# A Novel Roll and Pitch Estimation Approach for a Ground Vehicle Stability Improvement Using a Low Cost IMU

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## Abstract

**:**

^{®}(CarSim, Ann Arbor, MI, USA). In the second phase of research, complementary and Kalman filters have been designed for attitude estimation. In the third phase, a low-cost inertial measurement unit (IMU) is mounted on a vehicle, and both the complementary filter (CF) and Kalman filter (KF) are applied independently to measure the data for both smooth and uneven terrains at four different frequencies. We compared the simulated and real-time results of roll and pitch angles obtained using the complementary and Kalman filters. Using the proposed method, the achieved root mean square error (RMSE) is less than 0.73 degree for pitch and 0.68 degree for roll, with a sample time of 2 ms. Thus, a warning signal can be generated to mitigate roll over. Hence, we claim that our proposed method can provide a low-cost solution to the roll-over problem for a road vehicle.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Mathematical Modelling and Validation

#### Mathematical Modeling

#### 2.2. Observer Based Estimation

#### 2.2.1. Luenberger Observers

^{®}(The MathWorks, Inc., Torrance, CA, USA) command L = place (A’, C’, [p])’ places the desired closed loop poles p by computation of a state feedback gain matrix L.

#### 2.2.2. Sliding Mode Observer

#### 2.3. Filter Based Estimation

#### 2.3.1. The Complementary Filter

- The product of pitch angle and yaw rate is small. The roll angle can be obtained by integration of the roll rate obtained by the gyroscope.
- If the vehicle is in steady state condition, the time derivative of ${\mathrm{v}}_{\mathrm{y}}$ would be small and roll angle can be calculated through Equation (37).
- Pitch angle can be determined from the Equation (38) when roll angle gets known.

#### 2.3.2. Kalman Filter Implementation

## 3. Experiment and Results

#### 3.1. Model Validation

^{®}(CarSim, Ann Arbor, MI, USA) is a system-level vehicle dynamics simulation software that is widely used in automotive industry. CarSim

^{®}is the “company standard” vehicle dynamics software in several automotive companies, and is in use for various purposes at many more of the world’s OEM companies and their suppliers. The same has been used in [32,33] to simulate the results. We have developed the vehicle’s analytical model that was simulated in MATLAB

^{®}(The MathWorks, Inc., Torrance, CA, USA). Validation is performed by conducting several standard tests and comparing them with CarSim

^{®}including step steer, Fishhook, and Double lane change.

#### 3.2. Simulated Results for Luenberger & Sliding Mode Observer

^{®}against which a roll angle of around 3 degree is observed as seen in Figure 8. It is observed that the sliding mode observer performed better by keeping better track of roll angle as compared to Luenberger during step steer input. The root mean square error obtained for sliding mode observer is 0.0906 degree where as Luenberger came up with a root mean square error of 0.2127 degrees.

^{®}is found to be 0.0872 degrees and 0.1458 degrees respectively.

#### 3.3. Simulated Results Comparison of Complementary Filter with CARSIM^{®}

#### 3.4. Real Time Complemenary Filter Implementation

#### Experimental Setup

#### 3.5. Real Time Complemenary Filter Implementation

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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Sno. | Name | Manufacturer | Technology | $\mathbf{Noise}\text{}\mathbf{Density}\text{}\mathit{d}\mathit{p}\mathit{s}/\sqrt{\mathit{H}\mathit{z}}$ |
---|---|---|---|---|

