Author: Hans-Gerd Maas
Institute of Geodesy and Photogrammetry
Swiss Federal Institute of Technology Switzerland

Abstract:

Today’s developments in Industrial robots focus on aims like gain of flexibility, improvement of the interactionbetween Robots and reduction of down-times. A very important method to achieve these goals are off-line Programming techniques. In contrast to conventional teach-in Robot programming techniques, where sequences of actionsare defined step-by-step via remote control on the real object, off-line programming techniques design completerobot (inter-)action programs in a CAD/CAM environment. This poses high requirements to the geometric accuracyof a robot. While the repeatability of robot poses in the teach-in mode is often better than 0.1mm, the absolutepose accuracy potential of industrial robots is usually much worse due to tolerances, eccentricities, elasticities,play, wear-out, load, temperature and insufficient knowledge of model parameters for the transformation fromposes into robot axis angles. This fact necessitates robot calibration techniques, including the formulation of a robot model describing kinematics and dynamics of the robot, and a measurement technique to provide reference data. Digital photogrammetry as an accurate, economic technique with realtime potential offers itself for this purpose.

The paper analyzes the requirements posed to a measurement technique by Industrial Robot calibration tasks. Afteran overview on measurement techniques used for robot calibration purposes in the past, a photogrammetric robot calibration system based on off-the-shelf low cost hardware components will be shown and results of pilot studieswill be discussed. Besides aspects of accuracy, reliability and self-calibration in a fully automatic dynamic photogrammetric system, realtime capabilities are discussed. In the pilot studies, standard deviations of 0.05-0.25mm inthe three coordinate directions could be achieved over a robot work range of 1.7 x 1.5 x 1.0 m3. The realtime capabilitiesof the technique allow to go beyond kinematic robot calibration and perform dynamic robot calibration aswell as photogrammetric on-line control of a robot in action.

1. Introduction

Since the first utilization of a robot in the US car industry in 1955, robots play an continuously increasing role in industrial manufacturing processes. It is estimated that today about 700’000 industrial robots are being used. Whilethe use of robots was restricted to simple tasks like spot welding and painting in the beginning, today’s tasksinclude complicated actions like arc welding and assembly. Recent trends are the improvement of flexibility in less deterministic environments, the optimization of the interaction of multiple robots, the design of man-machine interfaces and the reduction of down-times. Therein, off-line programming techniques are gaining importance overconventional teach-in procedures. While with teach-in techniques a new work program is designed step by step incontact with the real work piece, the use of off-line programming techniques enables the complete design ofcomplex work programs in a CAD/CAM environment, which is then downloaded to the robot. This enables tominimize down-times of production lines when changing work programs and a much higher degree of integration ofthe robot programming into the industrial design process.

A severe restriction for the use of off-lineprogramming techniques is the limited geometric accuracy of industrial robots: although therepeatability of end effector positioning in theteach-in mode is in the order of 0.1 mm or lesstoday, much higher errors may occur when absolutepositions defined in an off-line designedwork program have to be hit. Depending on thetype of robot and the type of motion these errorsmay amount to up to 10 mm, thus requiring expensive post-teaching measures and relativating the efficiency of off-line programming techniques. Reasons for pose errors (pose = six parameters describing position and orientation) of a robots endeffector are effects like tolerances, elasticities, wear-out, load, temperature and insufficient knowledge on the robots model parameters which are required for the transformations between real world coordinates, pose parameters and axis angles (Fig. 1). Therefore there is a need for robot calibration techniques, including models todescribe the geometry of a robot and measurement techniques for the determination of boundary values. Most of these techniques determine end effector coordinates or (preferrably) complete pose parameter sets at a number of locations and orientations over a robots work range and derive robot model parameters from these measurements.This publication is limited to the discussion of measurement techniques for the determination of pose parametersvia signalized points on a robots end effector. For mathematical models for the determination of robot modelparameters the reader is referred to the references, e.g. (Nitschke et al., 1992) for the determination of all or singleparameters of the kinematic structure of a robot following Denavit-Hartenberg methods or (Diewald, 1995) for the description of pose errors by polynomials.

2. Robot calibration measurement techniques

According to the variety of tasks of industrial robots, there is a wide range of requirements posed to calibration techniques. These requirements include:

• An accuracy potential of 0.1mm or better.
• In most cases the measurement of full poses (6-D) is preferred.
• The cost/performance ratio should not put a high burden on the economical benefit of the use of the robot.
• Ease of use of the technique, which should not require special skills.
• The measurement system must be brought to the robot, not vice-versa.
• The measurement system should work under factory floor conditions and should not pose special requirementsto the environment.

