# 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

- Ben-Ari, M.; Mondada, F. Robots and their applications. In Elements of Robotics; Springer: Berlin, Germany, 2018; pp. 1–20. [Google Scholar]
- Yang, G.Z.; Bellingham, J.; Dupont, P.E.; Fischer, P.; Floridi, L.; Full, R.; Jacobstein, N.; Kumar, V.; McNutt, M.; Merrifield, R.; et al. The grand challenges of Science Robotics. Sci. Robot.
**2018**, 3, eaar7650. [Google Scholar] [CrossRef] - Polverini, M.P.; Rossi, R.; Morandi, G.; Bascetta, L.; Zanchettin, A.M.; Rocco, P. Performance improvement of implicit integral robot force control through constraint-based optimization. In Proceedings of the 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Daejeon, South Korea, 9–14 October 2016; pp. 3368–3373. [Google Scholar]
- Mohamed, Z.M. Flexible Manufacturing Systems: Planning Issues and Solutions; Taylor & Francis: Oxfordshire, UK, 2018. [Google Scholar]
- Dattaprasad, S.; Rao, Y.V. A Survey of Various Robot Learning Techniques. Int. J. Pure Appl. Math.
**2018**, 118, 3823–3831. [Google Scholar] - Hogan, N. Impedance control: An approach to manipulation. In Proceedings of the 1984 American control conference, San Diego, CA, USA, 6–8 June 1984; pp. 304–313. [Google Scholar]
- Vukobratovic, M. Robot-environment dynamic interaction survey and future trends. J. Comput. Syst. Sci. Int.
**2010**, 49, 329–342. [Google Scholar] [CrossRef] - Roveda, L.; Pedrocchi, N.; Tosatti, L.M. Exploiting impedance shaping approaches to overcome force overshoots in delicate interaction tasks. Int. J. Adv. Robot. Syst.
**2016**, 13, 1729881416662771. [Google Scholar] [CrossRef][Green Version] - Roveda, L.; Pedrocchi, N.; Beschi, M.; Tosatti, L.M. High-accuracy robotized industrial assembly task control schema with force overshoots avoidance. Control. Eng. Pract.
**2018**, 71, 142–153. [Google Scholar] [CrossRef] - Roveda, L. Adaptive interaction controller for compliant robot base applications. IEEE Access
**2018**, 7, 6553–6561. [Google Scholar] [CrossRef] - Polverini, M.P.; Formentin, S.; Merzagora, L.; Rocco, P. Mixed Data-Driven and Model-Based Robot Implicit Force Control: A Hierarchical Approach. IEEE Trans. Control. Syst. Technol.
**2019**, 28, 1258–1271. [Google Scholar] [CrossRef] - Janot, A.; Vandanjon, P.O.; Gautier, M. A generic instrumental variable approach for industrial robot identification. IEEE Trans. Control. Syst. Technol.
**2013**, 22, 132–145. [Google Scholar] [CrossRef] - Chen, W.H.; Ballance, D.J.; Gawthrop, P.J.; O’Reilly, J. A nonlinear disturbance observer for robotic manipulators. IEEE Trans. Ind. Electron.
**2000**, 47, 932–938. [Google Scholar] [CrossRef][Green Version] - Colomé, A.; Pardo, D.; Alenya, G.; Torras, C. External force estimation during compliant robot manipulation. In Proceedings of the 2013 IEEE International Conference on Robotics and Automation, Karlsruhe, Germany, 6–10 May 2013; pp. 3535–3540. [Google Scholar]
- Hu, J.; Xiong, R. Contact force estimation for robot manipulator using semiparametric model and disturbance Kalman filter. IEEE Trans. Ind. Electron.
**2017**, 65, 3365–3375. [Google Scholar] [CrossRef] - Peng, G.; Yang, C.; He, W.; Chen, C.L.P. Force Sensorless Admittance Control With Neural Learning for Robots With Actuator Saturation. IEEE Trans. Ind. Electron.
**2020**, 67, 3138–3148. [Google Scholar] [CrossRef][Green Version] - Van Damme, M.; Beyl, P.; Vanderborght, B.; Grosu, V.; Van Ham, R.; Vanderniepen, I.; Matthys, A.; Lefeber, D. Estimating robot end-effector force from noisy actuator torque measurements. In Proceedings of the 2011 IEEE International Conference on Robotics and Automation, Shanghai, Cina, 9–13 May 2011; pp. 1108–1113. [Google Scholar]
- Linderoth, M.; Stolt, A.; Robertsson, A.; Johansson, R. Robotic force estimation using motor torques and modeling of low velocity friction disturbances. In Proceedings of the 2013 IEEE/RSJ International Conference on Intelligent Robots and Systems, Tokyo, Japan, 3–7 November 2013; pp. 3550–3556. [Google Scholar]
- Villagrossi, E.; Simoni, L.; Beschi, M.; Pedrocchi, N.; Marini, A.; Tosatti, L.M.; Visioli, A. A virtual force sensor for interaction tasks with conventional industrial robots. Mechatronics
**2018**, 50, 78–86. [Google Scholar] [CrossRef] - Sharifi, M.; Talebi, H.; Shafiee, M. Adaptive estimation of robot environmental force interacting with soft tissues. In Proceedings of the 2015 3rd RSI International Conference on Robotics and Mechatronics (ICROM), Tehran, Iran, 7–9 October 2015; pp. 371–376. [Google Scholar]
- Dong, A.; Du, Z.; Yan, Z. A sensorless interaction forces estimator for bilateral teleoperation system based on online sparse Gaussian process regression. Mech. Mach. Theory
**2020**, 143, 103620. [Google Scholar] [CrossRef] - Magrini, E.; Flacco, F.; De Luca, A. Estimation of contact forces using a virtual force sensor. In Proceedings of the 2014 IEEE/RSJ International Conference on Intelligent Robots and Systems, Chicago, IL, USA, 14–18 September 2014; pp. 2126–2133. [Google Scholar]
- Mendizabal, A.; Sznitman, R.; Cotin, S. Force classification during robotic interventions through simulation-trained neural networks. Int. J. Comput. Assist. Radiol. Surg.
