- Email: [email protected]
Intelligent Monitoring of an Industrial Robot
9th IFAC Workshop on Intelligent Manufacturing Systems Szczecin, Poland, October 9-10, 2008
Intelligent Monitoring of an Industrial Robot K. FAWAZ ∗ , R. MERZOUKI, B. OULD-BOUAMAMA ∗
LAGIS, UMR CNRS 8146, Ecole Polytechnique de Lille, Avenue Paul Langevin, 59655 Villeneuve d’Ascq, France. (e-mail: [email protected]).
Abstract: This paper deals with a model based real-time virtual simulator of industrial robot in order to detect eventual external collision. The implemented method concerns a model based Fault Detection and Isolation used to determine any lock of motion from an actuated robot joint after contact with static obstacles. Online implementation has been done in order to validate the proposed approach. Keywords: Fault Detection & Isolation (F DI), Industrial Robot, Dynamic Modelling, Co-Simulation. 1. INTRODUCTION The fast modernization of the production equipment makes that the industrial systems become increasingly complex and very sophisticated. In particular, the use of robots in modern manufacturing industries was intensively increased during these last decades. Robot technology has been applied in many aspects such as industry, agriculture, family service and medical etc. These robots carry out without slackening a repetitive tasks. In the assembly lines of auto industry for example, they replace the workmen in the painful and dangerous tasks like (painting, welding, stamping, etc.). Massive use of the robots requires monitoring in continuous time to avoid any kind of collisions or abnormal operations which is likely cause considerable losses. Simulation software proposed by the manufacturers of the robots in order to help users to validate their programs offline without interruption. Moreover, these tools does not make it possible to have a real-time monitoring on the operation of the real robots. In this paper, a 3D virtual simulator of an industrial robot with 6 degrees of freedom is developed. This simulator is based on the mathematical models of the robot and the six actuators which compose the joints of the robot. The main interest of this simulator is the real time monitoring of the real robot in order to detect a possible collisions. For modelling the joint actuator system, one needs an unified approach as bond graph tool, to represent the multiphysical aspect and to exploit the structural and causality properties for generating the diagnostic algorithm (OuldBouamama et al. (2003) and Djeziri et al. (2007)). The innovative contribution through this work concerns the use of the model based Fault Detection and Isolation (F DI) theory (Staroswiecki and Comtet-Varga (2001)), (Isermann (1997)), in detecting and isolating collisions on industrial robot manipulator. This is done by using online virtual simulator of the robot based on the robot and the joint actuators models, by informing the supervision
978-3-902661-40-1/09/$20.00 © 2008 IFAC
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Fig. 1. ABB Robot - IRB140 system of any external collisions after evaluation in time domain the residuals for each actuators. This paper is organized as follows: after the introduction section, the industrial robot system and online virtual simulator are presented in section 2. Then, section 3 regroups all the modelling of the studied system. The FDI algorithm is presented in section 4 while in section 5 the experimental results demonstrate the aim of the monitoring approach for industrial context. 2. INDUSTRIAL SYSTEM DESCRIPTION The industrial studied system is a manipulator robot IRB140 of Fig. 1. It carries out six degrees of freedom characterized by rotation motions. The IRB140 is an industrial robot which is not accessible to the control (Embedded Control Loop). To communicate with the robot, one used the W ebW are SDK @ software development kit, allowing to communicate with the robot through an Ethernet network. The developed virtual simulator allowing reading the current robot positions of the real robot through the W ebW are SDK @ support (see Fig. 2) in order to reconstruct the simulated dynamic from the identified system model. 3. SYSTEM MODELLING In this section, a description of the studied system parts models are introduced with the following scheduling:
10.3182/20081009-2-PL-4001.0024
In the presented work, a planned trajectory is considered (see Figure (3)), it consists to move the robot from position a to position b by varying the articular variables θs 1 and θs 2 while the other variables θs 3 , θs 4 , θs 5 and θs 6 remain known (θs 3 = 40, θs 4 = 0, θs 5 = 90andθs 6 = 0) Expressions of θs 1 and θs 2 are given as follows: Y θs 1 = arctan X √ (−0,313+0,889.Z+0,345. (3,54+17,6.Z−25.Z 2 )) √ θs 2 = arctan 2 (0,607−1,725.Z+0,1778.
Fig. 2.
(3.54+17,6.Z−25.Z ))
Communication Architecture
1. Direct geometric of the robot; 2. Inverse geometric model of the robot according to planned trajectory; 3. Dynamic model of the joint actuators. 3.1 Direct geometrical model
By applying the Denavit and Hartenberg convention, the direct geometrical model can be obtained as follow: X =(0,317.((-cos((θs1 ).cos(θs 2 ).sin(θs 3 )−cos(θs 1 ).sin(θs 2 ) .cos(θs 3 )).cos(θs 4 ) + sin(θs 1 ).sin(θs4 ))).cos(θ5 ) + (0, 317.(−cos(θs 1 ).cos(θs 2 ).cos(θs 3 ) + cos(θs 1 ).sin(θs 2 ) .sin(θs 3 ))).sin(θs 5 ) + 0, 380.cos(θs 1 ).cos(θs 2 ).cos(θs 3 ) −0, 380.cos(θs1 ).sin(θs 2 ).sin(θs 3 )+0, 36.cos(θs1 ). cos(θs 2 ) + 0, 07.cos(θs 1 )
Fig. 3.