• Polar measurement techniques with geodetic total stations or interferometric laser trackers (Kyle 1993, Filz et al.1995).
• Triangulation with theodolite systems (Kyle, 1993).
• Photogrammetry with film-based systems (Peipe, 1991) and high resolution digital systems (Diewald et al.,1993).
• Trilateration using wires, laserinterferometers or acoustic techniques.
• Tactile techniques using gauges or coordinate measurement machines.
• Inertial navigation systems, magnetic field systems.

3. Photogrammetric point determination

For the determination of pose parameters the endeffector of the robot was signalized with a platemarked with 13 circular targets (Fig. 2). The weightof the plate was adapted to medium load of therobot. For the study a two-dimensional signalizationwas used; to improve the accuracy of the endeffector orientation parameters a three-dimensionalsignalization is recommended for future applications.The signalized end effector was moved to 200poses distributed over a 1.7 x 1.5 x 1.0 m3 sector ofthe robots work range, following a scheme designedafter the requirements of model parameter determination.At each pose the 3-D coordinates of themarked points were determined from an imagetriplet acquired by three CCD cameras. From these coordinates the pose parameters were determined in a cartesianrobot coordinate system, taking advantage from the redundancy provided by 13 points which yields a gain in precisionand reliability.

3.1 System setup
As aspects of Automation realtime processing and cost optimizationwere of prime importance in the pilot study, the imaging systemwas based on standard off-the-shelf lowcost hardwarecomponents. Images were acquired with three synchronized CCDcameras (Sony XC77ce, European CCIR videonorm) connected toa Datacell S2200 RGB framegrabber in a SUN SparcStation computerworkstation. The connection of three synchronized monochromecameras to one RGB framegrabber with three A/Dconverters allows for simultaneous image acquisition and transfer,which is crucial for dynamic applications. One image triplet wasacquired at each pose. Due to the character of a pilot study and anon-optimized dataflow, online data processing was waived;instead, the calibration was conducted in a kinematic mode, andsequences of image triplets were stored and subsequently processedautomatically. Fig. 2 shows the camera arrangement duringdata acquisition, Table 1 lists the technical data of the components.

The use of non-metric cameras requires a thorough calibration of thephotogrammetric system itself to warrant a satisfactory accuracy potential.The determination of the orientation and camera model parametersof the three-camera system was performed simultaneously with the determinationof the 3-D coordinates of the marked targets by self-calibratingbundle adjustment. In many applications of self-calibration a stationarypoint field is imaged by a single camera from different viewing directionsand under different roll angles, thus reducing correlations betweenparameters to be determined. This strategy, however, is of limited practicabilityin the discussed application, as there is no stationary point field.A repetition of the robot poses under two or three different roll angles ofthe three cameras is restricted by the repeatability of end effector positioning;moreover, such a procedure would make data acquisition inconvenient.Instead, the robot pose sequence was driven only once, and oneimage sequence was acquired with each camera under constant orientation.To reduce correlations between subsets of parameters in the bundle adjustment and to define the scale, therobot was signalized with a reference bar of well known length (Fig. 3) after the actual robot calibration program of200 poses and moved to another 27 poses at different locations and orientations. The reference bar was signalizedwith two targets at a distance of approximately 1.0 m and had been calibrated interferometrically to a standarddeviation of 1 ìm. This procedure of simultaneous calibration with additional geodetic information depicts aninteresting alternative in tracking applications with a stationary multi-camera system and no stationary target field.A more detailed analysis of a similar procedure can be found in (Heikkilä, 1990).

3.2 Data processing
A typical image triplet and the dataflow in theautomatic image data processing are shown inFig. 4. The first two processing steps (detectionand recognition of marked targets) aretrivial due to possibility of image coordinateprediction via the pre-defined poses of the endeffector and the given accuracy potential ofthe uncalibrated robot. After a rough pre-orientationof the system by interactive measurementof a few points, the locations of all otherpoints can be predicted within a tolerance of afew pixels, thus providing sufficiently goodapproximate values for subsequent imagecoordinate measurement with subpixel accuracyusing a centroid operator or least squarestemplate matching. This means a significantsimplification of the dataflow in automaticphotogrammetric data processing, as also thecorrespondence problem is solved implicitly.The 3-D coordinates of the measured targetscan be determined directly by spatial intersectionor self-calibrating bundle adjustment.Even the interactive step of the pre-orientation of the system by manual measurement of a few points can easily beautomated, e.g. by the use of coded targets (van den Heuvel et al., 1992). Thus photogrammetric robot calibrationcan be fully automated.

