# Group theoretical approach in using canonical transformations and symplectic geometry in the control of approximately modelled mechanical systems interacting with an unmodelled environment

Title | Group theoretical approach in using canonical transformations and symplectic geometry in the control of approximately modelled mechanical systems interacting with an unmodelled environment |

Publication Type | Journal Article |

Year of Publication | 1997 |

Authors | Tar, J. K., I. J. Rudas, and J. Bitó |

Journal | ROBOTICA |

Volume | 15 |

Issue | 2 |

Pagination | 163 - 179 |

Date Published | 1997 |

Publication Language | eng |

Abstract | In spite of its simpler structure than that of the Euler-Lagrange equations-based model, the Hamiltonian formulation of Classical Mechanics (CM) gained only Limited application in the Computed Torque Control (CTC) of the rather conventional robots. A possible reason for this situation may be, that while the independent variables of the Lagrangian model are directly measurable by common industrial sensors and encoders, the Hamiltonian canonical coordinates are not measurable and can also not be computed in the lack of detailed information on the dynamics of the system under control. As a consequence, transparent and lucid mathematical methods bound to the Hamiltonian model utilizing the special properties of such concepts as Canonical Transformations, Symplectic Geometry, Symplectic Group, Symplectizing Algorithm, etc. remain out of the reach of Dynamic Control approaches based on the Lagrangian model. In this paper the preliminary results of certain recent investigations aiming at the introduction of these methods indynamic control are summarized and illustrated by simulation results. |