Dual conformance index-based robotic arm placement and adaptation

A method to decide the placement and structural adaptation of a robotic arm with respect to a set of tasks is presented. Commercialized CAD/CAM tools mostly limit the layout criterion of robotized cells to the reachability of a task. They furnish little assistance for the selection of the tool, the arm, or its placement. A robot-task conformance index is shown to overcome these limitations. Four volume ratios define the index. They are taken over a robot ellipsoid, a task constraints ellipsoid, and a minimum containing and a maximum contained ellipsoid. The strict equivalence of the four ratios is proven. A "dual" computational sequence and the concept of relevant singularities are introduced. This "dual" computation is shown to equal the original conformance index outside relevant singularities. The index is applied to cases of increasing difficulty. Internal motions of joints within the null space of the Jacobian are typically used to maximize the index. The cases of simultaneous multitask optimization, tool definition, and robotic structure definition are addressed. Its usefulness for the design of the cell layout is exemplified. (C) 1996 John Wiley & Sons, Inc.