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XPS-Q8 Controller
XPSDocumentation V1.4.x (EDH0301En1060 — 10/17)
8.2
Splines
8.2.1
Trajectory Terminology
Trajectory: Continuous multidimensional motion path. Spline trajectories are defined
in a three-dimensional XYZ space. They are available with XYZ groups only. The
major benefit provided by a spline trajectory is to hit all points (except for the first and
the last point that are needed to define the start and the end) and to maintain an almost
constant speed (speed being the scalar of the vector velocity) throughout the entire path
(except during the acceleration and deceleration periods). Please note that the trajectory
speed can vary in some areas depending on the distribution of the reference points. This
is related to the spline algorithm used.
Trajectory element (segment): An element of a spline trajectory is defined by a 3rd
order polynomial curve joining two consecutive control points.
Trajectory velocity: The tangential linear velocity (speed) along the trajectory during
its execution.
Trajectory acceleration: The tangential linear acceleration used to start and end a
trajectory. Trajectory acceleration and trajectory deceleration are always equal and by
default.
8.2.2
Trajectory Conventions
When defining and executing a spline trajectory, a number of rules must be followed:
• The motion group must be an XYZ group.
• All trajectories must be stored in the controller's memory under ..\public\trajectories
(one file for each trajectory). Once a trajectory is started, it executes in the
background allowing other groups or positioners to work independently and
simultaneously.
• Each trajectory must have a defined beginning and end. Endless (infinite)
trajectories are not allowed. Although, N-times (N defined by user) non-stop
execution of a trajectory is allowed. As the trajectory is stored in a file, the
trajectory's maximum size (maximum elements number) is unlimited for practical
purposes.
• Spline trajectory elements (segments) are 3
joining the positions P
normalized time parameter that varies from 0 (corresponding to P
(corresponding to P
• Spline trajectories form a continuous path (each segment's output position is equal
to the next segment's input position), and the segment tangential angles at the
connection point of any two consecutive segments are continuous, including its
derivative. For reference, this discontinuity is categorized as R
and velocity are continuous, but not acceleration.
8.2.3
Geometric Conventions
The Spline trajectory's coordinate system is an XYZ orthogonal system.
The X-axis of this system correlates to the XPositioner, the Y-axis to the YPositioner,
and the Z-axis to the ZPositioner of the XYZ group as defined in the stages.ini.
The origin of the XYZ coordinate system is in the lower left corner, with positive values
up (Z), to the right (X) and forward (Y).
All angles are measured in degrees, presented as floating point numbers. Angle origin
and sign follow the trigonometric convention: positive angles are measured counter-
clockwise.
rd
(X
, Y
, Z
) and P
i-1
i-1
i-1
i-1
).
i
96
Motion Tutorial
order polynomial curve segments S
(X
, Y
, Z
). Here "u" is the
i
i
i
i
) to 1
i-1
, wherein position
1
(u),
i
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