### Abstract

Continuum robots are flexible manipulators capable of working in a complex workspace. In this regard, they are widely used in medicine and industry. However, existing methods of solving the inverse kinematics problem based on Jacobian inverse have high computational cost and singularity problems. In its turn, methods based on the geometric approach cannot find a solution for some points. This paper presents a novel approach for solving the inverse kinematics issue for multi-section continuum robots based on the Forward And Backward Reaching Inverse Kinematics (FABRIK) algorithm. The approach enables to reach the target point, controlling the robot tip orientation. During forward reaching, the bending sections of the robot are replaced by chords, connected together by spherical joints. During backward reaching, the arcs are restored from the chords and then the end-points and their orientations are updated. We also present a solution of the forward and inverse kinematics for a single-section robot, which is necessary for arcs restoration during backward reaching. To minimize the angular error, the last link of the robot is adjusted. The results of the simulation proved that the algorithm is able to reach 98.5±1.3% of the robot workspace and of 92.7±4.6% dexterity. The mean operating time of the algorithm is 1.45±1.32 ms per section. The results and possible modifications are also discussed.

Original language | English |
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Title of host publication | Proceedings of the 2018 18th International Conference on Mechatronics - Mechatronika, ME 2018 |

Editors | Dusan Maga, Alexandr Stefek, Tomas Brezina |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

ISBN (Electronic) | 9788021455443 |

Publication status | Published - 23 Jan 2019 |

Event | 18th International Conference on Mechatronics - Mechatronika, ME 2018 - Brno, Czech Republic Duration: 5 Dec 2018 → 7 Dec 2018 |

### Publication series

Name | Proceedings of the 2018 18th International Conference on Mechatronics - Mechatronika, ME 2018 |
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### Conference

Conference | 18th International Conference on Mechatronics - Mechatronika, ME 2018 |
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Country | Czech Republic |

City | Brno |

Period | 5.12.18 → 7.12.18 |

### Fingerprint

### Keywords

- continuum robot
- FABRIK
- inverse kinematics

### ASJC Scopus subject areas

- Mechanical Engineering
- Artificial Intelligence
- Electrical and Electronic Engineering

### Cite this

*Proceedings of the 2018 18th International Conference on Mechatronics - Mechatronika, ME 2018*[8624888] (Proceedings of the 2018 18th International Conference on Mechatronics - Mechatronika, ME 2018). Institute of Electrical and Electronics Engineers Inc..

**FABRIK-Based Inverse Kinematics for Multi-Section Continuum Robots.** / Kolpashchikov, Dmitrii Yu; Laptev, Nikita V.; Danilov, Viacheslav V.; Skirnevskiy, Igor P.; Manakov, Roman A.; Gerget, Olga M.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the 2018 18th International Conference on Mechatronics - Mechatronika, ME 2018.*, 8624888, Proceedings of the 2018 18th International Conference on Mechatronics - Mechatronika, ME 2018, Institute of Electrical and Electronics Engineers Inc., 18th International Conference on Mechatronics - Mechatronika, ME 2018, Brno, Czech Republic, 5.12.18.

}

TY - GEN

T1 - FABRIK-Based Inverse Kinematics for Multi-Section Continuum Robots

AU - Kolpashchikov, Dmitrii Yu

AU - Laptev, Nikita V.

AU - Danilov, Viacheslav V.

AU - Skirnevskiy, Igor P.

AU - Manakov, Roman A.

AU - Gerget, Olga M.

PY - 2019/1/23

Y1 - 2019/1/23

N2 - Continuum robots are flexible manipulators capable of working in a complex workspace. In this regard, they are widely used in medicine and industry. However, existing methods of solving the inverse kinematics problem based on Jacobian inverse have high computational cost and singularity problems. In its turn, methods based on the geometric approach cannot find a solution for some points. This paper presents a novel approach for solving the inverse kinematics issue for multi-section continuum robots based on the Forward And Backward Reaching Inverse Kinematics (FABRIK) algorithm. The approach enables to reach the target point, controlling the robot tip orientation. During forward reaching, the bending sections of the robot are replaced by chords, connected together by spherical joints. During backward reaching, the arcs are restored from the chords and then the end-points and their orientations are updated. We also present a solution of the forward and inverse kinematics for a single-section robot, which is necessary for arcs restoration during backward reaching. To minimize the angular error, the last link of the robot is adjusted. The results of the simulation proved that the algorithm is able to reach 98.5±1.3% of the robot workspace and of 92.7±4.6% dexterity. The mean operating time of the algorithm is 1.45±1.32 ms per section. The results and possible modifications are also discussed.

AB - Continuum robots are flexible manipulators capable of working in a complex workspace. In this regard, they are widely used in medicine and industry. However, existing methods of solving the inverse kinematics problem based on Jacobian inverse have high computational cost and singularity problems. In its turn, methods based on the geometric approach cannot find a solution for some points. This paper presents a novel approach for solving the inverse kinematics issue for multi-section continuum robots based on the Forward And Backward Reaching Inverse Kinematics (FABRIK) algorithm. The approach enables to reach the target point, controlling the robot tip orientation. During forward reaching, the bending sections of the robot are replaced by chords, connected together by spherical joints. During backward reaching, the arcs are restored from the chords and then the end-points and their orientations are updated. We also present a solution of the forward and inverse kinematics for a single-section robot, which is necessary for arcs restoration during backward reaching. To minimize the angular error, the last link of the robot is adjusted. The results of the simulation proved that the algorithm is able to reach 98.5±1.3% of the robot workspace and of 92.7±4.6% dexterity. The mean operating time of the algorithm is 1.45±1.32 ms per section. The results and possible modifications are also discussed.

KW - continuum robot

KW - FABRIK

KW - inverse kinematics

UR - http://www.scopus.com/inward/record.url?scp=85062735133&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85062735133&partnerID=8YFLogxK

M3 - Conference contribution

T3 - Proceedings of the 2018 18th International Conference on Mechatronics - Mechatronika, ME 2018

BT - Proceedings of the 2018 18th International Conference on Mechatronics - Mechatronika, ME 2018

A2 - Maga, Dusan

A2 - Stefek, Alexandr

A2 - Brezina, Tomas

PB - Institute of Electrical and Electronics Engineers Inc.

ER -