### Abstract

In this paper the properties of a novel adaptive non-linear control recently developed at Budapest Tech for "Multiple Input-Multiple Output (MIMO) Systems" is comapred with that of the sophisticated "Adaptive Control by Slotine & Li" widely used in robot control literature. While this latter traditional method utilizes very subtle details of the structurally and formally exact analytical model of the robot in each step of the control cycle in which only the exact values of the parameters are unknown, the novel approach is based on simple geometric considerations concerning the method of the "Singular Value Decomposition (SVD)". Furthermore, while the proof of the asymptotic stability and convergence to an exact trajectory tracking of Slotine's & Li's control is based on "Lyapunov's 2^{nd} Method", in the new approach the control task is formulated as a Fixed Point Problem for the solution of which a Contractive Mapping is created that generates an Iterative Cauchy Sequence. Consequently it converges to the fixed point that is the solution of the control task. Besides the use of very subtle analytical details the main drawback of the Slotine & Li method is that it assumes that the generalized forces acting on the controlled system are eaxctly known and are equal with that exerted by the controlled drives. So unknown external perturbations can disturb the operation of this sophisticated method. In contrast to that, in the novel method the computationally relatively costly SVD operation on the formally almost exact model need not to be done within each control cycle: it has to be done only one times before the control action is initiated. In the control cyle the inertia matrix is modeled only by a simple scalar. In a more general case the SVD of some approximate model can be done only in a few typical points of the state space of a Classical Mechanical System. To illustrate the usability of the proposed method adaptive control of a Classical Mechanical paradigm, a cart plus crane plus hamper system is considered and discussed by the use of simulation results.

Original language | English |
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Title of host publication | 12th International Conference on Intelligent Engineering Systems - Proceedings, INES 2008 |

Pages | 24-30 |

Number of pages | 7 |

DOIs | |

Publication status | Published - 2008 |

Event | 12th International Conference on Intelligent Engineering Systems, INES 2008 - Miami, FL, United States Duration: Feb 25 2008 → Feb 29 2008 |

### Other

Other | 12th International Conference on Intelligent Engineering Systems, INES 2008 |
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Country | United States |

City | Miami, FL |

Period | 2/25/08 → 2/29/08 |

### Fingerprint

### ASJC Scopus subject areas

- Artificial Intelligence
- Computer Graphics and Computer-Aided Design
- Software
- Control and Systems Engineering

### Cite this

*12th International Conference on Intelligent Engineering Systems - Proceedings, INES 2008*(pp. 24-30). [4481264] https://doi.org/10.1109/INES.2008.4481264

**Analysis of the fixed point transformation based adapive robot control.** / Tar, J.; Rudas, I.

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

*12th International Conference on Intelligent Engineering Systems - Proceedings, INES 2008.*, 4481264, pp. 24-30, 12th International Conference on Intelligent Engineering Systems, INES 2008, Miami, FL, United States, 2/25/08. https://doi.org/10.1109/INES.2008.4481264

}

TY - GEN

T1 - Analysis of the fixed point transformation based adapive robot control

AU - Tar, J.

AU - Rudas, I.

PY - 2008

Y1 - 2008

N2 - In this paper the properties of a novel adaptive non-linear control recently developed at Budapest Tech for "Multiple Input-Multiple Output (MIMO) Systems" is comapred with that of the sophisticated "Adaptive Control by Slotine & Li" widely used in robot control literature. While this latter traditional method utilizes very subtle details of the structurally and formally exact analytical model of the robot in each step of the control cycle in which only the exact values of the parameters are unknown, the novel approach is based on simple geometric considerations concerning the method of the "Singular Value Decomposition (SVD)". Furthermore, while the proof of the asymptotic stability and convergence to an exact trajectory tracking of Slotine's & Li's control is based on "Lyapunov's 2nd Method", in the new approach the control task is formulated as a Fixed Point Problem for the solution of which a Contractive Mapping is created that generates an Iterative Cauchy Sequence. Consequently it converges to the fixed point that is the solution of the control task. Besides the use of very subtle analytical details the main drawback of the Slotine & Li method is that it assumes that the generalized forces acting on the controlled system are eaxctly known and are equal with that exerted by the controlled drives. So unknown external perturbations can disturb the operation of this sophisticated method. In contrast to that, in the novel method the computationally relatively costly SVD operation on the formally almost exact model need not to be done within each control cycle: it has to be done only one times before the control action is initiated. In the control cyle the inertia matrix is modeled only by a simple scalar. In a more general case the SVD of some approximate model can be done only in a few typical points of the state space of a Classical Mechanical System. To illustrate the usability of the proposed method adaptive control of a Classical Mechanical paradigm, a cart plus crane plus hamper system is considered and discussed by the use of simulation results.

AB - In this paper the properties of a novel adaptive non-linear control recently developed at Budapest Tech for "Multiple Input-Multiple Output (MIMO) Systems" is comapred with that of the sophisticated "Adaptive Control by Slotine & Li" widely used in robot control literature. While this latter traditional method utilizes very subtle details of the structurally and formally exact analytical model of the robot in each step of the control cycle in which only the exact values of the parameters are unknown, the novel approach is based on simple geometric considerations concerning the method of the "Singular Value Decomposition (SVD)". Furthermore, while the proof of the asymptotic stability and convergence to an exact trajectory tracking of Slotine's & Li's control is based on "Lyapunov's 2nd Method", in the new approach the control task is formulated as a Fixed Point Problem for the solution of which a Contractive Mapping is created that generates an Iterative Cauchy Sequence. Consequently it converges to the fixed point that is the solution of the control task. Besides the use of very subtle analytical details the main drawback of the Slotine & Li method is that it assumes that the generalized forces acting on the controlled system are eaxctly known and are equal with that exerted by the controlled drives. So unknown external perturbations can disturb the operation of this sophisticated method. In contrast to that, in the novel method the computationally relatively costly SVD operation on the formally almost exact model need not to be done within each control cycle: it has to be done only one times before the control action is initiated. In the control cyle the inertia matrix is modeled only by a simple scalar. In a more general case the SVD of some approximate model can be done only in a few typical points of the state space of a Classical Mechanical System. To illustrate the usability of the proposed method adaptive control of a Classical Mechanical paradigm, a cart plus crane plus hamper system is considered and discussed by the use of simulation results.

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U2 - 10.1109/INES.2008.4481264

DO - 10.1109/INES.2008.4481264

M3 - Conference contribution

AN - SCOPUS:50249150141

SN - 9781424420834

SP - 24

EP - 30

BT - 12th International Conference on Intelligent Engineering Systems - Proceedings, INES 2008

ER -