Rational motion design - a survey

In the last years many efforts have been made to transfer geometric CAD methods to motion design: The generation of a (one-parametric) motion with given properties. An object (arm of a robot...) is moved with respect to a fixed system. Methods from freeform curve design provide powerful tools to handle such problems. Some of these methods and results shall be presented in this survey. Here one can find a (geometric) approach including solutions of interpolation problems. First attempts an studied. Then we state two principal demands on the result of such a design process: The motions should be rational and invariant with respect to changes of coordinates in fixed and moving frame, respectively. We use quaternions to describe displacements and motions and give an overview on rational spline motions. Some known results on interpolating motions are reviewed. Then a third demand is presented: The design process should be 'repeatable' in the following sense: If a solution is computed the algorithm should give the same solution (including parametrisation), if we start with new input data generated by our first solution. The paper includes suggestions for further research. (C) 1998 Elsevier Science Ltd. All rights reserved.