# A Genetic Algorithm-Controlled Solar Tracker Robot with Increased Precision Due to Evolution

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## Abstract

**:**

## 1. Introduction

## 2. Problem Solving

#### 2.1. Theoretical Background

#### 2.2. The Proposed Genetic Algorithm

#### 2.3. Hardware Implementation

## 3. Results

#### 3.1. Experimental Results

#### 3.2. Discussions

## 4. Conclusions

**original**:

- The algorithm was used by the solar tracker robot to track the Sun with more precision.
- The algorithm was put in an implementable form for the computer source code.
- The idea of how to
**glue the two motors in order for the solar tracker to be able to make horizontal and vertical movements**is original. - The genesis of all formulas was demonstrated and validated through controlled robotic movement.
- The robot was built, the circuit was made, and the software was written by the authors.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

CdTe | Cadmium tellurium |

CIGS | Copper indium gallium selenide |

PDW | Passive dynamic walking |

DoF | Degrees of freedom |

3D | Three-dimensional |

AC | Alternating current |

DSP | Digital signal processing |

$(0x,0y)$ | Coordinates |

MEMS | Microelectromechanical systems |

ASCII | American Standard Code for Information Interchange |

f | Fitness function |

${g}_{i}$ | Gene (character) |

${t}_{i}$ | Target gene (character) |

${C}_{p}$ | Crossover parameter |

${G}_{n}$ | Generation number |

${G}_{T}$ | Total generation number |

$MIN$, $MAX$ | Minimum, maximum |

${P}_{m}$ | Random middle point |

${M}_{p}$ | Mutation rate or parameter |

N | Number of joints ($N=2$) |

K | Total kinetic energy |

P | Potential energy |

${\theta}_{i}$ | Joint variable for the ${i}^{th}$ joint |

$\dot{{\theta}_{i}}$ | First time derivative for ${\theta}_{i}$ |

${\tau}_{i}$ | Generalized force (torque) at the ${i}^{th}$ joint |

$\theta $ | Generalized joint coordinates |

$M(\theta )$ | Mass matrix or kinetic energy matrix |

$C(\theta ,\dot{\theta})$ | Centrifugal and Coriolis forces |

$G(\theta )$ | Gravity force |

$\Phi (\theta ,\dot{\theta},\ddot{\theta})$ | Generalized forces |

${m}_{kk}(\theta )$ | Inertia at joint k when joint k accelerates (${m}_{kk}>0$) |

${m}_{kj}(\theta )$ | Inertia observed at joint k when joint j accelerates |

${c}_{kii}(\theta )$ | Coefficient of the centrifugal force at joint k when joint i is moving (${c}_{iii}=0,\phantom{\rule{0.277778em}{0ex}}\forall i$) |

${c}_{kij}(\theta )$ | Coriolis force at joint k when both joints i and j are moving |

${m}_{1}$, ${m}_{2}$ | Masses |

M | Mass matrix, all the mass |

$\ddot{\theta}$ | Linear acceleration terms |

$\dot{\theta}$ | Quadratic velocity terms |

$\theta $ | Nonlinear configuration terms |

g | Gravity acceleration vector |

${r}_{ci}$ | Location of the center of mass for link i |

${r}_{cm}$ | Place of the center point of the mass |

r | Place of reference |

$dm$ | Differential component of the mass at point r |

${m}_{i}$ | Mass of particle i |

${r}_{i}$ | Distance to particle i |

DNAs | Deoxyribonucleic acids |

$x0y$ | Cartesian coordinate system |

FPGA | Field-programmable gate arrays |

SoC | System on a chip |

GA | Genetic algorithm |

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**Figure 7.**Circuitry for the solar tracker robot using an ATmega328 microcontroller development board.

Total population | 150 | Generation number | 50 |

Crossover rate | 0.75 | Mutation rate | 0.01 |

String length | 8bits | ||

Fitness function | $f=\frac{s}{n},\phantom{\rule{0.277778em}{0ex}}{g}_{i}={t}_{i},\phantom{\rule{0.277778em}{0ex}}i\in \{0,\dots n\}$ |

**Table 2.**Comparison of the parameters of the genetic algorithm of the proposed approach with other similar methods.

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**MDPI and ACS Style**

Szabo, R.; Ricman, R.-S. A Genetic Algorithm-Controlled Solar Tracker Robot with Increased Precision Due to Evolution. *Machines* **2023**, *11*, 430.
https://doi.org/10.3390/machines11040430

**AMA Style**

Szabo R, Ricman R-S. A Genetic Algorithm-Controlled Solar Tracker Robot with Increased Precision Due to Evolution. *Machines*. 2023; 11(4):430.
https://doi.org/10.3390/machines11040430

**Chicago/Turabian Style**

Szabo, Roland, and Radu-Stefan Ricman. 2023. "A Genetic Algorithm-Controlled Solar Tracker Robot with Increased Precision Due to Evolution" *Machines* 11, no. 4: 430.
https://doi.org/10.3390/machines11040430