Calibration Procedure For An Industrial Robot

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1 Calibration Procedure For An Industrial Robot by B. W. Mooring and T. J. Pack Department of Mechanical Engineering Texas A&M University College Station, Texas Manufacturing Systems Division, IBM P.O. Box 1328 Boca Raton, FL Abstract A number of investigators in the recent past have examined aspects of robot calibration such as model development, data acquisition, and parameter identification algorithms. The large majority of these studies involve either purely analytical work or experiments with a manipulator in a laboratory environment. The purpose of this work is to investigate a calibration procedure for a manipulator in a typical industrial environment. In the following paper, the calibration problem is posed and the constraints are listed for the particular task to be addressed. The robot geometry is investigated to locate the primary sources of inaccuracy. A calibration procedure is then proposed that combines design modifications in the robot with active calibration fixtures in the workspace. Results of several tests are then tabulated to demonstrate the success of the calibration procedure. Introduction In the recent past, much attention has been given to the problem of manipulator calibration. Much of this work is reviewed in a recent paper by Roth [3]. Given the state of the art in robot calibration, it would seem that implementation of a calibration procedure for a robot in a typical industrial setting would be a straight forward task. Unfortunately, when a set of practical constraints me placed on the calibration process, many of the published approaches must be discarded. The purpose of this paper is to describe a calibration package developed for an industrial robot subject to constraints on size, complexity, and cost. Description of the Problem The robot to be calibrated was the 6 degree of freedom spherical manipulator illustrated in Figure 1. The arm was designed to manipulate light objects in a clean room environment. A typical task would be to remove silicon wafers from a cartridge and place them in a specific pattern on a pallette or fixture for further processing. The measured position repeatability of the robot is.005 inches and the orientation repeatability is better than.1 deg [2]. Most of the mhot tasks consist of a number of taught points. The ability of the robot to continually achieve these taught locations determines the success or failure of the application. The repeatability of the robot is such that the robot can successfully perform these tasks under normal operating conditions. Problems arise, however, when the robot is stopped due to a component failure or for routine maintanence. In these cases, the robot must be partially disassembled to reach components inside the machine. When the robot is reassembled, it is usually unable to perform the task without reteaching the various points. The reasons for this loss of accuracy will be addressed in the next section. The important point to note here is that maintenance of the robot necessitates reteaching which is time consuming and tedious. This process is 6 undesirable in any manufacturing environment, but it is especially costly in a clean room where human presence should be minimized. Axis for Joint 1 (Rwol:jte) Figure 1 Joint 3 (Pri m at ic ) '(3 Revolute \Axis for Joint 2 ( Revolute) - Robot to be Calibrated CH2555-1/88/OOO0/0786$01.OO IEEE 786

2 The goal of the calibration work was, therefore, to provide a means whereby robot maintenance could be performed without the need for reteaching. There were several constraints on this process. The most significant constraint was that the calibration process should be automated as much as possible. This was to help minimize both the down time and the contamination from human workers in the dean environment. Other constraints involved the instrumentation used during the calibration process. Because of the variety of workstation layouts, the location of the calibration sensors had to be as flexible as possible. Also, the cost of the calibration equipment had to be low enough so that its use could be economically justified. For the applications under consideration, the maximum cost for the calibration package was set at $2000. In the following sections we describe the system that was developed to address these problems. Sources of Inaccuracy The major source of inaccuracy in the robot under study relates to the position feedback system. The motor for each joint is instrumented with an incremental encoder. When the robot is powered up, each joint must go through a homing procedure to identify the reference position for that axis. This procedure consists of moving the joiiit until a sensor indicates that the joint is close to the reference position. The joint motion is then continued until the index mark on the encoder is sensed. The joint is then stopped and the counter in the controller is loaded with a reference value for the joint displacement. Once an encoder or the motor to which it is mounted has been removed and replaced, the index mark on the encoder will have rotated to another position with respect to the home sensor. When the robot homes, the joint position could be in error by as much as 1 motor revolution. Given gear ratios BS low as 100:1, the actual joint error could be as much as 3.6 degrees. If the home sensor itself is moved, the errors could be even larger. Other sources of inaccuracy include geometric errors such as axis misalignment and nongeometric errors such as gear backlash or compliance. In a typical calibration scheme, the goal is to determine the variations between the robot under study and a nominal or perfect robot. The problem addressed in this work, however, differs from the standard calibration problem in that we are interested in the changes in a given machine after maintenance has been performed. lherefore, we need riot concern ourselves with parameters that will not be affected by the maintenance process. For example, compliance is primarily a function of the robot design. Since replacing structural components or gears will not significantly dect the compliance, we may ignore this effect. The design of the robot is such that effects due to backlash are within the repeatability range and may also be neglected. IJnfortunately, the probleni of axis alignment is not so easily discarded. It is possible that some maintenance work could result in the realignment of joint axes. The joints where this is most likely are joints 3, 4, 5, and 6. As illustrated in Figure 2, joint 3 consists of two sets of linear bearings which form a prismatic axis. If these bearings must be removed or \ Extension Arm Linear Bearing.Rack & Pinion Gear.Linear Bearing Motor Figure 2 - Cross Sectlon of Jolnt 3 adjusted, it is probable that the axis alignment will be altered. Joints 4, 5, and 6 form the wrist and are illustrated in Figure 3. Since the wrist was designed to be a sniall package and modular, any maintenance on a wrist joint requires that the entire joint be disassembled. The structural components in the wrist are made to tolerances that insure very little variation in the axis alignment when the wrist is reassembled. IJnfortunately, this was not true about the attachment of the wrist to the arm. It was possible to reattach the wrist to the arm with significant varicltions in wrist orientation. For the purpose of this work, the two major sources of inaccuracy were variations in the joint reference position (joint offset) and axis misalignment in joints 3, 4, 5, and 6. Calibration Procedure In an effort to meet the practical constraints that had been imposed on the calibration process, it was decided to develop a technique to correct for joint angle offsets and to redesign the wrist interface to allow the wrist to be attached to the arm with a minimum of variation. This approach offers two advantages. First, a redesign of the wrist interface minimizes the effects of axis misalignment in the wrist. Since the structural components in the wrist are manufactured to a high tolerance and since the wrist is a physically small package, disassembly and even motor replacement results in negligible changes in axis geometry. Redesign of the interface allows the entire wrist to be removed and replaced without having to reteach the robot. The second advantage of this approach is that the entire wrist can be treated as a replacement part. If a 787

