In the present research, a trajectory planning strategy is developed for maintaining the tool positioning accuracy in high speed contouring applications. Real-Time Pythagorean hodograph (P-H) curve CNC interpolators are used for high speed corner machining. There are large contouring errors around sharp corners when low-bandwidth servo controllers are used. Also backlashes can impose additional errors during tracking a corner. It is possible to construct a P-H curve in the region of sharp corners in order to decrease the amount of cornering error. The over- and under-corner P-H approaches are revised when low-bandwidth servo controllers (such as P-PI servo control) and high-bandwidth servo controllers (such as sliding mode control) are used, respectively. The geometric parameters of the over- and under-corner P-H curve, such as end-points, end-derivatives and correction angles along with the feed rate along the modified tool path are computed by Pattern Search Algorithm in order to reduce the maximum cornering error.

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