An Automated Method to Calibrate Industrial Robot Kinematic

Cyber Technology in Automation, Control and Intelligent Systems

June 4-7, 2014, Hong Kong, China

An Automated Method to Calibrate Industrial Robot Kinematic Parameters Using Spherical Surface Constraint Approach

Yong Liu, Senior Member, IEEE, Dingbing Shi and Jixiang Ding

advanced applications, such as robotic surgery, accuracy plays

Abstract—This paper describes our new method and updated

a significant role. Consequently, a simple, fast, and accurate robot kinematic model with real parameters identified through a calibration process is needed. Physical errors, such as machining tolerances, assembly errors and elastic deformations, cause the geometric properties of a manipulator to be different from their ideal values. Calibration of the geometrical parameters of a manipulator is important to ensure the accuracy of robot positioning.

To improve robot accuracy several calibration techniques have been used, including open and closed-loop methods. Open-loop methods [1][2] require an external metrology system to measure the end-effector pose, such as theodolites. Obtaining open-loop measurements is generally very costly and time consuming, and must be performed regularly for very high precision systems and replies on the operator’s skill. In contrast, closed-loop methods only need joint angle sensing, and the robot becomes self-calibrating.

These closed-loop [3]-[9] methods impose some constraints on the end effector, and the joint readings alone are used to calibrate the robot using kinematic closed-loop equations. Marco A. Meggiolaro first proposed a method called Single Endpoint Contact (SEC) calibration, the robot endpoint is constrained to a single contact point. However, it is almost impossible to exactly fit point constraint Newman et al. [10] and Chen et al. [11] proposed a calibration method using laser line tracking. This approach relies upon constraining the point on the end-effector moving along a stationary laser beam. However, it is difficult to exactly and automatically fit the line constraint.

A new method called “virtual closed kinematic chain”

system for industrial robot kinematic parameters calibration. The system consists of an IRB 120 industrial robot, a laser tool attached to the robot’s end-effector, a rotatable position sensitive detector (PSD), and a PC based controller. In the process of calibration, the surface of the PSD can be rotated around a fixed center, and the center points of PSD surface keep in a same 3D spherical surface. In the each position, the laser beams with small angles are aimed at the surface of the PSD and the laser spots are automatically located to the center of rotatable PSD. The calibration algorithm with different optimization objective functions have been adopt to identify the robot parameters. The simulation results verify the effectiveness of both the sensitivity analysis and the developed system.

I. INTRODUCTION

I

t is common issue that industrial robots are highly repeatable but not accurate. Accuracy has not been deemed necessary in

some simple industrial application. However, for more

This work was supported in part by the National Natural Science Foundation of China under grants 61175082, Jiangsu prospective joint research project under grants BY2013046, Jiangsu Science & Technology Pillar Program under grants BE2011192 and and󰀃Lianyungang󰀃joint󰀃research󰀃project󰀃under󰀃grants󰀃CXY1310, A beforehand research project under grants 9140A03030713BQ02033, the Jiangsu key laboratory of image and video understanding for social safety (Nanjing university of science and technology) under grant No.30920130122006.

Yong Liu, Dingbing Shi and Jixiang Ding are with the of Computer Science and Technology, Nanjing University of Science and Technology, Nanjing, China (corresponding author to e-mail: liuy1602@njust.edu.cn).

978-1-4799-3669-4/14/$31.00 © 2014 IEEE

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(ViCKi) [12] is proposed. Unlike previous closed-loop methods, this approach does not require any physical constraints. In the proposed method, a laser pointer tool, attached to the robot’s end effector, aims at a constant but unknown location on a fixed object, effectively creating a virtual 7 DOFs closed kinematic chain.

An industrial robot joint offset calibration method called the virtual line-based single-point constraint approach[13] is proposed, this proposed method relies mainly upon a laser pointer attached on the end-effector and single position-sensitive detector (PSD) arbitrarily located on the workcell. The automated calibration procedure involves aiming the laser lines loaded by the robot towards the center of the PSD surface from various robot positions and orientations. However, in order to keep laser lines intersect at a same point in high accuracy, the laser lines should approximately perpendicular aiming towards the center of the PSD surface. So the working area of robot is narrowed, in this paper a rotatable PSD is adopted to solve this problem.

