# Vision-Based Assisted Tele-Operation of a Dual-Arm Hydraulically Actuated Robot for Pipe Cutting and Grasping in Nuclear Environments

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Challenges in a Nuclear Environment

#### 1.2. Operator Feedback and User Interface

#### 1.3. The Microsoft Kinect

#### 1.4. Objectives and Organisation

## 2. Materials and Methods

#### 2.1. Manipulator Kinematics

_{n}) multiplied by rotations (R

_{n}), the end-effector position P for known joint angles is determined in the standard manner as follows,

#### 2.2. Robot Dynamics

_{k}and y

_{k}are the input voltage and output joint angle respectively, while ${a}_{i}\left\{{\mathit{\chi}}_{k}\right\}$ and ${b}_{j}\left\{{\mathit{\chi}}_{k}\right\}$ are n and m state dependent parameters that is, functions of a non-minimal state vector ${\mathit{\chi}}_{k}$ (see worked example below). In the case of a hydraulic manipulator, the model is identified in three stages as follows:

**Step 1.**Open-loop step experiments using the manipulator suggest that a first order linear difference equation, that is,

**Step 2.**The values of $\left\{{a}_{1},{b}_{\tau}\right\}$ are not repeatable for experiments with different input magnitudes. However, SDP analysis of experimental data suggests that n = m = 1, a

_{1}= −1 is time invariant and ${b}_{\tau}\left\{{\mathit{\chi}}_{k}\right\}={b}_{\tau}\left\{{v}_{k-\tau}\right\}$ is a static nonlinear function [43,44].

**Step 3.**Finally, ${b}_{\tau}\left\{{v}_{k-\tau}\right\}$ is parameterized, here using exponential functions for the nonlinearity. To illustrate using the right hand side ‘shoulder’ joint, denoted J

_{2}, with Δt = 0.01 s and $\tau =15$, RIV estimates ${b}_{\tau}$ for step input experiments of varying magnitudes are shown in Figure 3, demonstrating the clear state-dependency on the input.

#### 2.3. Robot Control

^{−1}in either direction, and it seems unlikely that faster movement would be desirable in practice. This approximation is the so called Static Non-Linear (SNL) element of Figure 4 and is defined as follows (cf. Equation (6)),

## 3. User Interface and Assisted Tele-Operation

#### 3.1. Stage 1: Positioning

#### 3.2. Stage 2: Image Capture and Edge Detection

#### 3.3. Stage 3: Operator Image Adjustment

#### 3.4. Stage 4: Operator Target Selection

#### 3.5. Stage 5: Grasp and Cut Location

#### 3.6. Stage 6: End-Effector Positioning

## 4. Results and Discussion

## 5. Conclusions and Future Work

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Brokk-HydroLek robotic platform. Further images: https://tinyurl.com/yd3bvslo.

**Figure 3.**

**Left Hand Side**: State-dependent parameter plotted against input magnitude (i.e., steady state voltage to NI-CFP, ${v}_{\infty}$), showing Refined Instrumental Variable (RIV) estimates ${b}_{\tau}$ for individual step experiments (circles) and optimised State Dependent Parameter (SDP) ${b}_{\tau}\left\{{\mathit{\chi}}_{k}\right\}$ (solid).

**Right Hand Side**: Angular velocity $\dot{\theta}$ (degrees/s) plotted against input magnitude (i.e., steady state voltage to NI-CFP, ${v}_{\infty}$), showing RIV estimates ${b}_{\tau}\times {v}_{\infty}/\mathsf{\Delta}t$ for individual step experiments (circles) and SDP ${b}_{\tau}\left\{{\mathit{\chi}}_{k}\right\}\times {v}_{\infty}/\mathsf{\Delta}t$ (solid trace). The estimated dead-zone and angular velocity saturations are also shown (dashed).

**Figure 4.**Schematic diagram of the joint angle control system, in which C, IDZ, SNL and LD represent the Controller, Inverse Dead-Zone element, Static Non-Linearity and Linear Dynamics, respectively.

**Figure 5.**IDZ approximation, showing angular velocity ${q}_{k}$ (degrees/sample, $\mathsf{\Delta}t=0.05$ s) against input (i.e., steady state voltage to NI-CFP, ${v}_{\infty}$), showing ${b}_{\tau}\left\{{\mathit{\chi}}_{k}\right\}\times {v}_{\infty}/\mathsf{\Delta}t$ (thin solid trace) and linearised model (thick). The estimated dead-zone and chosen velocity saturation limits are highlighted (dashed).

**Figure 7.**Preliminary image processing to remove background: (

**a**) original image and (

**b**) simplified image with out of reach areas removed.

**Figure 8.**Image contrast examples: original simplified image (top left) and the three different levels of contrast used for edge detection.

