A Relational Positioning Methodology for Robot Task Specification and Execution

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> This paper presents a relational positioning methodology that allows to restrict totally or partially the movements of an object by specifying its allowed positions in terms of a set of intuitive geometric constraints. In order to derive these positions, a <emphasis emphasistype="italic">geometric constraint solver</emphasis> must be used. To this end, positioning mobile with respect to fixed (PMF), a geometric constraint solver for the relational positioning of rigid objects in free space is introduced. The solver exploits the fact that, in a set of geometric constraints, the rotational component can often be separated from the translational one and solved independently. PMF may be used as an interface for specifying offline-programmed robot tasks, as well as for assisting the execution of teleoperated tasks requiring constrained movements. Examples describing both the solver's operation and typical applications are discussed. </para>