Investigation of positioning accuracy of industrial robots for robotic-based X-Ray Computed Tomography

In this research work we investigated the accuracy of a standard industrial robot. We wanted to find out, how accurate an X-Ray Computed Tomography (CT) scan can be performed when using such a robot as a manipulator. The accuracy was measured using a laser-interferometer. The measured deviations were used to run an X-Ray simulation via Fraunhofer EZRT’s Scorpius X-Lab. Metrological analysis was performed as a measure for the quality of the simulated CT-scan. The metrological deviations reflect the feasible accuracy of a CT-scan in a real CT-setup.

Industrial computed tomography demands stiff and precise manipulators to obtain sharp images.On the other hand, flexible manipulators like six-axis-robots are highly interesting for scanning e.g.large objects or unusually shaped objects [1].A flexible manipulator allows the operator to scan different tasks without long setting-up times.It can be used for specimen placement as well as for specimen rotation.Thus, a robotic based CT could be more flexible and faster than a standard circular CT with a turntable.Flexible and fast CT is important to foster CT as a standard-task in industry [3].By enabling more flexible trajectories than the standard circular CT, more detailed information of the object can be obtained [2].Those reasons show that a robot based CT has advantages towards standard CT.Robotic CT has been implemented so far by Siemens [4] in commercial medical systems.A drawback of manipulators with many degrees of freedom is a reduced accuracy and rigidness, compared to classical air-beared turntables.The poor performance of standard industrial robots in terms of absolute and repeatability precision hampers high resolution CT-scans.To find out the impact of a robotic arms errors to the CT-scan, the experiments below were conducted.The aim is to find out the obtainable picture quality when using such a manipulator.

Robot
A Kuka KR 15-2 robotic arm built in 2001 was inspected.The experiments were conducted reflecting DIN EN ISO 9283.More precise robots would be available [5], but we chose this one, because it reflects typical robots used in production industry.Further, there are several calibration techniques for industrial robots to improve their precision.In terms of geometry, robots are no perfect manipulators.They have systematic and stochastic deviations.In order to tackle these deviations, various methods have been investigated in literature.Firstly, there are live-tracking approaches, where a sensor system constantly supervises the robots position.This can be achieved by watching the specimen using a camera in the Robot's end effector [6] or by a Sensor that is frequently referencing itself using a fixpoint [7].Tracking in a larger scale can be found as "indoor-GPS" [8].Another approach is to precalibrate the robot e.g. using X-Rays [9], laser-trackers [10] or a combination of laserpointer and camera [11].
A third approach is to determine a mathematical model including stiffness, joint backlash, temperature drift and geometric parameters.This approach is mainly found for machining applications such as milling [12].
In the described experiments, we omitted calibration steps to measure the pure mechanic behaviour of the robotic manipulator in terms of systematic and random geometric error.

Measuring System
An API XD laser interferometer was used to measure the robot's deviations.This device is capable of tracking linear and angular errors in 5 degrees of freedom as long as the robot's end effector moves along a linear path (+/-0.5 mm).As a first step, a working space was identified, which corresponds to the working space within a CT system.The working space was determined in dependence on the world coordinate system, which has its origin in the base flange of the robot.The size of the working space is: • X: 700 to -700 mm, • Y: 740 to 1340 mm, • Z: 200 to 1000 mm.
This working space was divided in a grid of measuring positions.In ISO 9283, five measuring points are used to characterize the robot by one single numerical set of values for omni-directional absolute precision (AP) and repeatability precision (RP).
As opposed to the standard, we measured plenty of positions to simulate the behavior of the robot space-resolved in its working space.This shall yield more realistic simulation results.In order to keep the workload low and still obtain sufficient measuring accuracy, a step size of 200 mm was selected between the individual measuring points.The grid was measured one line of points at a time with 10 repetitions.We had to align the individual datasets of the measured lines to each other in a postprocessing step.Thus each point was measured 30 times in total.RP and AP were calculated according to ISO 9283 for each measured point.

Measured characteristics of the robot
According to DIN EN ISO 9283 the robot can be characterized by the facts and numbers in table 1.We divided the repeatabiltiy precision (RP) in multi-directional and unidirectional.multi-directional means the robot approaches its position from various (six) starting points.Unidirectional means, the robot approaches a point alwas from the same starting point.3 Simulation based on Scorpius X-Lab Simulations of CT-scans were conducted using Scorpius X-Lab.It is capable to simulate arbitrary trajectories.Different experiments were conducted to show the impact of the individual errors in Figure 3.