3 failure occurs in a wrist joint, the complete wrist may be removed and replaced with a spare while the other wrist is repaired and calibrated. This removes the repair and calibration process from the clean room environment and reduces robot down time. Since the wrist interface allows the wrist to be calibrated seperately, the calibration process may now be addressed in two seperate steps. One step is the determination of joint offsets for the fist 3 axes and the other step is calibration of the wrist. It should be noted that this approach accounts for all the major sources of accuracy variation except axis alignment in joint 3. It waa decided that since a calibration procedure to include this effect would be significantly more complicated than the proposed approach, misalignment of joint 3 would be ignored. In the relatively few number of cases where this joint requires maintenance, the task would be retaught. Wrist Calibration The redesigned wrist interface is illustrated in Figure 4. As shown in the figure, the interface consists of a reference surface and rrgister pins to insure proper alignment of the wrist axes. With this redesign, the problem of axis misalignment is minimized. The problem with unknown joint offsets, however, still exists. This was addressed through the development of a wrist calibration fixture. This fixture is illustrated in Figure 5. As shown in the figure, the wrist is attached to a reference surface on the fixture which matches the surface on the robot. An end effector is then mounted on the wrist as illustrated in Figure 6. The wrist is rotated so that the tooling ball on the end effector is pressed against one of the reference surfaces and the resulting joint angles are recorded. The fixture allows for 8 configurations of the wrist. In each configuration, the tooling ball is pressed against the reference surface with a constant force which is regulated by the wrist controller. At each configuration, a, there is a vector of three correct joint displacements, e, and a set of actual joint displacements, go, as measured by the controller. The correct joint displacements may be expressed as follows. gci = (goi + eo,) + G (1) where represents the error due to the measurement process and $,,, is the unknown vector of joint offsets. This quation may be restated as where Ei is the error vector at position i and [I] represents the identity matrix. The equation above is then written for each of the 8 measurement positions. The results are combined in the following equation. where [HI = [q IS (4) (5) Top View Joint 5 Joint 6 Side View Figure 3 - Wrist Figure 4 - Wrist Interface 788