**2019**, 14, 1601–1610. [Google Scholar] [CrossRef][Green Version] - Marban, A.; Srinivasan, V.; Samek, W.; Fernández, J.; Casals, A. A recurrent convolutional neural network approach for sensorless force estimation in robotic surgery. Biomed. Signal Process. Control.
**2019**, 50, 134–150. [Google Scholar] [CrossRef][Green Version] - Roveda, L.; Piga, D. Interaction Force Computation Exploiting Environment Stiffness Estimation for Sensorless Robot Applications. In Proceedings of the 2020 IEEE International Workshop on Metrology for Industry 4.0 & IoT, Rome, Italy, 3–5 June 2020; pp. 360–363. [Google Scholar]
- Wan, E.A.; Van Der Merwe, R. The unscented Kalman filter for nonlinear estimation. In Proceedings of the IEEE 2000 Adaptive Systems for Signal Processing, Communications, and Control Symposium (Cat. No. 00EX373), Lake Louise, AL, Canada, 4 October 2000; pp. 153–158. [Google Scholar]
- Andrieu, C.; Doucet, A.; Holenstein, R. Particle markov chain monte carlo methods. J. R. Stat. Soc. Ser.
**2010**, 72, 269–342. [Google Scholar] [CrossRef][Green Version] - Chopin, N.; Jacob, P.E.; Papaspiliopoulos, O. SMC2: An efficient algorithm for sequential analysis of state space models. J. R. Stat. Soc. Ser.
**2013**, 75, 397–426. [Google Scholar] [CrossRef][Green Version] - Urteaga, I.; Bugallo, M.F.; Djurić, P.M. Sequential Monte Carlo methods under model uncertainty. In Proceedings of the 2016 IEEE Statistical Signal Processing Workshop (SSP), Palma de Mallorca, Spain, 26–29 June 2016; pp. 1–5. [Google Scholar]
- Martino, L.; Read, J.; Elvira, V.; Louzada, F. Cooperative parallel particle filters for online model selection and applications to urban mobility. Digit. Signal Process.
**2017**, 60, 172–185. [Google Scholar] [CrossRef][Green Version] - Siciliano, B.; Villani, L. Robot Force Control, 1st ed.; Kluwer Academic Publishers: Norwell, MA, USA, 2000. [Google Scholar]
- Chang, P.R.; Lee, C.G. Residue arithmetic VLSI array architecture for manipulator pseudo-inverse Jacobian computation. In Proceedings of the 1988 IEEE International Conference on Robotics and Automation, Philadelphia, PA, USA, 24–29 April 1988; pp. 297–302. [Google Scholar]
- Pedrocchi, N.; Villagrossi, E.; Vicentini, F.; Molinari Tosatti, L. On robot dynamic model identification through sub-workspace evolved trajectories for optimal torque estimation. In Proceedings of the 2013 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Tokyo, Japan, 3–7 November 2013; pp. 2370–2376. [Google Scholar]
- Roveda, L.; Iannacci, N.; Tosatti, L.M. Discrete-time formulation for optimal impact control in interaction tasks. J. Intell. Robot. Syst.
**2018**, 90, 407–417. [Google Scholar] [CrossRef] - Corke, P. Robotics, Vision and Control: Fundamental Algorithms in MATLAB
^{®}Second, Completely Revised; Springer: Berlin, Germany, 2017; Volume 118. [Google Scholar] - Gaz, C.; Cognetti, M.; Oliva, A.; Giordano, P.R.; De Luca, A. Dynamic identification of the franka emika panda robot with retrieval of feasible parameters using penalty-based optimization. IEEE Robot. Autom. Lett.
**2019**, 4, 4147–4154. [Google Scholar] [CrossRef][Green Version] - Roveda, L.; Pallucca, G.; Pedrocchi, N.; Braghin, F.; Tosatti, L.M. Iterative learning procedure with reinforcement for high-accuracy force tracking in robotized tasks. IEEE Trans. Ind. Inform.
**2017**, 14, 1753–1763. [Google Scholar] [CrossRef] - Çimen, T. Approximate nonlinear optimal SDRE tracking control. In Proceedings of the 17th IFAC Symp. Automatic Control in Aerospace, Toulouse, France, 25–29 June 2007; pp. 147–152. [Google Scholar]

**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