Interpolation Types for Profiles

The curves defined by an array of MC_PProfile hold master position points and according slave positions. When the master position is between 2 points, the according position for the slave is interpolated. Different types of interpolation are possible. The type is defined in MC_ABB_iTYPES_ENUM. The master could be a real axis or some virtual axis which could be created by just writing values for position and velocity to the Axis_master variable as shown in the example. The same interpolation types could be used on MC_TProfile.

Overview of different Interpolations

Interpolation Types	Results in	Requires
MCA_LINEAR	Linear interpolation with constant velocity between interpolation points.	profile.MC_PProfile_Array[x].master_position, profile.MC_PProfile_Array[x].interpolation_point
MCA_SPLINE_NATURAL	Cubic spline interpolation without jerk.	profile.MC_PProfile_Array[x].master_position, profile.MC_PProfile_Array[x].interpolation_point
MCA_SPLINE_COMPLETE	Cubic spline interpolation without jerk, start and end of profile with velocity=0.	profile.MC_PProfile_Array[x].master_position, profile.MC_PProfile_Array[x].interpolation_point
MCA_POLY3	Polynomial interpolation with linear velocity between interpolation points.	profile.MC_PProfile_Array[x].master_position, profile.MC_PProfile_Array[x].interpolation_point, profile.MC_PProfile_Array[x].velocity_ratio
MCA_POLY5	Polynomial interpolation with linear acceleration between interpolation points.	profile.MC_PProfile_Array[x].master_position, profile.MC_PProfile_Array[x].interpolation_point, profile.MC_PProfile_Array[x].velocity_ratio, profile.MC_PProfile_Array[x].acceleration_ratio

The interpolations allow to run on smooth curves without the need to define a large number of points. The following chapter shows the results with different interpolation modes for a sinus-curve with 10 interpolation points. The following table gives the mean deviation.

Interpolation Type	Mean deviation [ppm]
MCA_LINEAR	19686 =1.9%
MCA_SPLINE_NATURAL	151=0.0151%
MCA_SPLINE_COMPLETE	25510=2.5%
MCA_POLY3	131=0.0131%
MCA_POLY5	0.37

The original curve is represented by y_sinus for position and v_sinus for velocity. The diagrams show the result which is achieved by different interpolation types.

MCA_LINEAR

Results from linear interpolation

The velocity is constant between the interpolation points.

MCA_POLY3

Results from polynomial interpolation

The result looks almost identical to the original curve. The mean deviation shows that MCA_POLY3, MCA_POLY5 and MCA_SPLINE_NATURAL produce results which follow the original curve really good and are almost identical. The spline interpolation produces a jerk-free curve without the need of providing velocity values and acceleration values in advance.

MCA_COMPLETE

Results from complete spline interpolation

In the beginning and the end, the curve does not follow the original curve. The reason is that it starts with velocity=0 and produces a jerk free result.

So the favoured result has to be considered in advance to choose the right interpolation method. With these different methods it is not necessary to provide a large number of interpolation points to get good results and smooth acceleration and deceleration ramps.