Design of Experiment
We suppose, we perform a circular CT-Scan using the robot as a manipulator.The specimen is placed on the robot's hand using any kind of fixture.The robot turns the specimen round on a virtual axis (see figure 1).Therefore it has to move all 6 robot axes synchronous.A perfect robot would perform a perfect circle.Our real robot has pose deviations, thus its trajectory is not perfect.The CT reconstruction algorithm (we use Feldkamp) has no information of the actual deviations.Thus, the spatial errors of the robot are passed over into the generated voxeldataset.We determine an STL surface out of the voxeldataset to perform metrology on it using the software "WinWerth 8.34".On a perfect system, we would measure the same diameters and lengths as in the surface file we started with in our simulation.Since our system is not perfect, we measure different values, even with no superimposed error like in experiment Type A. The deviations to the perfect values are plotted in table 2. The measuring strategy was to select the patches on the 3D-model as depicted in figure 4 with an edge distance of 0.1 mm and gaussian fit of planes or respectively cylinders.Distances are measured as orthogonal projections of the patches' barycenter points.X-Ray parameters for the aluminum specimen were 225 KV tube voltage, 0.02 µA tube current, 1 s exposure time and 512 by 512 pixels at 0.4 mm pixel pitch.Object scatter and detector noise were activated.The number of projections was set to 800.Focus-detector-distance was set to 2 m at a magnification factor of 2. The test specimen is 33 mm tall and has a diameter of 30 mm at its base.
To obtain those misaligned radiographs, the arbitrary geometry module of X-Lab was used.The arbitrary geometry module demands 18 parameters for each radiograph image: Rotation in X, Y and Z as well as translation from the origin in X, Y and Z for source, object and detector.Source and detector were meant to be fixed, thus we changed only rotation and translation for the object in each radiograph image.To generate the 800 datasets for the object, a matlab script was used.We supposed that the specimen is mounted on the robot's tool flange using a lever of 200 mm.The robot performs the circular trajectory as depicted in fig. 1 superimposed by transversal and angular error.This error is transferred onto the specimen using coordinate transformation calculation.The value of the error distinguishes between the absolute precision and the repeatability precision.AP was calculated for X, Y and Z separately.Thus, X error was multiplied by a random number, Y was multiplied with another random number and Z was multiplied with a third random number.Those values for AP were simply added to the tool flange center position of the robot.The value of the repeatability error depicts a spread radius.It is generated as a random point out of a uniform distribution of points in a three-dimensional sphere-shaped space.The radius of this sphere is the value of RP at the corresponding position (again linearly interpolated from the surrounding points).This value is added to the position of the robot's tool flange, too.In total, six subsets with 800 projections each were simulated, the parameters are listed below.The whole projection set was reconstructed as a circular scan without passing any correction information for misalignment.This was done using Fraunhofer EZRT's Feldkamp reconstruction module.

Metrological evaluation
To deliver significant facts and numbers, a metrological evaluation of the simulated experiments was performed.Figure 4 shows the areas where we measured.One can clearly see that even the experiment without any superimposed error (type A) does not meet the desired values completely since we have deviations through beam hardening, unsharpness in the reconstruction, surface determination and so on.Type B and type C show pretty good results, too.The highest obtained deviation is the roundness in measure 2 with 0.057 mm.Measures like diameters that rely on many supporting points so that they even reach deviations as good as 0.0081 mm for the diameter

Conclusions
Robotic CT using a robot out of the box delivers poor image quality.The uncalibrated KR 15-2 had systematic errors up to 1 mm.On the other hand, it was possible, to obtain directional repeatability down to +/-0.04 mm what is acceptable for various CT-applications.Thus, robotic CT-scans do rely on reasonable calibration procedures so that the systematic error of the robot vanishes and only the stochastic error, depicted by RP, remains as influence.
We have shown that an X-Ray CT scanner based on robots could deliver reasonable image quality and resolution, if the system is calibrated well.A key feature of the robo-CT is the use of non-circular scan path or arbitrary geometry.This means that the scan path could contain unique robot poses for each specimen and a terminated set of calibrated poses is not sufficient for real flexibility.Therefore a precalibration procedure for each individual specimen is necessary.To avoid precalibration before each scan, image-based calibration methods could help.Anyway, non-destructive testing as application for robo-CT is possible using currently available techniques on the market.

Figure 1 :
Figure 1: Setup and simulated trajectory of robot and specimen

Figure 2 :
Figure 2: Laser interferometer setup and measurable deviations (a) Experiment type A Reconstruction without error (b) Experiment type B Reconstruction with unidirectional RP error (c) Experiment type C Reconstruction with omni-directional RP error (d) Experiment type D Reconstruction with 25% AP error (e) Experiment type E Reconstruction with 50% AP error (f) Experiment type F Reconstruction with omni-directional RP and full AP error

Figure 4 :
Figure 4: At the hatched areas the measures 1-6 were applied.

Table 1 :
measured characteristics of the Robot The Robot manufacturer claims that the Robot KR 15-2 can reach a repeatability precision of +/-0.1 mm carrying a load of up to 15 kg.The robot does not meet it completely.

Table 2 :
1 in experiment type C. Type D, E and F show worse results with a maximum deviation of 2.2980 at the parallelism value of measure 6 for experiment type F. The detailed results are shown in table 2. Results of metrological evaluation