The Modified NURBS-Based C2 PH Spline Curve Following Task

In this paper, a new method is presented to design a robot path trajectory via C2 PH Spline curves. The method is based on using the specifications of nodal points on a non-uniform rational B-spline (NURBS) curve of degree three and defining the coefficients for the velocity and acceleration vectors on these points. Values of the velocity/acceleration vector coefficients corresponding to the nodal points on the original NURBS curve are computed by genetic algorithm. To this end, the normal distance between the constructed C2 PH Spline curve and its corresponding original NURBS curve is considered as the objective function. The position commands of the designed NURBS based C2 PH Spline curve are generated by combining the time-dependent feedrate interpolation in the acceleration/deceleration phase of the motion and the constant feedrate interpolation in the middle region of the motion. An example of the modified NURBS based C2 PH Spline curve-following tasks are implemented with pseudo-derivative feedback feed forward (PDFF) controller. Experimental results confirm that the devised interpolator with designed PDFF controller is not only feasible for complicated robot path trajectory following represented in the modified NURBS-based C2 PH spline form but also yields satisfactory contouring performance under variable feedrate.