4 / 6 Fixture Effector End 3 (r Figure 5 - Wrist Calibration Fixture I ' I Figure 6 - Wrist in Calibration Fixture Equation 3 represents a set of over determined linear equations. The fact that the coefficient matrix consists of identity matrices greatly simplifies the solution. When solving Equation 3 so as to minimize the square of the error, it may easily be shown that the result is simply the average of the errors, E,. This may be expressed as 8 e,,, = 1/8 E (7) I= 1 The values of the joint offsets as determined in Equation 7 are recorded and kept with the wrist. When the wrist is reinst,alled on a robot, these values are input in the controller. Major Axis Calibration The goal of the major axis calibration procedure is to determine the joint offsets for joints 1, 2, and 3 after robot maintenance. Unlike the wrist, it is not reasonable to remove the robot base from the work area for calibration. For this reason, a calibration fixture was designed that could be placed at any convenient location in the work area within the reach of the robot. This fixture serves to define a reference position for the robot. After maintenance, the robot is simply commanded to move the reference position. Because of the variations caused by the robot repair, the robot will riot be accurately positioned in the reference position. The Sensors in the fixture de- termine the error and command the robot to move until the robot is at the correct reference position. The joint offsets are then given by the difference between the actual joint madings and the correct joint displacements in the reference position. The reference position of the robot is drfined by positioning a tooling ball, which is attached to the end of joint 3, at a previously determined point in space. The tooling ball and the calibration fixture are illustrated in Figure 7. The sensors are digital dial gauges with a resolution of.0001 inch. The stroke of each gauge is such that the expected error of the robot altw maintenance will not be out of the sensor range. When the tooling ball is placed in the fixture, the error vector in the tool coordinate system, E, is obtained directly. The changes in the joint variables, e,,,, necessary to correct this error are estimated by where the matrix [J] is the Jacobian for the axes of interest. The joint angles are modified by the indicated amount and the sensors are read again. The process is continued until the tooling ball is in the desired position. This procedure is automatic and takes only a few minutes to complete. An important part of the calibration process is the establishnient of the reference position and the determination of the Jacobian, [J]. This is done when the robot is first installed in the workstation and the task points 789

5 are initially taught. The calibration fixture is placed at a convenient position and the robot is moved into the center of fixture. The sensor readings as well as the joint angles are stored at the reference position. Next, the robot goes through an automated procedure to identify the correct Jacobian for the reference position. The procedure for determining the Jacobian is based on a sequential regression technique described by Graupe [I]. The robot is commanded to make a number of small moves and the associated changes in the sensor readings are noted. The resulting rows in the Jacobian matrix are then given by J: = J:-] + P,p,6~~[68: - SE~J~-,] (9) P, = P,-1 - P,-iH,[l + HTP,-,H,]-'H,?P,-, (10) H, = 66 (11) where J: is row i of the Jacobian for measurement number r, 6a, is the change in the sensor readings at measurement number r, 60: is the change in joint variable i for measurement r, and q, is a weighting factor set to l in this problem. For the first measurement, the following initial values are used. J; = [O,O,O]* (12) PI = 1/C[II (13) where 10 < I/< < 10'. By repeating this sequence, the values in the Jacobian will be continually updated until they converge to a final value. Convergence typically takes 10 to 30 measurements because of the uncertainty in the measurement. As long as the fixture is not moved, the Jacobian determined through this procedure may be used in the calibration process. Example The calibration procedure described above was implemented in a pick and place application. In this task, a container of silicon wafers is delivered to the workstation and unloaded one at a time onto a wafer transfer device. The robot then picks up each wafer and positions it in an array on a plate for further processing. After the entire wafer array has been populated and the processing completed, the robot moves the wafers back to the transfer device to be loaded back in the container for further processing. Figure 8 is an illustration of the workspace and the calibration future. The fixture was mounted and the routine to identify the Jacobian was run prior to teaching the task points. To verify the validity of the calibration procedure, the robot task was stopped and a set of incorrect joint offsets was loaded into the controller. The calibration was then run and the offsets corrected. This process was repeated for 5 trials and the results are given in Table 1. Ball Wafer Transfer Mechanism 7 Location of Tooling Ball in Fixture Robot 2 Controller Figure 7 - Major Axis Calibration Fixture Figure 8 - Application Workspace 790

6 Conclusions While much work has been done on techniques for robot calibration, practical constraints in the industrial work environment limit the approaches that can be taken. This paper has described a simple calibration procedure that can be applied in a number of tasks to limit downtime due to reteaching after maintenance. By identifying the major contributors to variatioiis iii robot accuracy, a conibinatioii of redesign and active calibration was used to eliminate the requirement for reteaclling after a majority of maintenance tasks. The procedure has proved to be successful in laboratory tests as well as an actual induslrial application. Trial 1 Trial 2 Trial 3 (Joints 1, 2, and 3) (Xl y, Z) , , , , , , , , I References Trial 4 [I] Graupe, D., Identification of Systems, Robert E. Krieger Publishing Co., Inc., New York, Trial , , , , [2] Mooring, B. W., and Pack, T. P., Determination and Specification of Robot Repeatability, IBM Technical Report Number TR , Boca Raton, Florida, Table 1: Results of Major Axis Calibration [3] Roth, Z., Mooring, B. W., and Ravani, B., An Overview of Robot Calibration, IEEE Journal of Robotics and Automation, Volume RA-3, Number 5, October 1987, pages I

Inverse Kinematics. Given a desired position (p) & orientation (R) of the end-effector

Inverse Kinematics. Given a desired position (p) & orientation (R) of the end-effector Inverse Kinematics Given a desired position (p) & orientation (R) of the end-effector q ( q, q, q ) 1 2 n Find the joint variables which can bring the robot the desired configuration z y x 1 The Inverse