# Joint Reconfiguration after Failure for Performing Emblematic Gestures in Humanoid Receptionist Robot

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Namo Robot

#### 2.2. Gesture Similarity Measurement

_{elbow}·d

_{elbow}) + (w

_{wrist}·d

_{wrist}) + (w

_{tip}·d

_{tip}) + (w

_{s}·d

_{s}),

_{s}is the angular distance between the reconfigured hand orientation and the reference hand orientation.

_{wrist_LR}, and the distance between the fingertip of the left and right hands, d

_{tip_LR}, in the gesture similarity measurement, as

_{elbow}·d

_{elbow}) + (w

_{wrist}·d

_{wrist}) + (w

_{tip}·d

_{tip}) + (w

_{s}·d

_{s})

+ (w

_{wrist_LR}·d

_{wrist_LR}− d

_{offset})

+ (w

_{tip_LR}·d

_{tip_LR}− d

_{offset}),

_{offset}is the offset value for the thickness of the hand. In this study, the weight values for (1) and (2) were set as equal weight values for all components.

#### 2.3. Bio-Inspired Joint Reconfiguration Method for Failure Recovery

#### 2.4. Performance Analysis

#### 2.4.1. Genetic Algorithm

#### 2.4.2. Bacteria Foraging Optimization Algorithm

#### 2.4.3. Artificial Bee Colony Algorithm

## 3. Results and Discussion

#### 3.1. Parameter Set Tuning for Optimal Solution

#### 3.2. Joint Reconfiguration for All Possible Joint Failures

#### 3.3. The Analysis of Output Gestures through the Gesture Similarity Measurement

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Namo’s main emblematic gestures used in this study: (

**a**) Wai (or Thai greeting), (

**b**) Bye, (

**c**) Salute, and (

**d**) Side Invite.

**Figure 2.**Namo’s right arm: (

**a**) the joint structure; (

**b**) the kinematic chains with Denavit–Hartenberg frames.

**Figure 3.**The gesture similarity measurement: (

**a**) Namo’s model in simulation; (

**b**) the frame-based comparison between the reconfigured gesture and the reference gesture of Namo’s right arm; (

**c**) the concept for hand orientation similarity measurement.

**Figure 5.**The emblematic gestures expressed by the Namo robot in simulation: (

**a**) the reference gestures, (

**b**) the output gestures from GA, (

**c**) the output gestures from BFOA, and (

**d**) the output gestures from ABC.

**Figure 6.**The comparison between gesture similarity scores from gradient descent (GD) and ABC algorithms over the iterations.

**Figure 7.**The best reconfiguration outputs of the Wai (Thai greeting) emblematic gesture in all possible joint failures on the Namo robot compared to the reference gesture: (

**a**) reference gesture; (

**b**) joint 1 failure; (

**c**) joint 2 failure; (

**d**) joint 3 failure; (

**e**) joint 4 failure; (

**f**) joint 5 failure; (

**g**) joint 6 failure; (

**h**) joint 7 failure.

**Figure 8.**The boxplot of the distance components between the best reconfiguration outputs and the reference gestures in all possible joint failures on the Namo robot: (

**a**) distance of the elbow component; (

**b**) distance of the wrist component; (

**c**) distance of the fingertip component; (

**d**) distance of the palm orientation component; (

**e**) distance between the left and right wrists for the Wai gesture; (

**f**) distance between the left and right fingertips for the Wai gesture.

Joint No. | ${\mathit{\theta}}_{\mathit{i}}$ (Degree) | ${\mathit{d}}_{\mathit{i}}$ (mm) | ${\mathit{a}}_{\mathit{i}-1}$ (mm) | ${\mathit{\alpha}}_{\mathit{i}-1}$ (Degree) |
---|---|---|---|---|

1 | ${\theta}_{r1}+90\xb0$ | 182 | 0 | $90\xb0$ |

2 | ${\theta}_{r2}+90\xb0$ | 0 | 0 | $90\xb0$ |

3 | ${\theta}_{r3}-90\xb0$ | 206.5 | 0 | $-90\xb0$ |

4 | ${\theta}_{r4}$ | 0 | 0 | $-90\xb0$ |

5 | ${\theta}_{r5}+90\xb0$ | 206 | 0 | $90\xb0$ |

6 | ${\theta}_{r6}-90\xb0$ | 0 | 0 | $90\xb0$ |

7 | ${\theta}_{r7}$ | 0 | 0 | $-90\xb0$ |

E | 0 | 0 | −130 | 0 |

Gesture | Joint Angle (Degree) | ||||||
---|---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | 7 | |

