# Disturbance-Observer-Based Dual-Position Feedback Controller for Precision Control of an Industrial Robot Arm

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Design of the DOB-DPF Controller

#### 2.1. DOB Design

#### 2.2. DPF Controller

#### 2.3. DOB-DPF Controller

## 3. Design of a Five-DOF Robot Arm

#### 3.1. Hardware Design

#### 3.2. Controller Design

_{J5}, y

_{J5}, z

_{J5})

^{J1}indicates the position of joint 5 in the J1 coordinate system, [X

_{J1}, Y

_{J1}, Z

_{J1}], which is rotated by θ

_{1}in accordance with the global coordinate system [X

_{G}, Y

_{G}, Z

_{G}]. The angular position of joint 1, (${\theta}_{1}$) can be calculated from the target position of the end effector in the global coordinate, (${x}_{TP}$, ${y}_{TP}$, ${z}_{TP}$)

^{G}, as follows:

^{J1}is derived from ${\theta}_{1}$ and the unit vector of the target orientation in the global coordinate (V

_{TO}= (x

_{TO}, y

_{TO}, z

_{TO})

^{G}) using a rotational transformation matrix as follows:

^{J1}and the DH parameters, respectively. The angular position of joint 3 (${\theta}_{3}$) is the sum of the angle between ${D}_{4}$ and ${L}_{3}$, and ${\theta}_{{3}^{\prime}}$, which denotes the angle between ${A}_{2}$ and ${L}_{3}$.

_{1}) and the z-axis unit vector of the coordinate system of joint 5 (${Z}_{5}$), which can be calculated as follows:

#### 3.3. Measurement of Stiffness

## 4. Evaluation of DOB-DPF Controller

#### 4.1. Implementation of DOB-DPF Controller

#### 4.2. External Position Sensing

_{b}, C

_{w}, and C

_{G}) used to calculate the actual position and contour error of the end effector. C

_{b}is the coordinate of the Vive base station. The Vive acquires the three-dimensional position of the trackers with respect to the coordinates of the base station. The accuracy of the position measurement was 0.1 mm in our experimental setup. C

_{w}and C

_{G}denote the coordinates of the worktable and robot arm, respectively. The actual position of the robot arm was measured by attaching a tracker (T1) to the end effector; subsequently, it was converted to the worktable coordinate using a homogeneous transformation matrix (HTM). The HTMs of the worktable and base station coordinates were derived from the unit direction vectors of the worktable coordinates measured by three trackers (T2, T3, and T4) installed on the worktable. The target position of the robot arm was generated in the worktable coordinate and converted to the robot arm coordinate for position control. The contour error was calculated based on the target and actual positions of the end effector in the worktable coordinate. The HTMs of the robot arm and worktable coordinates were derived from the unit direction vectors of the robot arm coordinates calculated by measuring the position of tracker T1 when the robot was linearly moving along the x, y, and z axes.

