A look-ahead command generator with control over trajectory and chord error for NURBS curve with unknown arc length

There are currently no analytical methods available which determine the exact arc length for NURBS curves and for this reason, a smooth feedrate profile with desired trajectory cannot be achieved. Numerical methods used to calculate the arc length are time-consuming processes which make generating a feedrate profile with desired accelerations difficult in real-time. This paper introduces a look-ahead trajectory generation method which determines the deceleration stage according to the fast estimated arc length and the reverse interpolation of each curve at every sampling time. This results in a feedrate trajectory generation with jerk-limited acceleration profiles for the NURBS curves. The feedrate profile is adjusted dynamically according to the geometrical path constraint determined by chord error for the curved path. A NURBS curve by two different kinematics conditions was used as a means to test the feasibility of the developed interpolation scheme and command generator.