Robot Model
Real robot
geometry
: Inverse i ; int
Desired 3- s Drive 5 Axes Forward True
D Pose Transform Control Drive Transform 3D
ation ation Pose
I
Axe Position
Measurement
2 Real Robot Pose
! Measurement
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Figure 1 Robot Control Loop
The work flow for measuring the real robot pose by using the
resection or the forward intersection process is very similar.
Figure 2 gives an overview of this process. On the right side
the work flow of the real-time process is displayed. The
camera calibration (Section 4.1) and the hand-eye-calibration
(Section 5) are done during the initialisation of the system.
The hand-eye-calibration is obligatory for the coordinate
transformation from the camera system to the robot system.
| | Camera calibrati
| | 1
| | |
| ll |
| | Hand-Eye-Calbralion-- 9d — Compute robot pose |
| [^| |
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Figure 2 Work Flow
The real-time process starts with grabbing of the images. If
images are available, targets have to be identified as
described in section 4.2. After transforming the measured
image coordinates of the targets into the ideal image
coordinate system (section 4.1) the resection process (section
4.3) or the forward intersection process (section 4.4) can be
used to get the camera pose in relationship to the test field
coordinate system. To get the camera pose in association to
the robot system a normal coordinate transformation by using
the parameter from the hand-eye-calibration is done.
Before exactly describing the work flow, some remarks
concerning robot control loop and some investigations in
finding the absolute accuracy of the robot are necessary.
2. ROBOT CONTROL
Figure 1 shows typical components of a robot control unit.
Starting from a given pose in 3D space, the inverse
234.
transformation is used to compute values for all joints. In this
transformation, a model of the real robot is used for all
constants regarding translation and rotation offsets in the
links and joints. Those constants are known from the robot
design, however they are subject to manufacturing tolerances.
The computed joint values are set and the forward transform
is performed by the actual (real) robot. In order to control the
movement of the robot, control loops exist which consist of
axes measurement devices such as rotational encoders and a
feedback to the drive control. Since these loops do not
include the inverse or forward transform, they are not able to
compensate for differences between the assumed and actual
link and joint constants.
Using an additional measurement system in order to obtain
the true 3-D pose of the robot end effector, an external
control loop can be built (see Figure 1). The differences
between required and actual pose can be used to estimate the
constants of the robot model employed in the inverse
transform. As there is usually quite a large number of
constants, many robot poses have to be measured in order to
obtain enough observations for a parameter estimation. This
is done for example during a factory calibration of industrial
robots. After calibration the obtained parameters are norr
alterable. Errors which do not occur during calibration will be
disregarded later.
3. ACCURACY OF A ROBOT
For this experiment we used a KUKA KR 125/2 industrial
robot which is able to handle loads of up to 125 kg and has a
reach of 2410 millimetres. The manufacturer specifies a
repeatability of better than +0.2 mm. The robot is used
mainly for automotive production and packing tasks.
The robot moves to six uniformly distributed positions in his
working cell. After that the moves are repeated in the inverse
order. In the table, the deviations of the position and
orientation of the end effector are itemized. The second
column contains the reached accuracy in the determination of
the deviations. The statements of the deviations in x, y and =
