Trajectory-planning through interpolation by overlapping cubic arcs and cubic splines

A new path-planning interpolation methodology is presented with which the user may analytically specify the desired path to be followed by any planar industrial robot. The user prescribes a set of nodal points along a general curve to be followed by the chosen working point on the end-e ector of the mechanism. Given these speci ed points along the path and additional prescribed kinematical requirements, Overlapping Cubic Arcs are tted in the Cartesian domain and a cubic Spline interpolation curve is tted in the time-domain. Further user-speci ed information is used to determine how the end-e ector orientation angle should vary along the speci ed curve. The proposed trajectory-planning methodology is embodied in a computer-algorithm (OCAS), which outputs continuous graphs for positions, velocities and accelerations in the time-domain. If a varying end-e ector orientation angle is speci ed, the OCAS-algorithm also generates continuous orientation angle, orientation angular velocity and orientation angular acceleration curves in the time-domain. The trajectory-planning capabilities of the OCAS-algorithm are tested for cases where the prescribed nodal points lie along curves de ned by analytically known non-linear functions, as well as for nodal points speci ed along a non-analytical (free-form) test-curve. The proposed trajectory-planner may be implemented as part of kinematic and kinetic simulation software, and it also has the potential application for controlling machine tools in cutting along free-form curves