#### 4.3. Evaluation Result

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Caro, S.; Dumas, C.; Garnier, S.; Furet, B. Workpiece placement optimization for machining operations with a KUKA KR270-2 robot. In Proceedings of the 2013 IEEE International Conference on Robotics and Automation, Karlsruhe, Germany, 6–10 May 2013; pp. 2921–2926. [Google Scholar]
- Wang, J.; Zhang, H.; Fuhlbrigge, T. Improving machining accuracy with robot deformation compensation. In Proceedings of the 2009 IEEE/RSJ International Conference on Intelligent Robots and Systems, St. Louis, MO, USA, 10–15 October 2009; pp. 3826–3831. [Google Scholar]
- Zhang, H.; Wang, J.; Zhang, G.; Gan, Z.; Pan, Z.; Cui, H.; Zhu, Z. Machining with flexible manipulator: Toward improving robotic machining performance. In Proceedings of the 2005 IEEE/ASME Interna-tional Conference on Advanced Intelligent Mechatronics, Monterey, CA, USA, 24–28 July 2005; pp. 1127–1132. [Google Scholar]
- Lee, W.; Lee, C.-Y.; Jeong, Y.H.; Min, B.-K. Distributed component friction model for precision control of a feed drive system. IEEE/ASME Trans. Mechatron.
**2015**, 20, 1966–1974. [Google Scholar] [CrossRef] - Chen, Y.; Dong, F. Robot machining: Recent development and future research issues. Int. J. Adv. Manuf. Technol.
**2012**, 66, 1489–1497. [Google Scholar] [CrossRef] [Green Version] - Belchior, J.; Guillo, M.; Courteille, E.; Maurine, P.; Leotoing, L.; Guines, D. Off-line compensation of the tool path deviations on robotic machining: Application to incremental sheet forming. Robot. Comput.-Integr. Manuf.
**2013**, 29, 58–69. [Google Scholar] [CrossRef] [Green Version] - Munasinghe, S.R.; Nakamura, M.; Goto, S.; Kyura, N. Optimum contouring of industrial robot arms under assigned velocity and torque constraints. IEEE Trans. Syst. Man Cybern.
**2001**, 31, 159–167. [Google Scholar] [CrossRef] - Olabi, A.; Damak, M.; Bearee, R.; Gibaru, O.; Leleu, S. Improving the accuracy of industrial robots by offline compensation of joints errors. In Proceedings of the 2012 IEEE International Conference on Industrial Technology, Athens, Greece, 19–21 March 2012; pp. 492–497. [Google Scholar]
- Schneider, U.; Drust, M.; Ansaloni, M.; Lehmann, C.; Pellic-ciari, M.; Leali, F.; Gunnink, J.W.; Verl, A. Improving robotic machining accuracy through experimental error investigation and modular compensation. Int. J. Adv. Manuf. Technol.
**2016**, 85, 3–15. [Google Scholar] [CrossRef] - Xu, K.-J.; Li, C.; Zhu, Z.-N. Dynamic modeling and compensation of robot six-axis wrist force/torque sensor. IEEE Trans. Instrum. Meas.
**2007**, 56, 2094–2100. [Google Scholar] [CrossRef] - Park, S.-K.; Lee, S.-H. Disturbance observer based robust control for industrial robots with flexible joints. In Proceedings of the 2007 International Conference on Control, Automation and Systems, Seoul, Republic of Korea, 17–20 October 2007. [Google Scholar]
- Moeller, C.; Schmidt, H.C.; Koch, P.; Boehlmann, C.; Kothe, S.; Wollnack, J.; Hintze, W. Real time pose control of an industrial robotic system for machining of large scale components in aerospace industry using laser tracker system. SAE Int. J. Aerosp.
**2017**, 2, 100–108. [Google Scholar] [CrossRef] [Green Version] - Furuta, K.; Kosuge, K.; Mukai, N. Control of articulated robot arm with sensory feedback: Laser beam tracking system. IEEE Trans. Ind. Electron.
**1988**, 35, 31–39. [Google Scholar] [CrossRef] - Park, J.; Chung, W. Design of a robust H∞ PID control for industrial manipulators. J. Dyn. Sys. Meas. Control
**2000**, 122, 803–812. [Google Scholar] [CrossRef] - Zhang, G.; Li, J.; Jin, X.; Liu, C. Robust adaptive neural control for wing-sail-assisted vehicle via the multiport event-triggered approach. IEEE Trans. Cybern.
**2021**, 52, 12916–12928. [Google Scholar] [CrossRef] [PubMed] - Zhang, G.; Li, J.; Liu, C.; Zhang, W. A robust fuzzy speed regulator for unmanned sailboat robot via the composite ILOS guidance. Nonlinear Dyn.
**2022**, 110, 2465–2480. [Google Scholar] [CrossRef] - Li, J.; Zhang, G.; Shan, Q.; Zhang, W. A Novel Cooperative Design for USV-UAV Systems: 3D Mapping Guidance and Adaptive Fuzzy Control. IEEE Trans. Control. Netw. Syst.
**2022**. [Google Scholar] [CrossRef] - Liu, S.; Wang, L.; Wang, X. Sensorless force estimation for industrial robots using disturbance observer and neural learning of friction approximation. Robot. Comput.-Integr. Manuf.
**2021**, 71, 102168. [Google Scholar] [CrossRef] - Tong, S.; Min, X.; Li, Y. Observer-based adaptive fuzzy tracking control for strict-feedback nonlinear systems with unknown control gain functions. IEEE Trans. Cybern.
**2020**, 50, 3903–3913. [Google Scholar] [CrossRef] [PubMed] - Cheng, X.; Tu, X.; Zhou, Y.; Zhou, R. Active disturbance rejection control of multi-joint industrial robots based on dynamic feedforward. Electronics
**2019**, 8, 591. [Google Scholar] [CrossRef] [Green Version] - Yin, X.; Li, P. Enhancing trajectory tracking accuracy for industrial robot with robust adaptive control. Robot. Comput.-Integr. Manuf.
**2018**, 51, 97–102. [Google Scholar] [CrossRef] - Mohammadi, A.; Tavakoli, M.; Marquez, H.J.; Hashemzadeh, F. Nonlinear disturbance observer design for robotic manipulators. Control. Eng. Pract.
**2013**, 21, 253–267. [Google Scholar] [CrossRef] [Green Version] - Spong, M.W.; Hutchinson, S.; Vidyasagar, M. Robot Dynamics and Control, 2nd ed.; Wiley: Hoboken, NJ, USA, 2004; pp. 205–207. [Google Scholar]
- Kim, N.; Kim, H.; Lee, W. Hardware-in-the-loop simulation for estimation of position control performance of machine tool feed drive. Precis. Eng.
**2019**, 60, 587–593. [Google Scholar] [CrossRef]

