maxon motor control
EPOS Application Note: Interpolation Position Mode
EPOS Positioning Controller
Edition December 2008 / Subject to change
maxon motor control
5
Finally, the interpolated position mode can be qualified as follows: The resulting smooth driving profiles as well as
the close temporal synchronization allow it in a drive system, to superpose several high-dynamic single movements
to a precise total movement.
2.2
General Description
The Interpolated Position Mode descript in the CiA specification DSP402 V3.0 is a general case. The objects are
well specified for a linear interpolation (PT). The interpolation type can also be extended by manufacturer specific
algorithms (selectable by „Interpolation submode selection“, object 0x60C0).
2.3
Spline Interpolation
For the Interpolated Position Mode the interpolation type is a cubic spline interpolation. The higher-level trajectory
planer sends a set of interpolation points by PVT reference point. Each PVT reference point contains the position,
velocity, and time information of a profile segment end point. The trajectory generator of the drive performs a third
order interpolation between the actual and the next reference point.
Figure 1:
Interpolated Position PVT Principle
The interpolation parameters
a
,
b
,
c
, and
d
can be calculated for each segment from the two successive PVT
reference points:
d = P[t
0
] = P[n]
c = V[t
0
] = V[n]
b = T
-2
[n] * (3 * (P[n] – P[n-1]) + T[n] * (V[n] + 2 * V[n-1]))
a = T
-3
[n] * (2 * (P[n] – P[n-1]) + T[n] * (V[n] + V[n-1]))
The interpolated values for the position, the velocity, and the acceleration will be calculated as follows:
P(t) = a * (t – t
0
)
3
+ b * (t – t
0
)
2
+ c * (t – t
0
) + d
V(t) = 3a * (t – t
0
)
2
+ 2b * (t – t
0
) + c
A(t) = 6a * (t – t
0
) + 2b
t
0
: time of interpolation segment end (
Æ
in this calculation
t
0
is greater then
t
!)
It is not mandatory that the time intervals are identical.
