# Simultaneous Estimation of Vehicle Sideslip and Roll Angles Using an Event-Triggered-Based IoT Architecture

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## Abstract

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## 1. Introduction

- Using the velocities and accelerations of the axes X, Z;
- Merging the lateral accelerations and the roll rate [20];
- Combining the data obtained using a gyroscope and an inertial angle sensor [21];
- Operating using the values obtained using a six-dimensional IMU [22];
- Using a low-cost GPS together with the values from sensors located on the wheels [23].

- The sampling rate of the sensors must be high in order to ensure that information is received fast enough to act in case of a particular event;
- It is necessary to obtain information from low-cost sensors or devices already included in series-production automobiles in order to ensure the vehicle prices are reasonable;
- Whenever data cannot be obtained directly, they must be estimated from direct measurements;
- The elapsed time to perform computational tasks should be as short as possible in order to guarantee a rapid response to different events;
- The developed system must have a low power consumption in order not to exhaust the vehicle resources.

## 2. Research Approach

#### 2.1. IoT Hardware and Communications Perspective

- Racelogic IMU04. This sensor measures pitch, roll, and yaw rates using three rate gyroscopes. Moreover, it obtains the accelerations in the x, y, and z directions via three accelerometers with a ±20 g linear acceleration range and a $0.00004$ g acceleration resolution, and a ±450${}^{\circ}$/s angular rate range with a 0.00085${}^{\circ}$/s resolution;
- Racelogic VBOX 3i Dual Antenna. Depending on the mounting configuration, this sensor can be used to measure the roll, pitch, and sideslip angles, and determine vehicle positioning with a 1 cm distance resolution, a $0.01$ km/h velocity resolution, less than a $0.{2}^{\circ}$ sideslip angle RMS accuracy, and a $0.{14}^{\circ}$ roll angle RMS accuracy;
- Kistler steering wheel DTI sensor. This sensor can measure the steering wheel angle and torque with the following specifications: a $\pm 250$ Nm steering moment range, a $\pm {1250}^{\circ}$ steering angle range, a maximum 2000${}^{\circ}$/s steering speed, and a $0.{015}^{\circ}$ steering angle resolution.

#### 2.2. Event-Triggered Vehicle Sideslip and Roll Angles ${\mathcal{H}}_{\infty}$ Observer

- When $q\left(t\right)=0$, the system (5) is asymptotically stable;
- Under the zero initial condition, $\left|\right|{z}^{\top}{z\left|\right|}_{2}<{\gamma}^{2}\left|\right|{q}^{\top}q{\left|\right|}_{2}$ holds for $q\left(t\right)\ne 0\in {\mathcal{L}}_{2}\phantom{\rule{4pt}{0ex}}[0,\infty )$, with $\gamma $ being the ${\mathcal{H}}_{\infty}$ performance index.

**Theorem 1.**

**Proof.**

#### 2.3. Software Perspective

- a.
- Network. This component incorporates the essential logic required to facilitate communication among the computers within the system. At the time of writing this article, the system employed a client–server model utilizing TCP sockets for data exchange. This component furnishes various implementations for distinct operations, including:
- Establish communication: (a) receives the IP and port of the machine; and (b) returns a socket descriptor that is used to exchange data with the process;
- Set socket listener port: (a) receives the port number in which the server will be listening for new connections; and (b) returns a number that will be used by the server as socket descriptor;
- Send message: (a) receives the message to send, the length of the message, and one socket descriptor; and (b) returns 0 in case of success and −1 if an error occurs;
- Receive message; (a) receives a buffer where the message will be stored, the length of the message, and one socket descriptor; and (b) returns 0 in case of success and −1 if an error occurs.

- b.
- Math operators. The programs in development must execute various mathematical operations, including matrix calculations. The responsibility of this block is to ensure the efficient implementation of these operators. Among the functions offered by this component are:
- Create matrix;
- Multiply matrix by number;
- Add matrices;
- Multiply matrices;
- Transpose matrix;
- Convert degrees to radians.

- c.
- Sensors. This component represents the array of sensors utilized by the Raspberry Pi for environmental data collection. To enhance the system modularity, it was determined that this component should employ the network interface for data transmission instead of being integrated into the event-triggering block. This choice enables developers to separate the data collection process from its subsequent processing.
- d.
- Event triggering. This block executes the event-triggering algorithm. It processes data from sensors and transmits that information to the observer. Given that the algorithm involves matrix operations, it is imperative to ensure the availability and integration of the math component for its proper functionality.
- e.
- Observer. This component is the last piece of the algorithm. It processes the data sent by the event-triggering program and estimates both the vehicle sideslip and roll angles.Note: Both the event-triggering program and the observer are required not only to communicate with each other and perform mathematical operations, but also to generate graphics once the programs have finished. This is why they are connected to the library component.

