A Novel Task Coordinate Frame Reduced-Dimension 3-D Contouring Control

In typical contour-following applications such as computer numerical control (CNC) machining, contouring error characterizes the surface quality of final workpieces. The traditional task coordinate frame (TCF)-based approach transforms the contouring control problem into a 3-D regulation problem along the axes of the local Frenet frame. The contouring error is then controlled indirectly by two decoupled regulation systems. In order to achieve a satisfactory contouring error performance, two sets of control parameters must be tuned for the two systems, respectively. In this paper, a novel TCF (nTCF) is proposed. Given the nearest position from the actual position to the desired (or approximated) contour, one axis is set along the line passing the actual position and the nearest position and another axis is along the advancing direction. The system dynamics in the world Cartesian coordinate frame is transformed into nTCF. The contouring control problem for 3-D contours can be reduced and it locally becomes a 2-D regulation problem, one in contouring direction and the other in advancing direction. By implementing the computed-torque control, two proportional-derivative controllers are integrated to regulate the advancing error and the contouring error, respectively. The contouring error is directly regulated by tuning a single set of control parameter, which becomes much simpler than that in the TCF-based approach, where two sets of control parameters are needed to tune. Experiments on an industrial three-axis glass engraving computer numerical control (CNC) machine show the validity of the proposed nTCF-based approach with two typical 3-D contours.