### Abstract

The traditionally viable way for the solution of the inverse kinematic task for general open kinematic structure is the differential approach in which the Jacobian of the robot arm usually is inverted by the use of some generalized matrix inverse. These approaches suffer from the kinematic singularities nearby which these 'inverses' are ill-conditioned and behave in a very inconvenient way. For dealing with the singularities complementary tricks used to be introduced that so deform the original task that the obtained 'solution' behaves conveniently though it cannot solve the original task that does not have exact solution. In this paper an alternative approach is suggested that requires only the computation of the Jacobian but does not need the calculation of its 'generalized inverse'. Instead of that it applies an iterative sequence that has nice convergence properties. The method automatically handles the problem of the singularities, ambiguity, redundancies, and non-existing exact solutions without the application of any complementary trick or artificial parameter. Its operation is demonstrated for a simple 2 Degree of Freedom (DoF) arm, and for an 8 DoF arm, that is an irregular extension of a 6 DoF PUMA-type robot.

Original language | English |
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Title of host publication | CINTI 2016 - 17th IEEE International Symposium on Computational Intelligence and Informatics: Proceedings |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 61-66 |

Number of pages | 6 |

ISBN (Electronic) | 9781509039098 |

DOIs | |

Publication status | Published - Feb 7 2017 |

Event | 17th IEEE International Symposium on Computational Intelligence and Informatics, CINTI 2016 - Budapest, Hungary Duration: Nov 17 2016 → Nov 19 2016 |

### Other

Other | 17th IEEE International Symposium on Computational Intelligence and Informatics, CINTI 2016 |
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Country | Hungary |

City | Budapest |

Period | 11/17/16 → 11/19/16 |

### Fingerprint

### Keywords

- Fixed Point Transformations
- Inverse Kinematic Task
- Open Kinematic Chain
- Redundant Robot Arms

### ASJC Scopus subject areas

- Control and Optimization
- Artificial Intelligence
- Information Systems

### Cite this

*CINTI 2016 - 17th IEEE International Symposium on Computational Intelligence and Informatics: Proceedings*(pp. 61-66). [7846380] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CINTI.2016.7846380

**Matrix inversion-free quasi-differential approach in solving the inverse kinematic task.** / Csanadi, Bertalan; Tar, J.; Bito, Janos F.

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

*CINTI 2016 - 17th IEEE International Symposium on Computational Intelligence and Informatics: Proceedings.*, 7846380, Institute of Electrical and Electronics Engineers Inc., pp. 61-66, 17th IEEE International Symposium on Computational Intelligence and Informatics, CINTI 2016, Budapest, Hungary, 11/17/16. https://doi.org/10.1109/CINTI.2016.7846380

}

TY - GEN

T1 - Matrix inversion-free quasi-differential approach in solving the inverse kinematic task

AU - Csanadi, Bertalan

AU - Tar, J.

AU - Bito, Janos F.

PY - 2017/2/7

Y1 - 2017/2/7

N2 - The traditionally viable way for the solution of the inverse kinematic task for general open kinematic structure is the differential approach in which the Jacobian of the robot arm usually is inverted by the use of some generalized matrix inverse. These approaches suffer from the kinematic singularities nearby which these 'inverses' are ill-conditioned and behave in a very inconvenient way. For dealing with the singularities complementary tricks used to be introduced that so deform the original task that the obtained 'solution' behaves conveniently though it cannot solve the original task that does not have exact solution. In this paper an alternative approach is suggested that requires only the computation of the Jacobian but does not need the calculation of its 'generalized inverse'. Instead of that it applies an iterative sequence that has nice convergence properties. The method automatically handles the problem of the singularities, ambiguity, redundancies, and non-existing exact solutions without the application of any complementary trick or artificial parameter. Its operation is demonstrated for a simple 2 Degree of Freedom (DoF) arm, and for an 8 DoF arm, that is an irregular extension of a 6 DoF PUMA-type robot.

AB - The traditionally viable way for the solution of the inverse kinematic task for general open kinematic structure is the differential approach in which the Jacobian of the robot arm usually is inverted by the use of some generalized matrix inverse. These approaches suffer from the kinematic singularities nearby which these 'inverses' are ill-conditioned and behave in a very inconvenient way. For dealing with the singularities complementary tricks used to be introduced that so deform the original task that the obtained 'solution' behaves conveniently though it cannot solve the original task that does not have exact solution. In this paper an alternative approach is suggested that requires only the computation of the Jacobian but does not need the calculation of its 'generalized inverse'. Instead of that it applies an iterative sequence that has nice convergence properties. The method automatically handles the problem of the singularities, ambiguity, redundancies, and non-existing exact solutions without the application of any complementary trick or artificial parameter. Its operation is demonstrated for a simple 2 Degree of Freedom (DoF) arm, and for an 8 DoF arm, that is an irregular extension of a 6 DoF PUMA-type robot.

KW - Fixed Point Transformations

KW - Inverse Kinematic Task

KW - Open Kinematic Chain

KW - Redundant Robot Arms

UR - http://www.scopus.com/inward/record.url?scp=85015272229&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85015272229&partnerID=8YFLogxK

U2 - 10.1109/CINTI.2016.7846380

DO - 10.1109/CINTI.2016.7846380

M3 - Conference contribution

AN - SCOPUS:85015272229

SP - 61

EP - 66

BT - CINTI 2016 - 17th IEEE International Symposium on Computational Intelligence and Informatics: Proceedings

PB - Institute of Electrical and Electronics Engineers Inc.

ER -