This paper is structured as follows: the calibration system is presented in Section II. The methodology of kinematic parameter calibration is described in Section III. The simulation and experimental results are demonstrated in Section IV. Finally, we conclude the work.

II. CALIBRATION SYSTEM

The structure of this industrial-robot calibration system, is shown in Fig.2 and the actual, physical system is shown in Fig.1. The figures show the main components of the robot calibration system, which consists of an industrial robot, a designed end-effector fixture, a rotatable PSD and an industrial computer. A focusable laser pointer with its adapter is fixed and rigidly attached on the end-effector of the robot. The laser beam is adjusted to align its orientation toward the X-axis of the end-effector frame. The robot loads the laser to shoot a beam onto the surface of the PSD.

The rotatable PSD is shown in Fig.3. The surface of the PSD can rotate around a fixed point, which keeps that the center point of PSD always in a same 3D spherical surface. In the process of calibration, the laser lines should approximately perpendicular (or small angle with the vertical of PSD surface)

aiming towards the center of the PSD surface. The rotatable PSD not only expands the working area of robot but also improves the accuracy of positioning.

Laser IRB 120

PSD Camera

A/D interface

Rotatable PSD

Fig.1 The developed industrial robot calibration system

Fig.2The designed structure of industrial robot calibration system

PSD surface

LED

Rotation mechanism

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Fig.3 The developed industrial robot calibration system

The position of beam point can be checked by PSD sensor and be acquired to the computer by AD board. The errors, between target position and actual current position of the laser spot on the surface of the PSD, are used to guide the robot to move to the desired position precisely.

The computer communicates with the ABB robot via sockets based on TCP/IP protocol and can send orders to control the robot according to joint-level instructions or Cartesian instructions. The PC-based controller can obtain the current robot position information (task space and joint space) from the robot controller and send the control command to the robot controller as well as update the target position in real-time.

III. CALIBRATION METHODOLOGY

Aǃ Kinematic Error Model

The Denavit-Hartenberg (J. Denavit, R.S. Hartenberg 1955) convention is widely used for defining frames of reference for describing the forward kinematics. A model of the IRB120 robot according to D-H conventions is given in Table 1.

T 0T11T22T33T44T55T66T7

BǃCalibration Methodology

(2)

The calibration method relies mainly upon a laser pointer attached on the end-effector of a robot and a rotatable PSD. The surface of the PSD can rotate around a fixed point, which keeps that the center point of PSD always in a same 3D spherical surface. As shown in Fig.4, the calibration procedure is first fixing the PSD at an appropriate angle and aiming a laser beam from the laser pointer at the same point from various positions and orientations by using hybrid visual/PSD servoing. Then changing the pose of the PSD driven by the motor, and aiming laser beams at the same point by the method above. The same point is the center point of the PSD and the coordinates of the point in the robot base frame are unknown. Suppose M*N Sets of robot joint angles are recorded during the localization. There are M groups joint angles and N joint angles in each group, that means N laser beams intersecting at a same point and M point locating at a same spherical surface. Substituting the recorded joint angle into the forward kinematics (Equation (2)), the homogeneous transformations of end-effector fame with regard to the robot base frame are given by

Ti)󰀐sin(Ti)cosDisin(Ti)sinDiaicos(Ti)ºªcos(«sin(Ti)cosDi󰀐cos(Ti)sinDiaisin(Ti)» i󰀐1«Ti)cos(» (1) Ti «0Didi»sinDicos

»«

001¼¬0where

i󰀐1

Tirepresents the homogeneous transformation from

pxº

py»» (3)

y3z3pz»

»

001¼

A laser tool, a focusable laser pointer with its adapter, is rigidly attached on the end-effector of the robot. The laser line is adjusted to roughly align its orientation toward the x-axis in the end-effector frame. Once the laser pointer and the adapter is fixed, the laser line in the end-effector frame is given by

ªx1«x«2«x3«¬0

y1y2z1z2

i-1th frame to ith frame, ai,Di,di,Tiare generally named as link length, link twist, link offset, and joint angle ,respectively.

