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Problem
Problem
Noncontact measurement of a workpiece can be achieved by a robot holding a LDS (Laser Displacement Sensor) in the terminal arm, which is important for robot off-line programming. Calibration of the robotic TCF (Tool/Terminal Control Frame) is to find the position and orientation of the LDS relative to the end link frame.
Fig 1. Schematic diagram of the TCF calibration model based on a planar template
1: robot 2: laser displacement sensor 3: laser 4: planar template
Method
Method
According to the forward kinematics, we have
and by expanding T_{BE} and T_{ET}, we have
The equation of the plane is expressed as
And thus the problem can be formulated as
where
The quadratic penalty function method is used to solve this problem,
where u is the penalty factor.
Experiment
Experiment
To validate the accuracy of the algorithm proposed in this paper, we performed a series of experiments, one of them being described below.
First, we used the optical table as the planar template and carried out the TCF calibration using the proposed method, as shown in Fig 2.
Fig 2. Calibration based on a planar template
Obtaining the parameters, we further validate the accuracy by measuring points on adjacent perpendicular surfaces of a calibration block. The experiment setup is shown in Fig 3.
Fig 3. Measurement of points on adjacent perpendicular surfaces of the calibration block
The result is shown in Fig 4.
Fig 4. Validation result
And the angle between each pair of adjacent perpendicular surfaces is
Tab 1. Angles between adjacent perpendicular surfaces
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