# 6D Virtual Sensor for Wrench Estimation in Robotized Interaction Tasks Exploiting Extended Kalman Filter

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## Abstract

**:**

## 1. Introduction

#### 1.1. Context

#### 1.2. Related Works

#### 1.3. Paper Contribution

## 2. Sensorless Cartesian Impedance Control

**Remark**

**1.**

## 3. Extended Kalman Filter for External Wrench Estimation

## 4. Simulation Results

#### 4.1. $\#1$ Constant External Wrench

#### 4.2. $\#2$ Variable-Sinusoidal External Wrench

#### 4.3. $\#3$ Probing Task

#### 4.4. $\#4$ Sliding Task

## 5. Experimental Results

#### 5.1. $\#1$ Human–Robot Interaction

#### 5.2. $\#2$ Assembly Task

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Estimated interaction forces $\widehat{\mathbf{f}}$ and torques $\widehat{\mathbf{C}}$ (continuous line) vs. real interaction forces $\mathbf{f}$ and torques $\mathbf{C}$ (dashed line) for the $\#1$ simulation scenario.

**Figure 2.**Estimated interaction forces ${\widehat{\mathbf{e}}}_{f}$ and torques ${\widehat{\mathbf{e}}}_{C}$ errors for the $\#1$ simulation scenario.

**Figure 3.**Estimated interaction forces $\widehat{\mathbf{f}}$ and torques $\widehat{\mathbf{C}}$ (continuous line) vs. real interaction forces $\mathbf{f}$ and torques $\mathbf{C}$ (dashed line) for the $\#2$ simulation scenario.

**Figure 4.**Estimated interaction forces ${\widehat{\mathbf{e}}}_{f}$ and torques ${\widehat{\mathbf{e}}}_{C}$ errors for the $\#2$ simulation scenario.

**Figure 5.**Estimated interaction forces $\widehat{\mathbf{f}}$ and torques $\widehat{\mathbf{C}}$ (continuous line) vs. real interaction forces $\mathbf{f}$ and torques $\mathbf{C}$ (dashed line) for the $\#3$ simulation scenario.

**Figure 6.**Estimated interaction forces ${\widehat{\mathbf{e}}}_{f}$ and torques ${\widehat{\mathbf{e}}}_{C}$ errors for the $\#3$ simulation scenario.

**Figure 7.**Estimated interaction forces $\widehat{\mathbf{f}}$ and torques $\widehat{\mathbf{C}}$ (continuous line) vs. real interaction forces $\mathbf{f}$ and torques $\mathbf{C}$ (dashed line) for the $\#4$ simulation scenario.

**Figure 8.**Estimated interaction forces ${\widehat{\mathbf{e}}}_{f}$ and torques ${\widehat{\mathbf{e}}}_{C}$ errors for the $\#4$ simulation scenario.

**Figure 9.**Estimated interaction forces $\widehat{\mathbf{f}}$ and torques $\widehat{\mathbf{C}}$ (continuous line) vs. measured interaction forces $\mathbf{f}$ and torques $\mathbf{C}$ (dashed line) for the $\#1$ experimental scenario.

**Figure 10.**Estimated interaction forces ${\widehat{\mathbf{e}}}_{f}$ and torques ${\widehat{\mathbf{e}}}_{C}$ errors for the $\#1$ experimental scenario.

**Figure 11.**Experimental assembly task, including the Franka EMIKA panda manipulator and the target gear to be installed.

**Figure 12.**Estimated interaction forces $\widehat{\mathbf{f}}$ and torques $\widehat{\mathbf{C}}$ (continuous line) vs. measured interaction forces $\mathbf{f}$ and torques $\mathbf{C}$ (dashed line) for the $\#2$ experimental scenario.

**Figure 13.**Estimated interaction forces ${\widehat{\mathbf{e}}}_{f}$ and torques ${\widehat{\mathbf{e}}}_{C}$ errors for the $\#2$ experimental scenario.

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**MDPI and ACS Style**

Roveda, L.; Bussolan, A.; Braghin, F.; Piga, D.
6D Virtual Sensor for Wrench Estimation in Robotized Interaction Tasks Exploiting Extended Kalman Filter. *Machines* **2020**, *8*, 67.
https://doi.org/10.3390/machines8040067

**AMA Style**

Roveda L, Bussolan A, Braghin F, Piga D.
6D Virtual Sensor for Wrench Estimation in Robotized Interaction Tasks Exploiting Extended Kalman Filter. *Machines*. 2020; 8(4):67.
https://doi.org/10.3390/machines8040067

**Chicago/Turabian Style**

Roveda, Loris, Andrea Bussolan, Francesco Braghin, and Dario Piga.
2020. "6D Virtual Sensor for Wrench Estimation in Robotized Interaction Tasks Exploiting Extended Kalman Filter" *Machines* 8, no. 4: 67.
https://doi.org/10.3390/machines8040067