Table 1 D-H parameters for ABB IRB 120 Robot

Axis ș 1 2 3 4 5 6

ș1 ș2 ș3 ș4 ș5 ș6

d d1 0 0 d4 0 d6

a 0 a2 a3 0 0 0

Į Į1 0 Į3 Į4 Į5 0

x󰀐xly󰀐ylz󰀐zl (4)

MENEPE

where 󰀋xl,yl,zl󰀌is the position of one point of the laser line in the end-effector fame and 󰀋ME,NE,PE󰀌 is the unit vector of the laser line orientation in the end-effector fame.

Suppose N sets of joint angle in each group are recorded after calibration. From Equation (4) N laser lines are obtained. Each two laser lines have one intersection, so there are

Combining the six coordinate frames, nominal forward kinematics of the IRB120 become,

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/LQH󰀃LOLQH󰀃󰀔/LQH󰀃1/LQH󰀃󰀕OLQH󰀃󰀕OLQH󰀃LOLQH󰀃1OLQH󰀃󰀕OLQH󰀃LOLQH󰀃󰀔OLQH󰀃1

OLQH󰀃󰀔36'36'5RWDWH󰀃7KH󰀃36'5RWDWH󰀃7KH󰀃36'326,7,21󰀃LFig.4 The process of calibration

zyx{B}36'326,7,21󰀃󰀔326,7,21󰀃0

Combined with fig.4, the procedure is summarized in

sum of error from 1/2N(N󰀐1) intersections to the mean these steps. point in the x, y, z directions, respectively. Step 1: Change the pose of PSD driven by a motor. The So M mean pointsPl(xl,yl,zl), l 1,2,󰀖,M are constrained by one spherical. Spherical surface can be fitted by any four of M mean points.

1

N(N󰀐1) intersections from N lines. And the mean point of 2

the total intersections can be achieved. xG,yG,zG denotes the

CǃProcedure

󰀋󰀌center of PSD surface is always in a same spherical surface. Step 2: Guide by the visual servo, the robot is controlled to move and the spot of the laser pointer attached at the end-effector is located on the PSD active area at one pose.

Step 3: When the laser beam from the laser pointer shoots onto the surface of PSD, the controller is switched to the PSD guided servo for precision localization. That is, the position s2x2y2z21 0 ˄5˅

of beam point can be checked by PSD sensor and be acquired

s3x3y3z31to the computer by AD board. The errors, between target

position and actual current position of the laser spot on the s4x4y4z41

surface of the PSD, are used to guide the robot to move to the

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wheres x2󰀎y2󰀎z2,si xi󰀎yi󰀎zii 1,2,3,4, where desired position precisely. Thus the first line is obtained.

Step 4: Repeat step 2 and step 3. The same action is 󰀋xi,yi,zi󰀌 i 1,2,3,4 is the position of any four of M (M>4)

mean points. Qk,k 1,2,󰀖,Kdenote the center of the sphere , repeated. The difference is that robot changes to another pose.

Then we obtain another line. Each two lines have one

there are K 1/24M(M󰀐1)(M󰀐2)(M󰀐3)centers of sphere from M mean intersection point (or common perpendicular center), then points. Q(x,y,z) denotes mean point of K centers of the calculate the average point of these intersection points. sphere. The coordinate errors of the points betweenQk and

Step 5˖Repeat step 1 and step 4. The same action is

xyz

in the x, y, z directions, repeated. The difference is that PSD changes to another pose. Qare denoted as V,V,V

respectively. The kinematic parameters are identified by In each pose, one average intersection point will get and all minimizing the total sum of the coordinate errors. There are these points constrain at a same spherical surface. two kinds of optimization objective functions.

Step 6: Computing the parameters of the each four

The first kind is just using the error of centers of the sphere average intersection points. as the optimization objective function.

Step 7: Substituting the parameters into Equation (6) then the kinematic parameters are identified. G* argMin󰀋xV󰀎yV󰀎zV󰀌 ˄6˅

sxyz1

s1x1y1z11

The second kind combines the error of enters of the sphere

and error of intersections.

