A Geometric Method for Non-singular Path-planning in the Constant Orientation Workspace of a Stewart Platform Manipulator

This paper presents a novel geometric solution to the problem of finding singularity-free paths joining two arbitrary points in the constant orientation workspace of a semi-regular Stewart platform manipulator. The formulation builds upon the known closed-form expression for the gain-type singularity surface of the manipulator. Using a rational parametrisation of the surface, it computes the geodesic curve on this surface, connecting the projections of the two given points on this surface. A sequence of spheres is then constructed in such a manner that each sphere is tangential to a previous one as well as the singularity surface, at a point on the said geodesic curve. Thus the geodesic curve acts as a guide, over which the singularity-free sphere is rolled, till it reaches its destination. Multiple methods for computing such sequences of spheres are presented and compared with the help of a numerical example. Finally, a sequence of line segments connecting the centres of the spheres is constructed, which connects the two given points via a provably singularity-free path.