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# Global Robot Task Specification and Control Via Objective Functions on the Euclidean Group: End-Point Tasks

#### *Center for Systems Science, Yale University*, April 1987

D. E. Koditschek

University of Pennsylvania

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Introduction |

The workspace of a robot arm is a compact set, *W* c SO(3) x **E**^3, within the group of rigid transformations or “euclidean group”. Thus, the general project of robot arm command via vector fields on workspace confronts from the very start the question of how to construct computationally effective vector fields on the euclidean group. In this section the task of moving to a desired point in workspace is translated into the problem of global “error equations” in *W*. Namely, a class vector fields is sought under whose flow any specified “end-point”, *w-sub-d Ε W* can be made globally asymptotically stable. Since it is desirable that the error equations lead directly to a feedback structure guaranteed to produce the same limit behavior in the robot control system (??) we restrict our attention to non-degenerate gradient vector fields, as described in Section ??. |

BibTeX entry |

@inproceedings{author-conference-2009,
author = {Daniel Koditschek},
title = {Global Robot Task Specification and Control Via Objective Functions on the Euclidean Group: End-Point Tasks},
year = {1987},
address = {Yale University},
month = {April},
} |