**Figure 1.**Block diagrams of (

**a**) a conventional semi-closed loop, (

**b**) fully closed loop, and (

**c**) the DPF control algorithm.

**Figure 3.**Experimental setup of the five-DOF robot arm: (

**a**) photo and (

**b**) Denavit–Hartenberg (DH) parameters, which represent the joint dimensions and relative angle.

**Figure 5.**Simulation result with respect to the initial position of (300 mm, 0 mm, 100 mm) to the target position of (500 mm, 200 mm, 300 mm), maintaining the target orientation as (0, 0, −1): (

**a**) target angles of joints 1 to 5 generated in the numerical control kernel and (

**b**) posture of the robot arm.

**Figure 6.**Simulation result of the dual-position feedback controller with sinusoidal wave disturbance: (

**a**) disturbance; (

**b**) position of the end effector measured by internal and external position sensors; (

**c**) peak position errors of the end effector with respect to the time constants of the dual-position feedback controller.

**Figure 7.**Simulation result of the dual-position feedback controller with square wave disturbance: (

**a**) disturbance; (

**b**) position of the end effector measured by internal and external position sensors; (

**c**) peak acceleration of the end effector with respect to the time constants of the dual-position feedback controller.

**Figure 8.**Three Cartesian coordinates (C

_{b}, C

_{w}, and C

_{G}) and four trackers used to calculate the actual position and contour error of the end effector.

**Figure 9.**Contouring performances of the conventional controller and the DOB-DPF controller before and after a constant weight of 2.2 kg was applied to the end effector: position of the end effector in (

**a**) three-dimensional and (

**b**) two-dimensional (XZ plane) graph and (

**c**) contour errors.

Control Method | Contour Error (mm) | ||
---|---|---|---|

Peak | RMS | STD | |

Conventional controller w/o disturbance | 1.80 | 0.59 | 0.31 |

Conventional controller w/ disturbance | 3.60 | 2.30 | 0.55 |

DOB-DPF controller w/ disturbance | 1.08 | 0.71 | 0.32 |

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**MDPI and ACS Style**

Kim, N.; Oh, D.; Oh, J.-Y.; Lee, W.
Disturbance-Observer-Based Dual-Position Feedback Controller for Precision Control of an Industrial Robot Arm. *Actuators* **2022**, *11*, 375.
https://doi.org/10.3390/act11120375

**AMA Style**

Kim N, Oh D, Oh J-Y, Lee W.
Disturbance-Observer-Based Dual-Position Feedback Controller for Precision Control of an Industrial Robot Arm. *Actuators*. 2022; 11(12):375.
https://doi.org/10.3390/act11120375

**Chicago/Turabian Style**

Kim, Namhyun, Daejin Oh, Jun-Young Oh, and Wonkyun Lee.
2022. "Disturbance-Observer-Based Dual-Position Feedback Controller for Precision Control of an Industrial Robot Arm" *Actuators* 11, no. 12: 375.
https://doi.org/10.3390/act11120375