Wai | 30 | 5 | −45 | 90 | −10 | −45 | 45 |

Bye | 46 | −11 | 24 | 95 | −53 | −32 | 41 |

Salute | 100 | −43 | −45 | 100 | 47 | 28 | 10 |

Side Invite | 34 | −8 | 45 | 72 | 51 | 26 | 26 |

Average | 52.5 | −14.25 | −5.25 | 89.25 | 8.75 | −5.75 | 30.5 |

Control Parameter | Values | Best Gesture Similarity Score | Computation Time (s) |
---|---|---|---|

GA | 58.1797 | 0.6540 | |

Population size | 80 | ||

Maximum iteration | 50 | ||

Crossover rate | 0.8 | ||

Mutation rate | 0.25 | ||

Mutation step size | 0.15 | ||

BFOA | 57.1479 | 0.5655 | |

Population size | 10 | ||

Swimming length | 0.5 | ||

Number of elimination-dispersal events | 2 | ||

Number of reproduction steps | 6 | ||

Number of chemotactic steps | 10 | ||

Number of swim steps | 15 | ||

Probability of elimination-dispersal | 0.3 | ||

The depth of the attractant signal | 0.4 | ||

The width of the attractant signal | 0.3 | ||

The height of the repellant effect | 0.4 | ||

The width of the repellant effect | 0.3 | ||

ABC | 57.1431 | 0.5457 | |

Population size | 5 | ||

Maximum iteration | 500 | ||

Limit | 150 |

**Table 4.**The descriptive statistics of difference from reference gestures of GA, BFOA, and ABC reconfigured gestures from 100 repetitions using the tuned parameter sets.

Emblematic Gestures | Descriptive Statistics of Difference from Reference Gestures | Kruskal–Wallis Test | |||||
---|---|---|---|---|---|---|---|

MIN | MAX | MEAN | SD | Median | Interquartile Range | ||

Wai | |||||||

GA | 58.1797 | 88.1129 | 70.7241 | 5.9783 | 70.6528 | 9.0588 | H(2) = 144.539 p = 0.000 |

BFOA | 57.1479 | 139.2824 | 64.4391 | 16.8914 | 58.4939 | 3.4149 | |

ABC | 57.1431 | 83.2653 | 59.1699 | 3.0858 | 58.1876 | 2.1447 | |

Bye | |||||||

GA | 6.0976 | 55.3328 | 26.9466 | 10.0887 | 25.6681 | 14.0880 | H(2) = 138.612 p = 0.000 |

BFOA | 3.4758 | 82.5701 | 16.8547 | 17.9914 | 9.4605 | 16.5519 | |

ABC | 3.2491 | 61.4498 | 6.8030 | 6.6568 | 5.6970 | 3.7215 | |

Salute | |||||||

GA | 37.2962 | 64.8065 | 48.6495 | 6.5060 | 48.4423 | 9.7109 | H(2) = 133.416 p = 0.000 |

BFOA | 35.4799 | 123.0403 | 51.0233 | 25.0001 | 37.5537 | 20.9101 | |

ABC | 35.4694 | 42.6509 | 36.2064 | 1.1113 | 35.8170 | 0.8266 | |

Side Invite | |||||||

GA | 8.8991 | 34.1130 | 19.6917 | 6.4367 | 19.4553 | 10.2574 | H(2) = 97.740 p = 0.000 |

BFOA | 7.5411 | 124.6998 | 27.7533 | 28.9818 | 11.0276 | 37.2525 | |

ABC | 7.4523 | 37.3143 | 9.3562 | 3.3229 | 8.6145 | 1.8183 |

**Table 5.**The descriptive statistics of computation time of GA, BFOA, and ABC output gestures reconfigured gestures from 100 repetitions using the tuned parameter sets.

Emblematic Gestures | Descriptive Statistics of Computation Time (Seconds) | Kruskal–Wallis Test | |||||
---|---|---|---|---|---|---|---|

MIN | MAX | MEAN | SD | Median | Interquartile Range | ||

Wai | |||||||

GA | 0.6120 | 0.7307 | 0.6635 | 0.0316 | 0.6531 | 0.0202 | H(2) = 192.905 p = 0.000 |

BFOA | 0.4658 | 0.6895 | 0.5669 | 0.0456 | 0.5674 | 0.0713 | |

ABC | 0.5427 | 0.5729 | 0.5504 | 0.0050 | 0.5500 | 0.0058 | |

Bye | |||||||

GA | 0.5529 | 0.6139 | 0.5725 | 0.0212 | 0.5604 | 0.0435 | H(2) = 151.510 p = 0.000 |