1 | TG6000 | KVH (Middle Town, CT, USA) | Fiber Optic | 0.001 |

2 | HG1700AG37 | Honeywell (Charlotte, NC, USA) | Ring Laser | 0.002 |

3 | VG700MB | Cross Bow (San Jose, CA, USA) | Fiber Optic | 0.006 |

4 | HG1700AG68 | Honeywell (Charlotte, NC, USA) | Ring Laser | 0.008 |

5 | LandMark10 | Gladiator Tech (Snoqualme, WA, USA) | MEMS | 0.012 |

6 | ADIS16355 | Analog Devices (Norwood, MA, USA) | MEMS | 0.033 |

7 | MTi-1 | Xsens (Enschede, The Netherlands) | MEMS | 0.01 |

8 | L3GD20 | ST Microelectronics (Geneva, Switzerland) | MEMS | 0.03 |

9 | MPU-6050 | TDK-InvenSense (San Jose, CA, USA) | MEMS | 0.005 |

Input | Rms Error Deg (SMO) | Rms Error Deg (Luenberger) | Maximum Error (SMO) | Maximum Error (Luenberger) |
---|---|---|---|---|

Step Input | 0.0906 | 0.2127 | 0.2223 | 0.3126 |

Sinusoidal Input | 0.1537 | 0.4471 | 0.2936 | 0.6742 |

ISO Fish Hook Maneuver | 0.0872 | 0.1458 | 0.1415 | 0.2132 |

ISO Double Lane Change | 0.0898 | 0.1823 | 0.2074 | 0.2487 |

Author | Estimation Parameter | Platform | Estimator | Computation Cost | Error Max (RMSE) (deg) |
---|---|---|---|---|---|

Qingyuan Zhu et al. [38] | Roll | Prototype Vehicle | GA | 100 ms | 1.8 (Roll) |

Pitch | BP NN | 2.1 (Pitch) | |||

Hamad Ahmed et al. [24] | Roll | Standard Vehicle | KF | 20–25 ms | 0.1 (Roll) |

Pitch | 0.13 (Pitch) | ||||

Yaw | 0.01 (Yaw) | ||||

Javier Garcia Guzman et al. [39] | Roll | Standard Vehicle | KF | 14.2 ms | 0.76 (Roll) |

Pitch | UKF | 6.76 ms | 0.63 (Pitch) | ||

Daehee Won et al. [40] | Roll | Standard Vehicle | EKF | 21.4 ms | 0.28 (Roll) |

Pitch | 0.55 (Pitch) | ||||

RobertoG.Valenti et al. [41] | Roll | Standard Vehicle | Pseudo | 1.42 μs | 1.32 (Roll) |

Pitch | Madwick | 1.19 (Pitch) | |||

Yaw | EKF | ||||

XudongWen et al. [42] | Roll | UAV | NCF | 41 ms | 1.16 (Roll) |

Pitch | DNCF | 0.50 (Pitch) | |||

Yaw | - | - | |||

Rodrigo Gonzalez et al. [43] | Roll | Standard Vehicle | KF | 0.2 s | 0.362 (Roll) |

Pitch | 0.339 (Pitch) | ||||

Yaw | 1.839 (Yaw) | ||||

Proposed scheme | Roll | Standard Vehicle | CF | 3.2 ms | 0.6738 (Roll) |

Pitch | 0.7280 (Pitch) |

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## Share and Cite

**MDPI and ACS Style**

Kamal Mazhar, M.; Khan, M.J.; Bhatti, A.I.; Naseer, N.
A Novel Roll and Pitch Estimation Approach for a Ground Vehicle Stability Improvement Using a Low Cost IMU. *Sensors* **2020**, *20*, 340.
https://doi.org/10.3390/s20020340

**AMA Style**

Kamal Mazhar M, Khan MJ, Bhatti AI, Naseer N.
A Novel Roll and Pitch Estimation Approach for a Ground Vehicle Stability Improvement Using a Low Cost IMU. *Sensors*. 2020; 20(2):340.
https://doi.org/10.3390/s20020340

**Chicago/Turabian Style**

Kamal Mazhar, Malik, Muhammad Jawad Khan, Aamer Iqbal Bhatti, and Noman Naseer.
2020. "A Novel Roll and Pitch Estimation Approach for a Ground Vehicle Stability Improvement Using a Low Cost IMU" *Sensors* 20, no. 2: 340.
https://doi.org/10.3390/s20020340