3.3 Joint actuator modelling There are six electromechanical actuators located inside the 6 D.O.F robot and used for the traction motion. They are constituted by three principal components (Fig. 4): the DC motor part, which is the combination of an electrical and a mechanical parts, the gears system part and the load part. In this subsection, dynamic bond graph models of all of these components are graphically synthesized then expressed by differential equations. The use of bond graph allows dealing with one tool from modelling to ARR generation. θs j
Y =0,317.((-sin(θs 1 ).cos(θs 2 ).sin(θs 3 ) − sin(θs 1 ).sin(θs 2 ) .cos(θs 3 )).cos(θ4 ) − cos(θs 1 ).sin(θs 4 ))).cos(θs 5 ) + (0, 317.(−sin(θs1 ).cos(θs 2 ).cos(θs 3 ) + sin(θs 1 ).sin(θs 2 ) .sin(θs 3 ))).sin(θs 5 ) + 0, 380.sin(θs1 ).cos(θs 2 ).cos(θs 3 ) −0, 380.sin(θs1 ).sin(θs 2 ).sin(θs 3 )+0, 36.sin(θs 1 ).cos(θs 2 ) + 0, 07.sin(θs 1 ) Z =0,352+(0,317.(-sin(θs2 ).sin(θs 3 ) + cos(θs 2 ).cos(θs 3 ))) .cos(θs 4 ).cos(θs 5 ) + (0, 317.(−sin(θs2 ).cos(θs 3 ) − cos(θs 2 ).sin(θs 3 ))).sin(θs 5 ) + 0, 380.sin(θs2 ) .cos(θs 3 ) + 0, 380.cos(θs 2 ).sin(θs 3 ) + 0, 36.sin(θs2 )
θei
3.2 Inverse Geometric Model Inversely to direct geometric model which allows to calculate the coordinates of the end-effector in the base frame, the inverse geometrical model allows to calculate the articular coordinates according to a known geometric position of the centre of the tool. Numbers of methods were proposed in the literature allowing to calculate the inverse geometric model such as (Paul (1981)) and (Pieper (1968)).
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Dead zone
Flexion Frictions
Fig. 4.
Where (X,Y,Z) are the coordinates of the centre of tool.
Trajectory of the Robot
j th D O F Lo ad
Direct geometrical model is the whole relations which allows to calculates the position of the end-effector, i.e. the operational coordinates of the robot according to the articular coordinates. In our application, we used the Denavit and Hartenberg convention (Hartenberg and Denavit (1955)) to find the direct geometrical model of the manipulator robot, by considering the bodies of the robot perfectly rigid.
jth D.O.F of the manipulator robot.
Electrical part of the DC motor: This part corresponds to RL electrical circuit of the j th DC motor (see Fig. 5(a)), composed by: input voltage source U0j , electrical resistance Rej , inductance Lj and back electromotive force EM F , which is linear to the angular velocity of the rotor θ˙ej and equal to kej .θ˙ej with kej the EM F constant. The index j ∈ [1, 2] corresponds to the j th motor of the robot. The corresponding RL circuit bond graph’ model is given in integral causality by Fig. 5(b).
Let’s note e1j , P1j , M1j , effort, momentum and algebraic value of element I of the j th motor (Fig. 5(b)). The gyrator element GY describes the power transfer from the electric to mechanic by a flow variable f4j of the link 4 and Se0j is
source (M Se : wj ) (Fig. 6). This torque is expressed as follows: 1 − e−γj .∆θj wj = Aj .K j .τ 0j . (3) 1 + e−γj .∆θj Fig. 5. (a):Electrical RL circuit-(b):Equivalent Bond Graph model of the j th DC motor the input voltage source, then the following state equation is obtained: P1 e1j = Se0j −Rej . j −k ej .f 4j (1) M1j P f0j = f 1 = f 2 = f 3 = 1 .e1j .dt = 1j = ij j j j Lj M1j with: Se = U 0 0 j j f4j = θ˙ ej
Thus, the corresponding dynamic equation of circuit of Fig. 5 is: dij = U 0j −Rej .ij −kej .θ˙ej (2) Lj . dt
Mechanical part of the DC motor: This part represents the mechanical part of the j th DC motor, characterizing by its rotor inertia Jes , viscous friction parameter fej , transmission axis rigidity Kj and a motorized torque Uj . In this part, the influence of backlash phenomenon expressed by a disturbing torque wj is represented by a modulated effort source for the bond graph model (Merzouki and Cadiou (2005)). The corresponding bond graph model in integral causality is given by Fig. 6.
where wj is the disturbing and nonlinear transmitted torque, ∆θj = θej − Nj .θsj defines the difference between input θej and output θsj motor positions, Nj a reducer constant, Aj a graphical parameter which is taken as a negative integer to describe the reaction effect of the disturbing torque, Kj the rigidity constant of the transmission system, τ0j is the dead zone amplitude and γj = 1/ 2.τ0j the sigmoid function slope of the j th DC motor (Merzouki and Cadiou (2005)).
