Orientational path planning for 6R robot

In this paper a simple method of orientational path planning for commonly used 6R manipulators is presented. The chosen criterion is to minimize changes of values of manipulator's joints. For a given set of locations a proper orientation of end-effector has to be computed. The three Euler angles (α, β, γ) have been replaced with one angle (δ). In order to reduce the number of variables describing the orientation an algorithm which derives a plane equation based on three neighboring points is proposed. The angle between normal vector to the plane and one of the vectors describing the coordinate system attached to the end-effector is equal to zero. The choice of right vector is based on end-effector construction and operator's knowledge. If three neighboring points are collinear, algorithm creates the plane based on two points of given path and the origin of base coordinate system. If these four points are collinear, the plane is created with use of the points projection to the base X0Y0 plane or plane parallel to X0Y0. In order to ensure the path between considered points an interpolation is made. A comparison of Hermite polynomials and linear segments with parabolic blends is presented. The angle δ describes the rotation angle of coordinate system at start of the first iteration. The angle change is chosen in order to minimize the joint values changes.