Parametric FIR filtering for G-code interpolation with corner smoothing and zero circular contour error for NC systems

Motion planning is an important topic in numerical control systems. It has two main schemes: acceleration/deceleration (acc/dec) before interpolation (ADBI) and acc/dec after interpolation (ADAI). An ADBI can interpolate command without contour error, but it causes a velocity discontinuity problem when passing through a corner. Meanwhile, an ADAI can generate a smooth cornering profile without discontinuous velocity, but it has contour error along circular trajectories. To have the benefits of both schemes and avoid their disadvantages, this study proposes a new scheme for G-code motion planning: parametric acc/dec interpolation (PADI). The PADI is a new scheme different from the ADAI and ADBI schemes. The PADI first plans a motion profile in a parametric space like an ADAI and then interpolates the blended parametric command in the working space like an ADBI. Through this approach, it can generate a smooth cornering profile like an ADAI and interpolate a circular command with zero contour error like an ADBI. These advantages can be observed in simulations and experiments. The proposed PADI scheme provides a brand-new motion planning strategy with multiple advantages that traditional methods cannot simultaneously achieve.