Let’s note e5j , P5j , M5j effort, momentum and algebraic value of element I of Fig. 6, f4j is the flow variable of link 4, f9j ,1/Kj flow and algebraic value of element C, then the following state equation (4) is obtained: Z P5 (4) e5j = −f ej . j +e4j +e6j −K j . f9j .dt M5j P5 1 .e5j .dt = j = θ˙ ej f4j = f 5j = f 6j = f 7j = f 8j = J M e 5j j Z e8j = e9j = K j . f9j .dt with: f9j = f 8j −f 10j = θ˙ej −N j .θ˙sj e4j = U j = k cj .ij e6j = wj
Thus, the corresponding dynamic equation of mechanical part is given as follows: dθ˙e Jej . j = −f ej .θ˙ ej +U j −wj −K j . θej −N j .θsj (5) dt
with Uj the input motor torque of the j th DC motor, given in function of the current ij and the torque constant kcj .
Fig. 6.
Bond graph model of the mechanical part of the j tj motor
DC
The backlash mechanism considered in this model is represented by a disturbing torque, hampering the smooth functioning of the system, and caused by simultaneous and evaluative reactions of the shock between the two sides of the gears system (Fig. 7) . This torque is chosen continuous, nonlinear and differentiable, compared to the size of the gears system and its effect on the global system.
Fig. 8.
τ0
Fig. 7.
Gears part: This part concerns the mechanical gears which links between the mechanical and the load parts with a reduction constant Nj (Fig. 4). Bond graph model of this part is given by Fig. 8 and represents a transformer element T F between the j th velocities of the motor axis θ˙ej and the wheel θ˙sj .
According to Fig. (8), let’s choose f10j and f11j as the corresponding flows variables of links 10 and 11:
j
Backlash mechanism for the jth
Bond graph model of jth gears part
DC
f10 = Nj .f11
motor
So, a smooth and continuous model of transmitted torque wj which is developed in (Merzouki and Cadiou (2005)) and illustrated in Fig. 7, is taken as a modulated effort
141
which corresponds to the mechanical equation: θ˙e = Nj .θ˙s j
j
(6)
(7)
Load part: This part represents the load part of the j th electromechanical system, characterizing by its inertia Jsj , viscous friction parameter fsj and backlash disturbing torque Nj .wj . The bond graph model of this part in integral causality is given by Fig. 9.
θs j
%
*
ϕ
'( ) &
"#$
Fig. 9. jth
!
Load part bond graph’ model
Let’s note e14j , P14j , M14j effort, momentum and algebraic value of element I of Fig. 9. f9j is the flow and of element C (Fig. 6), then the following state equation (8) is obtained: P14j + e13j + e11j + e27j e14j = −fsj . (8) M14j P14j 1 .e14j .dt = = θ˙sj ; f11j = f 12j = f 13j = f 14j = J M s 14 j j Z e11j = N j .e9j = N j .K j . f9j .dt; with: f9 = f −f = θ˙e −N j .θ˙ s ; j j 10j j 8j e13 = N j .w j ; j e27j = ϕj
Isermann (1997)) is build, in order to detect and to localize the presence of static obstacles on the j th joint of the manipulator robot. By using the F DI algorithms generated directly from the bond graph model (Ould-Bouamama et al. (2003)), a list of Analytical Redundancy Relation (ARR) along with the corresponding Fault Signature Matrix (F SM ) can be deduce. The principale of the presented approach is the use of (ARR) theory, not to detect a j th faulty actuator, but to detect an external joint obstacle which lock the normal operating of the j th actuator. The FDI proposed approach is based on the calculation of the residuals issued from the Analytical Redundancy Relation (ARR) and it makes the difference between the dynamic system in normal and faulty situations. Note that for an observable system, with none unresolved algebraic loops, the number of ARR generated is equal to the number of the measured states Merzouki et al. (2007). The main steps to generate the list of ARR and the F SM by using are summarized bellow (Ould-Bouamama et al. (2003)): • Build the bond graph model in preferred integral causality; • Put the bond graph model in preferred derivative causality after dualization of the sensors; • Write the constitutive relation for each junction; • Eliminate the unknown variables from each constitutive relation by covering the causal paths in the bond graph model; • Generate the list of ARR and the corresponding F SM .