- Main: this program is responsible for obtaining data from the sensors and transmitting them to the event-triggering program;
- Event triggering: this code receives data from the sensors and performs several mathematical operations in order to decide whether the processed information must be sent to the observer or not;
- Observer: this program calculates the slip and roll angles as its final outputs.

#### 2.4. Experimental Design

- a.
- Spiral. During a spiral movement, the driver steers the vehicle along a path that gradually narrows or widens in a spiral shape. The challenge is to maintain control and follow the curvature of the road.
- b.
- Slalom. The slalom is a driving course that consists of a series of gates or markers arranged in a zigzag pattern. The driver must navigate through the obstacles by making rapid turns and quick changes in direction.
- c.
- Lane change. The ability to change lanes is a crucial driving skill that has many practical applications in everyday driving scenarios. For example, changing lanes allows overtaking slower vehicles, adjusting to traffic conditions, and avoiding obstacles.

#### 2.5. Data Gathering

- Covariance between pitch and roll angles;
- Covariance between yaw and pitch angles;
- Covariance between yaw and roll angles;
- Altitude;
- Latitude;
- Longitude;
- Pitch angle;
- Pitch rate;
- Roll angle;
- Roll rate;
- Yaw angle;
- Yaw rate;
- Vehicle speed;
- Timestamp.

## 3. Experimental Results

- It was assumed that the longitudinal velocity was bounded in the interval [2 m/s, 20 m/s];
- The maximum variation in the tire cornering stiffness was 5% of its nominal value;
- The data sampling frequency was 100 Hz, with minimum and maximum transmission time delays of 5 and 20 ms, respectively.

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

ADS | Automated driving system |

GPS | Global positioning system |

NCS | Networked control system |

IMU | Inertial measurement unit |

IoT | Internet of Things |

LPV | Linear parameter varying |

RMS | Root mean square |

## Appendix A. Example of Data Logged During the Experiments

**Figure A1.**CSV file contents showcasing data logged by the VBOX kit throughout the course of the experiments.

**Figure A2.**JSON file contents showcasing data recorded by low-cost sensors throughout the execution of experiments.

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Parameter | Value | Description |
---|---|---|

a | 1.42 m | Distance of the front axle from the center of gravity (CoG) |

b | 0.85 m | Distance of the rear axle from the CoG |

${k}_{r}$ | 31,752 N m/rad | Roll stiffness |

${b}_{r}$ | 7025.4 N m s/rad | Roll damping coefficient |

${C}_{\alpha f}$ | 30,000 N/rad | Cornering stiffness of the front tire |

${C}_{\alpha r}$ | 25,000 N/rad | Cornering stiffness of the rear tire |

g | 9.81 m/s${}^{2}$ | Acceleration of gravity |

h | 0.35 m | Distance from roll center to CoG |

${I}_{x}$ | 520 kg m${}^{2}$ | Moment of inertia about the roll axis |

${I}_{z}$ | 1110.9 kg m${}^{2}$ | Moment of inertia about the yaw axis |

m | 650 kg | Vehicle mass |

${v}_{x}$ | m/s | Longitudinal speed |

Sideslip Angle ($\mathit{\beta}$) | Roll Angle ($\mathit{\varphi}$) | |
---|---|---|

MAX error | $2.{11}^{\circ}$ | $3.{44}^{\circ}$ |

RMS error | $0.{28}^{\circ}$ | $0.{25}^{\circ}$ |

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## Share and Cite

**MDPI and ACS Style**

Viadero-Monasterio, F.; García, J.; Meléndez-Useros, M.; Jiménez-Salas, M.; Boada, B.L.; López Boada, M.J.
Simultaneous Estimation of Vehicle Sideslip and Roll Angles Using an Event-Triggered-Based IoT Architecture. *Machines* **2024**, *12*, 53.
https://doi.org/10.3390/machines12010053

**AMA Style**

Viadero-Monasterio F, García J, Meléndez-Useros M, Jiménez-Salas M, Boada BL, López Boada MJ.
Simultaneous Estimation of Vehicle Sideslip and Roll Angles Using an Event-Triggered-Based IoT Architecture. *Machines*. 2024; 12(1):53.
https://doi.org/10.3390/machines12010053

**Chicago/Turabian Style**

Viadero-Monasterio, Fernando, Javier García, Miguel Meléndez-Useros, Manuel Jiménez-Salas, Beatriz López Boada, and María Jesús López Boada.
2024. "Simultaneous Estimation of Vehicle Sideslip and Roll Angles Using an Event-Triggered-Based IoT Architecture" *Machines* 12, no. 1: 53.
https://doi.org/10.3390/machines12010053