# Transformed Structural Properties Method to Determine the Controllability and Observability of Robots

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## Abstract

**:**

## 1. Introduction

## 2. Two Methods to Determine the Controllability and Observability of Robots

#### 2.1. Linearization Method to Determine the Controllability and Observability of Robots

#### 2.2. Transformed Structural Properties Method to Determine the Controllability and Observability of Robots

**Remark**

**1.**

**Remark**

**2.**

**Remark**

**3.**

## 3. Scara Robot

#### 3.1. Linearization Method

^{2}, ${J}_{2}={J}_{3}=0.0127$ kgm

^{2}, $g=9.81$ m/s

^{2}.

#### 3.2. Transformed Structural Properties Method

^{2}, ${J}_{2}={J}_{3}=0.0127$ kgm

^{2}, $g=9.81$ m/s

^{2}.

#### 3.3. Comparison of Results

## 4. Two-Link Robot

#### 4.1. Linearization Method

^{2}, ${C}_{2}=\mathrm{cos}({z}_{12})$, ${S}_{2}=\mathrm{sin}({z}_{12})$. ${m}_{2}=0.34$ kg, ${l}_{2}=0.293$ m, ${l}_{c2}={\scriptscriptstyle \frac{{l}_{2}}{2}}$, ${J}_{12}={J}_{1}+{J}_{2}$, ${J}_{1}=0.0208$ kgm

^{2}, ${J}_{2}=0.0127$ kgm

^{2}, and $g=9.81$ m/s

^{2}.

#### 4.2. Transformed Structural Properties Method

^{2}, ${C}_{2}=\mathrm{cos}({z}_{12})$, ${S}_{2}=\mathrm{sin}({z}_{12})$. ${m}_{2}=0.34$ kg, ${l}_{2}=0.293$ m, ${l}_{c2}={\scriptscriptstyle \frac{{l}_{2}}{2}}$, ${J}_{12}={J}_{1}+{J}_{2}$, ${J}_{1}=0.0208$ kgm

^{2}, ${J}_{2}=0.0127$ kgm

^{2}, and $g=9.81$ m/s

^{2}.

#### 4.3. Comparison of Results

## 5. Cylindrical Robot

#### 5.1. Linearization Method

^{2}, ${J}_{2}=0.02545$ kgm

^{2}, ${J}_{3}=0.03616$ kgm

^{2}, and $g=9.81$ m/s

^{2}.

#### 5.2. Transformed Structural Properties Method

^{2}, ${J}_{2}=0.02545$ kgm

^{2}, ${J}_{3}=0.03616$ kgm

^{2}, and $g=9.81$ m/s

^{2}.

#### 5.3. Comparison of Results

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**MDPI and ACS Style**

Martinez, D.I.; Rubio, J.d.J.; Garcia, V.; Vargas, T.M.; Islas, M.A.; Pacheco, J.; Gutierrez, G.J.; Meda-Campaña, J.A.; Mujica-Vargas, D.; Aguilar-Ibañez, C.
Transformed Structural Properties Method to Determine the Controllability and Observability of Robots. *Appl. Sci.* **2021**, *11*, 3082.
https://doi.org/10.3390/app11073082

**AMA Style**

Martinez DI, Rubio JdJ, Garcia V, Vargas TM, Islas MA, Pacheco J, Gutierrez GJ, Meda-Campaña JA, Mujica-Vargas D, Aguilar-Ibañez C.
Transformed Structural Properties Method to Determine the Controllability and Observability of Robots. *Applied Sciences*. 2021; 11(7):3082.
https://doi.org/10.3390/app11073082

**Chicago/Turabian Style**

Martinez, Dany Ivan, José de Jesús Rubio, Victor Garcia, Tomas Miguel Vargas, Marco Antonio Islas, Jaime Pacheco, Guadalupe Juliana Gutierrez, Jesus Alberto Meda-Campaña, Dante Mujica-Vargas, and Carlos Aguilar-Ibañez.
2021. "Transformed Structural Properties Method to Determine the Controllability and Observability of Robots" *Applied Sciences* 11, no. 7: 3082.
https://doi.org/10.3390/app11073082