Thus, the corresponding dynamic equation of mechanical part is given as follows: Note that for an observable system, the number of ARR dθ˙s Jsj . j = −f sj .θ˙sj +N j .w j +N j .K j . θej − Nj .θsj +ϕj (9) generated are equal to the number of detectors on the bond dt graph model (Ould-Bouamama et al. (2003)). ˙ ϕj are the all the nonlinear efforts, function θsj and θsj · ARR1j Generation and regroup Coriolis, centrifugal and gravitational forces applied at each joint. It includes also the unmodeled The first ARRj corresponds to those generated from the j th electromechanical system where its bond graph model dynamics and other unknown external disturbances. in derivative causality (see Fig. 11). In this model, the C After a concatenation of the different bond graph models, element is already in integral causality, because the system the global model of the j th electromechanical system is is sub-determined with the actual configuration. So, the deduced in Fig. 10. The measured and estimated states dualization of the sensors is possible in this case because are shown by detectors element Df : θ˙sj and Df ∗ : θ˙ej the initial conditions of this electromechanical system are deduced from derivation of the articular joint positions. supposed known, and then the C element can be presented in integral causality.
Fig. 10.
jth Global bond graph model of the electromechanical system
4. FAULT DETECTION AND ISOLATION ALGORITHM In this section, a model based Fault Detection & Isolation algorithm (F DI) (Staroswiecki and Comtet-Varga (2001),
142
Fig. 11.
jth Global bond graph model of the electromechanical system in derivative causality
The constitutive relations of the junctions 11 , 12 01 and 13 are given by the following equations: e2 = e0 − e1 − e3 ;
(10)
e15 = e4 − e5 + e6 − e7 − e8 ;
(11)
e11 = e12 + e14 + e16 − e13 − e28
(13)
f10 = f8 − f9 ;
(12)
Two structurally independent ARRj of the j th electromechanical system can be generated from equations 11 and 12 after eliminating the unknown variables. This elimination process is achieved by following the causal paths from unknown to known variables on the bond graph model.
d θ˙sj d Jsj . + fsj .θ˙sj − Nj .w j +ϕj ARR2j : N j . dt dt +K j . Nj .θ˙sj −θ˙ ej = 0
Once the list of possible ARRj is generated, the Fault Signature Matrix (F SM ) can be built by deducing the signature of the system components on each ARRj . Note that each component in the physical system can be represented by one or more variables in the ARRsj . In addition, From equation 11, the unknown variables are given by the in the residuals’ F SM are represented instead of ARR, following relations: where each residual rkj is a numerical evaluation of an ARRkj . The corresponding residuals r1j and r2j of ARR1j e = 0; 15 and ARR2j (j ∈ [1; 2]) are given by the following relations: d d e5 = Jej . (f5 ) = Jej . θ˙ej ; dt dt Lj .Jej d2 ˙ Lj Jsj d2 ˙ e6 = wj ; θej + θsj . . . r = 1 (14) j kej dt2 kej Nj dt2 e7 = fej .f7 = fej .θ˙ej ; ! Re .Je Lj .fej d ˙ dθ˙sj 1 e11 θej + + j j . ˙ fsj .θsj − Nj .wj + Jsj . k k dt e8 = e10 = N = N e e j j dt j j Rej .Jsj Lj ..fsj Re ..fej d ˙ + θsj + kej + j + . .θ˙ej Nj .kej Nj .kej dt kej From the junction 11 the following equations are deduced: Re Re ..fsj ˙ .θsj − U0j − 2. j .wj ; + j df3 N .k kej j ej e3 = U 0j −e2 −e1 = U 0j −Rej .f 3 −Lj . ; dt ˙ d θsj 1 d .e4 f3 = + fsj .θ˙sj − Nj .wj + ϕj r2j = Nj . Jsj . kej dt dt then + Kj . Nj .θ˙sj − θ˙ej Re Lj de4 e3 = U 0j − j .e4 − . = k ej .f 4 = k ej .θ˙ej (15) kej kej dt From equations 14 and 15 the following ARR1j is deduced: The corresponding F SM of the system under study is given in Fig 12. Rej d ˙ ˙ ˙ ARR1j : k ej .θej −U 0j + . Jej . θej −wj +f ej .θej kej dt D I r r r r r r r r r r r r 1 d ˙ + θsj fsj .θ˙sj − Nj .wj + Jsj . 1 0 1 1 0 0 0 0 0 0 0 0 0 0 2 Actuator 1 Nj dt 1 0 1 1 0 0 0 0 0 0 0 0 0 0 2 Lj d d ˙ 1 0 0 0 1 1 0 0 0 0 0 0 0 0 2 + . θej Jej . Actuator 2 kej dt dt 1 0 0 0 1 1 0 0 0 0 0 0 0 0 2 1 d 1 0 0 0 0 0 1 1 0 0 0 0 0 0 2 −wj + fej .θ˙ej + fsj .θ˙ sj − Nj .w j +J sj . θ˙sj =0 Actuator 3 Nj dt 1 0 0 0 0 0 1 1 0 0 0 0 0 0 2 b
b
11
21
12
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13
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14
24
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16
2 e4 Actuator 4 2 s4
1
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e1 s1
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e3 s3
The second ARRj can be deduced from equation 12, where the following system is obtained: f = N j .f 11 = N j .θ˙sj , 10 f8 = f 15 = θ˙ej , (16) 1 d (e9 ) 1 d f9 = . = .N j . (e12 + e14 + e16 − e13 ) Kj dt Kj dt where:
e13 = N j .wj ; e12 = f sj .f 12 = f sj .θ˙sj ; d (f14 ) d ˙ e = J . = J . θsj ; 14 s s j j dt dt e16 = 0; e27 = ϕj
(17)
· ARR2j Generation
The second ARRj is then deduced by replacing the unknown variables of equations 16 and 12 by their expressions in 17:
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6
Fig. 12.