G* argMin󰀋xV󰀎yV󰀎zV󰀎xG󰀎yG󰀎zG󰀌 (7)

IV. EXPERIMENTAL RESULTS AND DISCUSSION Simulation of the calibration experiment was performed using very accurate joint readings. A robot was created in Simulink with a known set of parameters as the factory design. The laser pointer was fixed on the end-effector toward the

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X-axis of the end-effector frame, as in the experimental the proposed method. design. A virtual rotatable PSD was built as a feedback to exactly locate the laser beam on the center of the PSD surface. The two different kinds of optimization objective functions have been used to calibrate the robot. The result of calibration with perfect data is shown in Table II. Column 2 shows the actual offset parameters used by the simulation. Column 3 shows the initial parameters for the LMA. Column 2 shows the solution of the optimization using equation (6) and the result shows that using this optimization objective function to calculate the error of robot parameters cannot be successful. Table 2 presents partial data of the final intersections of laser lines when the iterative of optimization stop. From the data of table 2, all the mean intersections are at a same spherical surface, but the intersections of laser lines in each group don’t converge to one point. The result of calibration in column 2 of table 2 are incorrect, therefore, using equation (6) as optimization objective function cannot solve this problem.

Table 2 THE INTERSECTIONS OF LASER LINES

Fig.5 The distribution of sphere centers

Table 3 CALIBRATION RESULTS (PRECISE DATA)

The intersections of laser lines

(752.708364 24.902123 111.511853) (779.470923 25.810713 75.258997) (765.517424 26.268866 95.033415) (672.186026 23.160547 28.616782) (679.762640 22.260981 115.164029) (675.853295 23.677631 121.726975) (740.859442 78.891738 63.776401) (669.888290 57.713157 179.267000) (762.359559 86.000925 22.433060) (733.581663 -27.370943 76.484291) (693.585793 -18.586751 143.306996) (713.166918 -24.626421 108.771789) (765.289146 21.528248 100.559554) (759.964842 21.024512 106.959947) (767.362034 21.435361 97.150865) (681.295289 19.475693 93.688693) (662.287993 19.061408 133.901320) (668.959645 19.654634 116.374301) (670.895036 23.604863 93.584571) (657.062795 24.068211 125.342953) (669.502523 22.466880 96.303557)

The mean intersections

(765.898904 25.660567 93.934755) (675.933987 23.033053 121.835929) (724.369097 74.201940 88.492154) (713.444791 -23.528038 109.521025) (764.205341 21.329374 101.556788) (670.847642 19.397245 114.654771) (665.820118 23.379985 105.077027)

First

Initial Actual

parameters optimization

value error

function second optimization function

0 0 0

0.0491

1)

2˅

a1D1T2d2a2 D2T3

d3

a3

0 0 -90e

0

0 0.05

0 0 -0.0480e 0 0.05 -0.1996 270

-0DŽ1

0.0342 -0.1105 0 -0.0494e

0.0031 0.0012

0 0 0 0 70 -90e 0 302 0 90e 0 0 0 -90e 0 72 0 0

0 -0.05 -0.04 -0.3e 0 0.04 0 -0DŽ06e 0 0.04 0 0 0 0 0 0

3˅

-0.1996 -0.0501 0.0995 -0.0400 0.4165e -0.0499e

-0.3010 0.0003

4)

5˅

D3T4d4

-0.0973 0.0399 -0.0010 0.0041 0.2099e -0.0500e

-0.0624 0.0003

6˅

a4 D4T5

d5

a5

0.1982 0.0430 -0.0073 0.0032 -0.2612e

-0.0018

7˅

Another improved optimization objective function (equation (7)) has been used to solve this problem, which the error of intersections of laser lines have been added into the function. Column 5 shows that the solution using equation (7) as optimization objective functions was perfect. Fig.5 shows that the sphere centers are discretely distributed in the 3D-space at beginning and all these centers converge to one point at last. In theory the result verified the effectiveness of

D5T6

d6

0.05 0.0039 -0.4910 -0.0014 0 0.0003 0.0001 0.0009

a6

D6

CONCLUSION V.

Robot calibration plays a significant role in improving the

robot accuracy of the current complicated manufacturing

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processes. Robot kinematic parameters have a much larger influence on robot positioning accuracy. To address this issue, a Spherical Surface constraint approach and well-developed kinematic parameters calibration system for industrial robots were presented in this paper. Simulation results verify the feasibility of the proposed method and demonstrate the developed system can fit the need of kinematic parameters calibration for the industrial robot user. The further simulations and experiments will be conducted on the real robot to verify the proposed method and the developed system.

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