**Figure 9.**Edge detection results: (

**a**) original edge detected image and (

**b**) combining four different contrast levels into one image.

Link | X (mm) | Y (mm) | Z (mm) | Name |
---|---|---|---|---|

J_{01} | 0 | 0 | 0 | L_{0} |

J_{12} | 70.00 | 0 | 0 | L_{1} |

J_{23} | 523.48 | 0 | 0 | L_{2} |

J_{34} | 165.00 | −212.60 | 0 | L_{3} |

J_{45} | 44.45 | 0 | 0 | L_{4} |

J_{56} | 284.80 | −18.47 | 0 | L_{5} |

J_{67} | 0 | 0 | 0 | L_{6} |

Joint | Axis of Rotation | Rotation Matrix | Name |
---|---|---|---|

J_{1} | Y-axis | $\left[\begin{array}{ccc}cos\left({\theta}_{1}\right)& 0& sin\left({\theta}_{1}\right)\\ 0& 1& 0\\ -sin\left({\theta}_{1}\right)& 0& cos\left({\theta}_{1}\right)\end{array}\right]$ | R_{1} |

J_{2} | Z-axis | $\left[\begin{array}{ccc}cos\left({\theta}_{1}\right)& -sin\left({\theta}_{1}\right)& 0\\ sin\left({\theta}_{1}\right)& cos\left({\theta}_{1}\right)& 0\\ 0& 0& 1\end{array}\right]$ | R_{2} |

J_{3} | Z-axis | $\left[\begin{array}{ccc}cos\left({\theta}_{1}\right)& -sin\left({\theta}_{1}\right)& 0\\ sin\left({\theta}_{1}\right)& cos\left({\theta}_{1}\right)& 0\\ 0& 0& 1\end{array}\right]$ | R_{3} |

J_{4} | Y-axis | $\left[\begin{array}{ccc}cos\left({\theta}_{1}\right)& 0& sin\left({\theta}_{1}\right)\\ 0& 1& 0\\ -sin\left({\theta}_{1}\right)& 0& cos\left({\theta}_{1}\right)\end{array}\right]$ | R_{4} |

J_{5} | Z-axis | $\left[\begin{array}{ccc}cos\left({\theta}_{1}\right)& -sin\left({\theta}_{1}\right)& 0\\ sin\left({\theta}_{1}\right)& cos\left({\theta}_{1}\right)& 0\\ 0& 0& 1\end{array}\right]$ | R_{5} |

J_{6} | X-axis | $\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]$ | R_{6} |

**Table 3.**Comparison of inverse kinematics (IK) algorithm mean run time and position error for various tolerances.

Position Error Tolerance (mm) | Mean Run Time (s) | Mean Position Error (mm) | Mean Position Error Ignoring Outliers > 10 (mm) |
---|---|---|---|

5 | 0.0230 | 6.3496 | 4.8278 |

2 | 0.0429 | 2.9087 | 1.9315 |

1 | 0.0553 | 2.7949 | 1.0274 |

0.5 | 0.0873 | 1.6577 | 0.5166 |

0.1 | 0.1817 | 1.3907 | 0.1397 |

**Table 4.**Comparison of direct tele-operation and vision based assisted tele-operation, showing time (Minutes:Seconds) to complete a pipe grasp task.

Tele-Operation | Assisted Tele-Operation |
---|---|

Inexperienced User | |

2:02 | 0:31 |

3:09 (Failed, damaged pipe) | 0:22 |

2:28 | 0:27 |

Experienced User | |

0:57 | 0:20 |

1:04 | 0:21 |

1:08 | 0:20 |

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**MDPI and ACS Style**

Bandala, M.; West, C.; Monk, S.; Montazeri, A.; Taylor, C.J.
Vision-Based Assisted Tele-Operation of a Dual-Arm Hydraulically Actuated Robot for Pipe Cutting and Grasping in Nuclear Environments. *Robotics* **2019**, *8*, 42.
https://doi.org/10.3390/robotics8020042

**AMA Style**

Bandala M, West C, Monk S, Montazeri A, Taylor CJ.
Vision-Based Assisted Tele-Operation of a Dual-Arm Hydraulically Actuated Robot for Pipe Cutting and Grasping in Nuclear Environments. *Robotics*. 2019; 8(2):42.
https://doi.org/10.3390/robotics8020042

**Chicago/Turabian Style**

Bandala, Manuel, Craig West, Stephen Monk, Allahyar Montazeri, and C. James Taylor.
2019. "Vision-Based Assisted Tele-Operation of a Dual-Arm Hydraulically Actuated Robot for Pipe Cutting and Grasping in Nuclear Environments" *Robotics* 8, no. 2: 42.
https://doi.org/10.3390/robotics8020042