Fault signature matrix of the manipulator robot system.
In this table 12, the rows represent the components signatures and the columns are respectively the fault detectability Db , the fault isolability Ib , and the twelve residuals r1j and r2j . A ‘1’ value on respectively Db and Ib columns means that faults on the corresponding components are detectable and isolable. The presence of ‘1’ value on the residual columns shows the influence of the corresponding component on the residual dynamics. In this application, the F SM helps to detect and to distinguish the presence of eventual obstacles, which lock the normal operating of the actuator.
5. EXPERIMENTAL RESULTS In this section, experimental results have been done on the IRB140 robot while following the planned trajectory of Fig. 3.Numerical values of the actuators parameters used for the online simulation are not given because the constraints of pages number. Fig. 13 shows the identified controls inputs of actuators models during normal operating. In this case the time domain variation of the angular joint positions and the whole residuals are represented successively by Fig. 14 and Fig. 15. It is noticed that the residuals still equal to 0 while there is no collision detection with the robot. By repeating the experiment after introducing a static obstacles on the first and the second D.O.F , the residuals r21 and r22 are sensitive to external collision (see Fig. 16) because it locks the normal motion of the appropriate actuated axis. Then the articular positions are given by Fig. 17. The virtual simulator Fig. 18 shows the variation state of the residuals two residuals in collision situation.
Fig. 13.
Control Input of Actuators 1 to 6
Fig. 16.
Residuals in collision situation
Fig. 17.
Articular positions in collision situation
Fig. 18.
Online collision detection on the real robot from a virtual simulator.
REFERENCES
Fig. 14.
Articular variables in normal operating
Fig. 15.
Residuals in normal operating
6. CONCLUSION In this work, a virtual simulator of an industrial robot is developed in order to make online supervision for possible collisions detection. The real and virtual systems are operating in parallel, while a model based F DI algorithm in running in real-time. This practical approach can help the user to avoid accidental situations without been closer to the system and by using a soft solution. The validation of the method is done after system modelling validation and online experiments.
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Djeziri, M.A., Merzouki, R., Ould-Bouamama, B., and G.Dauphin-Tanguy (2007). Bond graph model based for robust fault diagnosis. American Control Conference, 3017 – 3022. Hartenberg, R.S. and Denavit, J. (1955). A kinematic notation for loxer pair mechanisms based on matrices. Journal of Applied Mechanics, 77, 215–221. Isermann, R. (1997). Supervision, fault detection and fault diagnosis methods - an introduction. Control Engineering Practice, 5, 639–652. Merzouki, R. and Cadiou, J. (2005). Estimation of backlash phenomenon in the electromechanical actuator. Journal of Control Engineering practice, 13/8, 973–983. Merzouki, R., Medjaher, K., Djeziri, M.A., and B.OuldBouamama (2007). Backlash fault detection in mechatronics system. MECHATRONICS, 17, 299–310. Ould-Bouamama, B., Samantaray, A.K., Staroswiecki, M., and Dauphin-Tanguy, G. (2003). Derivation of constraint relations from bond graph models for fault detection and isolation. International Conference on Bond Graph Modeling and Simulation, 35, 104–109. Paul, R. (1981). Robot manipulators: mathematics, programming and control. MIT Press. Pieper, D. (1968). the kinematics of manipulators under computer control. Ph. D. Thesis, Stanford University. Staroswiecki, M. and Comtet-Varga, G. (2001). Analytical redundancy relations for fault detection and isolation in algebraic dynamic systems. Automatica, 37, 687–699.
Intelligent Monitoring of an Industrial Robot K. FAWAZ ∗ , R. MERZOUKI, B. OULD-BOUAMAMA ∗
LAGIS, UMR CNRS 8146, Ecole Polytechnique de Lille, Avenue Paul Langevin, 59655 Villeneuve d’Ascq, France. (e-mail: [email protected]).