3.3 Results
The standard deviations of the image coordinates obtained from least squares template matching were in the orderof 1/50 ... 1/40 pixel; related to the image format of 756 x 576 pixel, this corresponds to a relative precision ofapproximately 1 : 30’000. In the subsequent self-calibrating bundle adjustment the object coordinates of all 13marked targets at all 200 poses and of the two markers on the reference bar at 27 poses were determined simultaneouslywith camera orientation and calibration parameters. Eight camera model parameters per camera wereintroduced as unknowns: The camera constant, the principle point coordinates, two parameters modeling radiallens distortion, two parameters modeling decentering lens distortion and one horizontal scale factor compensatingfor different clock rates of cameras and framegrabber. By including the distance information of the 27 scale posesinto the adjustment, determinability of all parameters could be achieved. The results of the bundle adjustment aresummarized in the following table:
To get an indication the repeatability of coordinate determination some poses were measured twice without movingthe robot in between. The RMS of these double measurements was:
The precision parameters achieved in the pilot study do correspond to the expectations and could also be confirmedin another pilot study using a Robix educational robot (Favey/Schlatter, 1996).

No external reference measurements were available in the pilot studies. However, at least a partial external verificationcan obtained from known distances between the marked targets, assuming stability of the signalization plate.An examination of 800 horizontal and vertical check distances, derived from the photogrammetrically determinedcoordinates of the four corner points of the plate at all 200 poses, yielded the following results:
Herein, the standard deviation of the horizontal distances is by a factor of 1.7 larger than the value obtained fromthe standard deviations of the object point coordinates without consideration of correlations, while the value for thevertical check distances is about consistent. Check distances in depth direction were not available due to the orientationof the plate towards the cameras. The reason for the discrepancy in the horizontal check distances was foundafter a thorough examination of the images, which showed line jitter effects in the order of 1/10 pixel. Linejitter is aknown effect degrading the accuracy in horizontal direction in image space when grabbing images from cameraswith analog image data transfer; in most cases, however, the effect is smaller than 1/20 pixel and shows stochasticbehaviour, thus hardly influencing the accuracy potential of photogrammetric systems measuring targets with anextension of several pixels in image space. In the present application, linejitter was obviously enlarged by camerasynchronization problems which were possibly caused by electromagnetic fields of the robot. With the chosenthree-camera configuration, the horizontal image coordinate errors could not be detected by the network geometry.Using CCD cameras with internal A/D conversion and digital data transfer, this problem should not occur anymore.The same data was processed a second time using a fast centroid operator instead of least-squares templatematching. No significant difference could be found comparing the accuracy figures obtained with centroid operatorwith the results obtained from least-squares template matching. Only in cases of partly occulded targets a higherreliability can be expected from least-squares template matching.

A significant improvement of precision can be expected when using high resolution cameras: Standard deviations= 0.035mm/0.035mm/0.05mm over a range of 2.1m x 1.3m x 0.6m were obtained by (Diewald et al., 1993)using Rollei réseauscanning-cameras; (Peipe, 1991) achieved standard deviations of 0.05-0.1mm over a work rangewith a largest extension of 1.7m with a hybrid system with medium format film-based cameras and a réseauscannerfor image coordinate measurement.

3.4 Realtime processing potential
Besides the bundle adjustment, which is being performed off-line, the computational effort in photogrammetricrobot calibration is mainly influenced by the image coordinate determination. The average computation time pertarget, related to the performance of a SUN SparcStation20, are listed in the following table:
If the simultaneous bundle adjustment of the whole dataset is replaced by a system calibration using a smallernumber of poses before the actual experiment, 3-D coordinates can be determined by spatial intersection. Using thefast centroid operator and spatial intersections, the determination of the coordinates of the marked points can beperformed in video realtime (1/25 second) when the number of points is limited to 8-10. With further optimizationof the software and slightly smaller targets the task can also be performed in video realtime on a high-end PC.

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