation. (

**a**) Simulated scaled electric combat vehicle. (

**b**) Physically tested scaled electric combat vehicle.

**Figure 12.**Experimental result of 1st axle inner wheel angles (turn radius evaluation at maximum speed and maximum steering).

**Figure 13.**Experiment result of maximum (velocity turn radius evaluation at maximum speed and maximum steering).

**Figure 14.**Experiment result of yaw rate (turn radius evaluation at maximum speed and maxi mum steering).

**Figure 15.**Experiment result of lateral acceleration (turn radius evaluation at maximum speed and maximum steering).

**Figure 16.**Result of trajectory (turn radius evaluation at maximum speed and maximum steering). (

**a**) Experiment result. (

**b**) Simulation result.

**Figure 17.**Turn radius evaluation at maximum speed and maximum steering. (

**a**) Experimental result of turning radius calculated from measured velocity and measured yaw rate. (

**b**) Experimental result of turning radius calculated from measured 1st axle inner angle based on Ackermann condition equation.

**Figure 18.**Simulated scaled electric combat vehicle (

**left**), and trajectory of the physically tested scaled electric combat vehicle (

**right**) in double lane change evaluation.

**Figure 20.**Result of trajectory (DLC maneuver at a speed of 5 km/h). (

**a**) Experiment result. (

**b**) Simulation result.

**Figure 21.**Result of 1

^{st}axle left wheel angle (DLC maneuver at speed 5 km/h). (

**a**) Experimental result. (

**b**) Simulation result.

**Figure 22.**Result of longitudinal velocity (DLC maneuver at speed 5 km/h). (

**a**) Experimental result. (

**b**) Simulation result.

**Figure 23.**Result of yaw rate (DLC maneuver at speed 5 km/h). (

**a**) Experimental result. (

**b**) Simulation result.

**Figure 24.**Result of turning radius (DLC maneuver at speed 5 km/h). (

**a**) Experimental result calculated from measured 1st axle left angle based on Ackermann condition equation. (

**b**) Experimental result calculated from measured velocity and measured yaw rate.

Traditional | Fixed 3rd Axle | All Wheel | |
---|---|---|---|

Experimental result of 1st axle inner wheel angle (deg) | 20.53 | 20.00 | 20.14 |

Simulation result of 1st axle inner wheel angle (deg) | 20.5 | 19.85 | 19.85 |

Traditional | Fixed 3rd Axle | All Wheel | |
---|---|---|---|

Experiment result of maximum velocity (km/h) | 5.29 | 5.25 | 5.24 |

Simulation result of maximum velocity (km/h) | 5.30 | 5.20 | 5.20 |

Traditional | Fixed 3rd Axle | All Wheel | |
---|---|---|---|

Experiment result of yaw rates (deg/s) | 47.80 | 60.63 | 78.68 |

Simulation result of yaw rates (deg/s) | 49.3 | 61.0 | 80.5 |

Traditional | Fixed 3rd Axle | All Wheel | |
---|---|---|---|

Experimental result of lateral acceleration (g) | 0.137 | 0.173 | 0.209 |

Simulation result of lateral acceleration (g) | 0.129 | 0.167 | 0.207 |

Traditional | Fixed 3rd Axle | All Wheel | |
---|---|---|---|

Simulation result of vehicle sideslip angle (deg) | 4.8 | 1.4 | −3.9 |

Traditional | Fixed 3rd Axle | All Wheel | |
---|---|---|---|

Experiment result of trajectory from indoor GPS (m) | 1.74 | 1.33 | 1.00 |

Simulation result of trajectory from TruckSim (m) | 1.76 | 1.39 | 1.05 |

Experimental result of turning radius calculated from measured velocity and measured yaw rate (m) | 1.75 | 1.37 | 1.06 |

Experimental result of turning radius calculated from measured 1st axle inner angle based on Ackermann condition equation (m) | 1.44 | 1.22 | 0.97 |

Traditional | Fixed 3rd Axle | All Wheel | |
---|---|---|---|

Experiment result (km/h) | 5.014 | 5.018 | 5.040 |

Simulation result (km/h) | 4.995 | 4.995 | 4.995 |

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**MDPI and ACS Style**

Kim, J.; El-Gindy, M.; El-Sayegh, Z.
Simulation and Validation of an 8 × 8 Scaled Electric Combat Vehicle. *Machines* **2024**, *12*, 146.
https://doi.org/10.3390/machines12020146

**AMA Style**

Kim J, El-Gindy M, El-Sayegh Z.
Simulation and Validation of an 8 × 8 Scaled Electric Combat Vehicle. *Machines*. 2024; 12(2):146.
https://doi.org/10.3390/machines12020146

**Chicago/Turabian Style**

Kim, Junwoo, Moustafa El-Gindy, and Zeinab El-Sayegh.
2024. "Simulation and Validation of an 8 × 8 Scaled Electric Combat Vehicle" *Machines* 12, no. 2: 146.
https://doi.org/10.3390/machines12020146