Abstract: This paper deals with a model based real-time virtual simulator of industrial robot in order to detect eventual external collision. The implemented method concerns a model based Fault Detection and Isolation used to determine any lock of motion from an actuated robot joint after contact with static obstacles. Online implementation has been done in order to validate the proposed approach. Keywords: Fault Detection & Isolation (F DI), Industrial Robot, Dynamic Modelling, Co-Simulation. 1. INTRODUCTION The fast modernization of the production equipment makes that the industrial systems become increasingly complex and very sophisticated. In particular, the use of robots in modern manufacturing industries was intensively increased during these last decades. Robot technology has been applied in many aspects such as industry, agriculture, family service and medical etc. These robots carry out without slackening a repetitive tasks. In the assembly lines of auto industry for example, they replace the workmen in the painful and dangerous tasks like (painting, welding, stamping, etc.). Massive use of the robots requires monitoring in continuous time to avoid any kind of collisions or abnormal operations which is likely cause considerable losses. Simulation software proposed by the manufacturers of the robots in order to help users to validate their programs offline without interruption. Moreover, these tools does not make it possible to have a real-time monitoring on the operation of the real robots. In this paper, a 3D virtual simulator of an industrial robot with 6 degrees of freedom is developed. This simulator is based on the mathematical models of the robot and the six actuators which compose the joints of the robot. The main interest of this simulator is the real time monitoring of the real robot in order to detect a possible collisions. For modelling the joint actuator system, one needs an unified approach as bond graph tool, to represent the multiphysical aspect and to exploit the structural and causality properties for generating the diagnostic algorithm (OuldBouamama et al. (2003) and Djeziri et al. (2007)). The innovative contribution through this work concerns the use of the model based Fault Detection and Isolation (F DI) theory (Staroswiecki and Comtet-Varga (2001)), (Isermann (1997)), in detecting and isolating collisions on industrial robot manipulator. This is done by using online virtual simulator of the robot based on the robot and the joint actuators models, by informing the supervision
978-3-902661-40-1/09/$20.00 © 2008 IFAC
139
Fig. 1. ABB Robot - IRB140 system of any external collisions after evaluation in time domain the residuals for each actuators. This paper is organized as follows: after the introduction section, the industrial robot system and online virtual simulator are presented in section 2. Then, section 3 regroups all the modelling of the studied system. The FDI algorithm is presented in section 4 while in section 5 the experimental results demonstrate the aim of the monitoring approach for industrial context. 2. INDUSTRIAL SYSTEM DESCRIPTION The industrial studied system is a manipulator robot IRB140 of Fig. 1. It carries out six degrees of freedom characterized by rotation motions. The IRB140 is an industrial robot which is not accessible to the control (Embedded Control Loop). To communicate with the robot, one used the W ebW are SDK @ software development kit, allowing to communicate with the robot through an Ethernet network. The developed virtual simulator allowing reading the current robot positions of the real robot through the W ebW are SDK @ support (see Fig. 2) in order to reconstruct the simulated dynamic from the identified system model. 3. SYSTEM MODELLING In this section, a description of the studied system parts models are introduced with the following scheduling:
10.3182/20081009-2-PL-4001.0024
In the presented work, a planned trajectory is considered (see Figure (3)), it consists to move the robot from position a to position b by varying the articular variables θs 1 and θs 2 while the other variables θs 3 , θs 4 , θs 5 and θs 6 remain known (θs 3 = 40, θs 4 = 0, θs 5 = 90andθs 6 = 0) Expressions of θs 1 and θs 2 are given as follows: Y θs 1 = arctan X √ (−0,313+0,889.Z+0,345. (3,54+17,6.Z−25.Z 2 )) √ θs 2 = arctan 2 (0,607−1,725.Z+0,1778.
Fig. 2.
(3.54+17,6.Z−25.Z ))
Communication Architecture
1. Direct geometric of the robot; 2. Inverse geometric model of the robot according to planned trajectory; 3. Dynamic model of the joint actuators. 3.1 Direct geometrical model
By applying the Denavit and Hartenberg convention, the direct geometrical model can be obtained as follow: X =(0,317.((-cos((θs1 ).cos(θs 2 ).sin(θs 3 )−cos(θs 1 ).sin(θs 2 ) .cos(θs 3 )).cos(θs 4 ) + sin(θs 1 ).sin(θs4 ))).cos(θ5 ) + (0, 317.(−cos(θs 1 ).cos(θs 2 ).cos(θs 3 ) + cos(θs 1 ).sin(θs 2 ) .sin(θs 3 ))).sin(θs 5 ) + 0, 380.cos(θs 1 ).cos(θs 2 ).cos(θs 3 ) −0, 380.cos(θs1 ).sin(θs 2 ).sin(θs 3 )+0, 36.cos(θs1 ). cos(θs 2 ) + 0, 07.cos(θs 1 )
Fig. 3.
