# A Cooperative Control Algorithm for Line and Predecessor Following Platoons Subject to Unreliable Distance Measurements

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## Abstract

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## 1. Introduction

## 2. The Line-Following Platooning Control Problem

- Despite the simplification in the setup, the configuration retains fundamental challenges that arise in control of platoon formations, such as dealing with unreliable distance measurement, designing string stabilizing controllers, and considering communication issues, among others.
- The decoupling of the path-planning stage relieves the mathematical treatment from analytically studying platooning for more than one-dimensional paths, allowing to concentrate on the primary control problems.
- Enables the development of low-cost experimental platforms to evaluate platooning formations using low-cost sensors for line-following applications (e.g., infrared sensors), without requiring sophisticated hardware and software support for cameras or lidars that are normally required for the path-planning stage [16,20].

## 3. Description of the RUPU Platform

#### 3.1. Dynamical Model for Control Synthesis

#### 3.2. Distance Measurement Issues

## 4. Cooperative Control Strategy

## 5. Experimental Results

#### 5.1. Offline-Distance Measurement Results

#### 5.2. Experimental Results for the Non-Cooperative Case

#### 5.3. Experimental Results for the Cooperative Case

## 6. Conclusions

## Author Contributions

## Funding

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 5.**

**Top:**Unreliable measurement of the distance sensor, ${d}^{m}\left(t\right)$.

**Bottom:**offline estimation of the true distance $d\left(t\right)$ along the path.

**Figure 16.**Visual comparison of the performance with the non-cooperative case (

**top**) and the cooperative case (

**bottom**).

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**MDPI and ACS Style**

Escobar, C.; Vargas, F.J.; Peters, A.A.; Carvajal, G. A Cooperative Control Algorithm for Line and Predecessor Following Platoons Subject to Unreliable Distance Measurements. *Mathematics* **2023**, *11*, 801.
https://doi.org/10.3390/math11040801

**AMA Style**

Escobar C, Vargas FJ, Peters AA, Carvajal G. A Cooperative Control Algorithm for Line and Predecessor Following Platoons Subject to Unreliable Distance Measurements. *Mathematics*. 2023; 11(4):801.
https://doi.org/10.3390/math11040801

**Chicago/Turabian Style**

Escobar, Carlos, Francisco J. Vargas, Andrés A. Peters, and Gonzalo Carvajal. 2023. "A Cooperative Control Algorithm for Line and Predecessor Following Platoons Subject to Unreliable Distance Measurements" *Mathematics* 11, no. 4: 801.
https://doi.org/10.3390/math11040801