BFOA | 0.4291 | 0.6526 | 0.5256 | 0.0371 | 0.5215 | 0.0478 | |

ABC | 0.5290 | 0.5550 | 0.5365 | 0.0045 | 0.5356 | 0.0037 | |

Salute | |||||||

GA | 0.5441 | 0.6098 | 0.5608 | 0.0197 | 0.5496 | 0.0402 | H(2) = 88.890 p = 0.000 |

BFOA | 0.4186 | 0.6195 | 0.5415 | 0.0487 | 0.5433 | 0.0700 | |

ABC | 0.5274 | 0.5500 | 0.5356 | 0.0046 | 0.5352 | 0.0050 | |

Side Invite | |||||||

GA | 0.5431 | 0.6034 | 0.5601 | 0.0199 | 0.5492 | 0.0392 | H(2) = 103.477 p = 0.000 |

BFOA | 0.4427 | 0.6216 | 0.5338 | 0.0394 | 0.5375 | 0.0577 | |

ABC | 0.5261 | 0.5501 | 0.5356 | 0.0053 | 0.5344 | 0.0077 |

**Table 6.**The comparison of algorithm performance on joint reconfiguration for all joint failures using the tuned parameter sets.

Gestures/Joint Failure | Algorithm Performance | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

GA | BFOA | ABC | ||||||||||

Min. Diff. | Time | Median Diff. | IQR Diff. | Min. Diff. | Time | Median Diff. | IQR Diff. | Min. Diff. | Time | Median Diff. | IQR Diff. | |

Wai | ||||||||||||

Joint 1 | 49.1402 | 0.6566 | 69.6643 | 11.0471 | 42.8178 | 0.6187 | 50.5072 | 10.7610 | 41.0485 | 0.5774 | 44.3499 | 2.8718 |

Joint 2 | 58.1797 | 0.6540 | 70.6528 | 9.0588 | 57.1479 | 0.5655 | 58.4939 | 3.4149 | 57.1431 | 0.5457 | 58.1876 | 2.1447 |

Joint 3 | 98.6053 | 0.6567 | 107.8992 | 10.9072 | 93.7746 | 0.5258 | 93.9123 | 3.2764 | 93.7706 | 0.5617 | 93.8543 | 1.0137 |

Joint 4 | 18.9686 | 0.6536 | 45.7340 | 15.0691 | 2.2879 | 0.5539 | 14.2642 | 10.6975 | 2.2689 | 0.5570 | 6.0225 | 2.7596 |

Joint 5 | 39.3249 | 0.6435 | 55.4432 | 9.6103 | 23.1424 | 0.5179 | 29.7293 | 10.5429 | 24.2184 | 0.5498 | 30.7042 | 10.7042 |

Joint 6 | 35.2101 | 0.6485 | 43.5085 | 8.2551 | 32.8321 | 0.5077 | 36.2486 | 12.7388 | 33.0264 | 0.5456 | 35.3097 | 9.2949 |

Joint 7 | 19.5293 | 0.6496 | 39.3058 | 14.2708 | 8.8689 | 0.4662 | 12.9176 | 10.1463 | 8.8584 | 0.5688 | 10.0184 | 2.8088 |

Bye | ||||||||||||

Joint 1 | 18.1645 | 0.5614 | 32.6537 | 8.6828 | 14.5946 | 0.5371 | 14.9520 | 29.3480 | 14.5736 | 0.5344 | 14.8986 | 0.4006 |

Joint 2 | 6.0976 | 0.5573 | 25.6681 | 14.0880 | 3.4758 | 0.5088 | 9.4605 | 16.5519 | 3.2491 | 0.5413 | 5.6970 | 3.7215 |

Joint 3 | 41.6956 | 0.5581 | 53.1471 | 13.9760 | 38.5793 | 0.4468 | 46.0145 | 4.2315 | 38.5830 | 0.5342 | 39.3959 | 4.2612 |

Joint 4 | 11.2942 | 0.6028 | 35.2845 | 17.4609 | 9.5524 | 0.5492 | 9.9890 | 49.1354 | 9.5561 | 0.5338 | 9.7593 | 0.9447 |

Joint 5 | 54.8825 | 0.6036 | 58.8346 | 4.7642 | 52.7563 | 0.4211 | 53.8811 | 1.6746 | 52.6081 | 0.5304 | 53.5293 | 2.2006 |

Joint 6 | 31.7665 | 0.5477 | 44.6053 | 10.7182 | 27.5324 | 0.4849 | 28.2962 | 4.5840 | 27.6241 | 0.5431 | 31.1612 | 6.7783 |