3.3 Joint actuator modelling There are six electromechanical actuators located inside the 6 D.O.F robot and used for the traction motion. They are constituted by three principal components (Fig. 4): the DC motor part, which is the combination of an electrical and a mechanical parts, the gears system part and the load part. In this subsection, dynamic bond graph models of all of these components are graphically synthesized then expressed by differential equations. The use of bond graph allows dealing with one tool from modelling to ARR generation. θs j
Y =0,317.((-sin(θs 1 ).cos(θs 2 ).sin(θs 3 ) − sin(θs 1 ).sin(θs 2 ) .cos(θs 3 )).cos(θ4 ) − cos(θs 1 ).sin(θs 4 ))).cos(θs 5 ) + (0, 317.(−sin(θs1 ).cos(θs 2 ).cos(θs 3 ) + sin(θs 1 ).sin(θs 2 ) .sin(θs 3 ))).sin(θs 5 ) + 0, 380.sin(θs1 ).cos(θs 2 ).cos(θs 3 ) −0, 380.sin(θs1 ).sin(θs 2 ).sin(θs 3 )+0, 36.sin(θs 1 ).cos(θs 2 ) + 0, 07.sin(θs 1 ) Z =0,352+(0,317.(-sin(θs2 ).sin(θs 3 ) + cos(θs 2 ).cos(θs 3 ))) .cos(θs 4 ).cos(θs 5 ) + (0, 317.(−sin(θs2 ).cos(θs 3 ) − cos(θs 2 ).sin(θs 3 ))).sin(θs 5 ) + 0, 380.sin(θs2 ) .cos(θs 3 ) + 0, 380.cos(θs 2 ).sin(θs 3 ) + 0, 36.sin(θs2 )
θei
3.2 Inverse Geometric Model Inversely to direct geometric model which allows to calculate the coordinates of the end-effector in the base frame, the inverse geometrical model allows to calculate the articular coordinates according to a known geometric position of the centre of the tool. Numbers of methods were proposed in the literature allowing to calculate the inverse geometric model such as (Paul (1981)) and (Pieper (1968)).
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Dead zone
Flexion Frictions
Fig. 4.
Where (X,Y,Z) are the coordinates of the centre of tool.
Trajectory of the Robot
j th D O F Lo ad
Direct geometrical model is the whole relations which allows to calculates the position of the end-effector, i.e. the operational coordinates of the robot according to the articular coordinates. In our application, we used the Denavit and Hartenberg convention (Hartenberg and Denavit (1955)) to find the direct geometrical model of the manipulator robot, by considering the bodies of the robot perfectly rigid.
jth D.O.F of the manipulator robot.
Electrical part of the DC motor: This part corresponds to RL electrical circuit of the j th DC motor (see Fig. 5(a)), composed by: input voltage source U0j , electrical resistance Rej , inductance Lj and back electromotive force EM F , which is linear to the angular velocity of the rotor θ˙ej and equal to kej .θ˙ej with kej the EM F constant. The index j ∈ [1, 2] corresponds to the j th motor of the robot. The corresponding RL circuit bond graph’ model is given in integral causality by Fig. 5(b).
Let’s note e1j , P1j , M1j , effort, momentum and algebraic value of element I of the j th motor (Fig. 5(b)). The gyrator element GY describes the power transfer from the electric to mechanic by a flow variable f4j of the link 4 and Se0j is
source (M Se : wj ) (Fig. 6). This torque is expressed as follows: 1 − e−γj .∆θj wj = Aj .K j .τ 0j . (3) 1 + e−γj .∆θj Fig. 5. (a):Electrical RL circuit-(b):Equivalent Bond Graph model of the j th DC motor the input voltage source, then the following state equation is obtained: P1 e1j = Se0j −Rej . j −k ej .f 4j (1) M1j P f0j = f 1 = f 2 = f 3 = 1 .e1j .dt = 1j = ij j j j Lj M1j with: Se = U 0 0 j j f4j = θ˙ ej
Thus, the corresponding dynamic equation of circuit of Fig. 5 is: dij = U 0j −Rej .ij −kej .θ˙ej (2) Lj . dt
Mechanical part of the DC motor: This part represents the mechanical part of the j th DC motor, characterizing by its rotor inertia Jes , viscous friction parameter fej , transmission axis rigidity Kj and a motorized torque Uj . In this part, the influence of backlash phenomenon expressed by a disturbing torque wj is represented by a modulated effort source for the bond graph model (Merzouki and Cadiou (2005)). The corresponding bond graph model in integral causality is given by Fig. 6.
where wj is the disturbing and nonlinear transmitted torque, ∆θj = θej − Nj .θsj defines the difference between input θej and output θsj motor positions, Nj a reducer constant, Aj a graphical parameter which is taken as a negative integer to describe the reaction effect of the disturbing torque, Kj the rigidity constant of the transmission system, τ0j is the dead zone amplitude and γj = 1/ 2.τ0j the sigmoid function slope of the j th DC motor (Merzouki and Cadiou (2005)).
