# Human Robot Hand Interaction with Plastic Deformation Control

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Plastic Deformation Control

#### 2.1. Nominal Control Law

#### 2.2. Plastic Deformation Control with the Inner Position Loop

## 3. System Configuration

#### 3.1. High-Speed Finger with a Force Sensor

^{®}and a high-power mini actuator are installed in the finger link. The design of this actuator, which is based on the concept that the maximum power output, rather than rated power output, should be improved. Table 2 presents the specification of actuators used in this finger. This finger can close its joints at $180\mathrm{deg}\phantom{\rule{0.277778em}{0ex}}$ per $0.1\mathrm{s}\phantom{\rule{0.277778em}{0ex}}$; its maximum rotational speed is $300\mathrm{rpm}\phantom{\rule{0.277778em}{0ex}}$, and the maximum output force is $12\mathrm{N}\phantom{\rule{0.277778em}{0ex}}$.

#### 3.2. Real-Time Control System

## 4. Simulation

#### 4.1. Simulation with Fiction Error

#### 4.2. Simulation by Varying the Parameter with Error

## 5. Experiment

#### 5.1. Applying Virtual Constant Force

#### 5.2. Pushing the Fingertip with Human Finger

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 5.**Trajectory of displacements of the endpoint in the simulation with error added to the friction coefficient.

**Figure 6.**Trajectory of the joint angles in the simulation with error added to the friction coefficient: (

**a**) Joint 1. (

**b**) Joint 2.

**Figure 7.**Trajectory of displacements of the endpoint with varying parameters: (

**a**) With nominal control. (

**b**) With proposed control.

**Figure 8.**Simulation with applying force by separating in the X and Y directions. (

**a**) Applied force. (

**b**) Trajectories of end point.

**Figure 9.**Simulation with applying force while changing the direction to circular. (

**a**) Applied force. (

**b**) Trajectories of end point.

**Figure 10.**Trajectory of displacements of the endpoint in the simulation by varying the parameter with error: The labels in the legend starting with “Err: ” show the parameter with 20% error added. (

**a**) With nominal control. (

**b**) With proposed control.

**Figure 11.**Successive images of the experiment: virtually applying ${F}_{x}={F}_{y}=0.2\mathrm{N}\phantom{\rule{0.277778em}{0ex}}$ for $0.5$ s. (

**a**) With nominal control. (

**b**) With proposed control.

**Figure 12.**Response of the finger by applying a virtual constant force: (

**a**) Displacement of the end point. (

**b**) Trajectories of the joint angle.

**Figure 13.**Successive images of the experiment: pushing with a human finger. (

**a**) With nominal control. (

**b**) With proposed control.

**Figure 14.**Displacement of the endpoint of the finger. (

**a**) With nominal control. (

**b**) With proposed control.

**Figure 16.**Response of the finger with the proposed control: (

**a**) Trajectories of the endpoint. (

**b**) Trajectories of joint angle.

Model | Voigt Model | Maxwell Model |
---|---|---|

Deformation type | Elastic deformation | Plastic deformation |

Connection configuration | Parallel | Series |

Corresponding control law | Impedance control | Plastic deformation control |

Diagram |

Joint 1 | Joint 2 | |
---|---|---|

Reduction rate | 50 | 50 |

Maximum torque [Nm] | 0.9 | 0.21 |

Maximum speed [rpm] | 200 | 200 |

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**MDPI and ACS Style**

Murakami, K.; Ishimoto, K.; Senoo, T.; Ishikawa, M.
Human Robot Hand Interaction with Plastic Deformation Control. *Robotics* **2020**, *9*, 73.
https://doi.org/10.3390/robotics9030073

**AMA Style**

Murakami K, Ishimoto K, Senoo T, Ishikawa M.
Human Robot Hand Interaction with Plastic Deformation Control. *Robotics*. 2020; 9(3):73.
https://doi.org/10.3390/robotics9030073

**Chicago/Turabian Style**

Murakami, Kenichi, Koki Ishimoto, Taku Senoo, and Masatoshi Ishikawa.
2020. "Human Robot Hand Interaction with Plastic Deformation Control" *Robotics* 9, no. 3: 73.
https://doi.org/10.3390/robotics9030073