Joint 7 | 8.7007 | 0.5956 | 28.9101 | 15.9774 | 7.8289 | 0.4960 | 11.0214 | 37.2409 | 7.8396 | 0.5404 | 8.9075 | 4.0756 |

Salute | ||||||||||||

Joint 1 | 82.3338 | 0.5472 | 84.8872 | 3.4310 | 82.2325 | 0.6137 | 82.5707 | 31.2031 | 82.2782 | 0.5369 | 82.7736 | 0.4377 |

Joint 2 | 37.2962 | 0.5469 | 48.4423 | 9.7109 | 35.4799 | 0.6014 | 37.5537 | 20.9101 | 35.4694 | 0.5394 | 35.8170 | 0.8266 |

Joint 3 | 44.2610 | 0.5525 | 57.1333 | 11.2424 | 42.0222 | 0.5558 | 43.1040 | 46.4772 | 42.0221 | 0.5408 | 42.3335 | 0.7601 |

Joint 4 | 21.5768 | 0.6080 | 34.7085 | 13.3364 | 18.1860 | 0.5824 | 22.5206 | 54.7482 | 18.1818 | 0.5389 | 18.6810 | 1.8249 |

Joint 5 | 28.2134 | 0.5476 | 38.8455 | 10.0302 | 24.1045 | 0.4632 | 27.6639 | 30.6599 | 24.1781 | 0.5323 | 29.4687 | 5.8234 |

Joint 6 | 34.2160 | 0.5542 | 50.9548 | 11.3999 | 33.0824 | 0.5050 | 35.3237 | 35.8533 | 33.2683 | 0.5367 | 33.8175 | 16.5031 |

Joint 7 | 21.3601 | 0.5929 | 30.4201 | 8.2655 | 17.4007 | 0.5125 | 17.5952 | 21.4105 | 17.3955 | 0.5364 | 17.3971 | 0.0105 |

Side Invite | ||||||||||||

Joint 1 | 51.7017 | 0.5483 | 61.7445 | 7.1490 | 48.8570 | 0.5537 | 58.0899 | 54.1146 | 48.8454 | 0.5376 | 49.1610 | 0.5528 |

Joint 2 | 8.8991 | 0.5464 | 19.4553 | 10.2574 | 7.5411 | 0.5404 | 11.0276 | 37.2525 | 7.4523 | 0.5428 | 8.6145 | 1.8183 |

Joint 3 | 62.9119 | 0.5445 | 75.5241 | 8.7711 | 57.7096 | 0.4627 | 58.9446 | 20.0700 | 57.7082 | 0.5331 | 57.7507 | 0.2847 |

Joint 4 | 27.2899 | 0.5526 | 32.6247 | 6.0936 | 26.7073 | 0.5202 | 34.6626 | 28.3888 | 26.7035 | 0.5513 | 26.7821 | 0.3401 |

Joint 5 | 32.7265 | 0.5671 | 47.7179 | 8.7698 | 29.8469 | 0.4813 | 35.3923 | 18.5515 | 29.6142 | 0.5386 | 31.0482 | 2.3620 |

Joint 6 | 24.1722 | 0.5683 | 31.1570 | 8.5519 | 23.7687 | 0.5164 | 28.4278 | 42.2346 | 23.7868 | 0.5481 | 26.6748 | 4.3452 |

Joint 7 | 7.8360 | 0.5744 | 19.4936 | 10.9503 | 3.5024 | 0.5659 | 23.3782 | 50.3712 | 3.4910 | 0.5402 | 4.4502 | 1.5727 |

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**MDPI and ACS Style**

Jutharee, W.; Kaewkamnerdpong, B.; Maneewarn, T.
Joint Reconfiguration after Failure for Performing Emblematic Gestures in Humanoid Receptionist Robot. *Sensors* **2023**, *23*, 9277.
https://doi.org/10.3390/s23229277

**AMA Style**

Jutharee W, Kaewkamnerdpong B, Maneewarn T.
Joint Reconfiguration after Failure for Performing Emblematic Gestures in Humanoid Receptionist Robot. *Sensors*. 2023; 23(22):9277.
https://doi.org/10.3390/s23229277

**Chicago/Turabian Style**

Jutharee, Wisanu, Boonserm Kaewkamnerdpong, and Thavida Maneewarn.
2023. "Joint Reconfiguration after Failure for Performing Emblematic Gestures in Humanoid Receptionist Robot" *Sensors* 23, no. 22: 9277.
https://doi.org/10.3390/s23229277