Let’s note e5j , P5j , M5j effort, momentum and algebraic value of element I of Fig. 6, f4j is the flow variable of link 4, f9j ,1/Kj flow and algebraic value of element C, then the following state equation (4) is obtained: Z P5 (4) e5j = −f ej . j +e4j +e6j −K j . f9j .dt M5j P5 1 .e5j .dt = j = θ˙ ej f4j = f 5j = f 6j = f 7j = f 8j = J M e 5j j Z e8j = e9j = K j . f9j .dt with: f9j = f 8j −f 10j = θ˙ej −N j .θ˙sj e4j = U j = k cj .ij e6j = wj
Thus, the corresponding dynamic equation of mechanical part is given as follows: dθ˙e Jej . j = −f ej .θ˙ ej +U j −wj −K j . θej −N j .θsj (5) dt
with Uj the input motor torque of the j th DC motor, given in function of the current ij and the torque constant kcj .
Fig. 6.
Bond graph model of the mechanical part of the j tj motor
DC
The backlash mechanism considered in this model is represented by a disturbing torque, hampering the smooth functioning of the system, and caused by simultaneous and evaluative reactions of the shock between the two sides of the gears system (Fig. 7) . This torque is chosen continuous, nonlinear and differentiable, compared to the size of the gears system and its effect on the global system.
Fig. 8.
τ0
Fig. 7.
Gears part: This part concerns the mechanical gears which links between the mechanical and the load parts with a reduction constant Nj (Fig. 4). Bond graph model of this part is given by Fig. 8 and represents a transformer element T F between the j th velocities of the motor axis θ˙ej and the wheel θ˙sj .
According to Fig. (8), let’s choose f10j and f11j as the corresponding flows variables of links 10 and 11:
j
Backlash mechanism for the jth
Bond graph model of jth gears part
DC
f10 = Nj .f11
motor
So, a smooth and continuous model of transmitted torque wj which is developed in (Merzouki and Cadiou (2005)) and illustrated in Fig. 7, is taken as a modulated effort
141
which corresponds to the mechanical equation: θ˙e = Nj .θ˙s j
j
(6)
(7)
Load part: This part represents the load part of the j th electromechanical system, characterizing by its inertia Jsj , viscous friction parameter fsj and backlash disturbing torque Nj .wj . The bond graph model of this part in integral causality is given by Fig. 9.
θs j
%
*
ϕ
'( ) &
"#$
Fig. 9. jth
!
Load part bond graph’ model
Let’s note e14j , P14j , M14j effort, momentum and algebraic value of element I of Fig. 9. f9j is the flow and of element C (Fig. 6), then the following state equation (8) is obtained: P14j + e13j + e11j + e27j e14j = −fsj . (8) M14j P14j 1 .e14j .dt = = θ˙sj ; f11j = f 12j = f 13j = f 14j = J M s 14 j j Z e11j = N j .e9j = N j .K j . f9j .dt; with: f9 = f −f = θ˙e −N j .θ˙ s ; j j 10j j 8j e13 = N j .w j ; j e27j = ϕj
Isermann (1997)) is build, in order to detect and to localize the presence of static obstacles on the j th joint of the manipulator robot. By using the F DI algorithms generated directly from the bond graph model (Ould-Bouamama et al. (2003)), a list of Analytical Redundancy Relation (ARR) along with the corresponding Fault Signature Matrix (F SM ) can be deduce. The principale of the presented approach is the use of (ARR) theory, not to detect a j th faulty actuator, but to detect an external joint obstacle which lock the normal operating of the j th actuator. The FDI proposed approach is based on the calculation of the residuals issued from the Analytical Redundancy Relation (ARR) and it makes the difference between the dynamic system in normal and faulty situations. Note that for an observable system, with none unresolved algebraic loops, the number of ARR generated is equal to the number of the measured states Merzouki et al. (2007). The main steps to generate the list of ARR and the F SM by using are summarized bellow (Ould-Bouamama et al. (2003)): • Build the bond graph model in preferred integral causality; • Put the bond graph model in preferred derivative causality after dualization of the sensors; • Write the constitutive relation for each junction; • Eliminate the unknown variables from each constitutive relation by covering the causal paths in the bond graph model; • Generate the list of ARR and the corresponding F SM .
Thus, the corresponding dynamic equation of mechanical part is given as follows: Note that for an observable system, the number of ARR dθ˙s Jsj . j = −f sj .θ˙sj +N j .w j +N j .K j . θej − Nj .θsj +ϕj (9) generated are equal to the number of detectors on the bond dt graph model (Ould-Bouamama et al. (2003)). ˙ ϕj are the all the nonlinear efforts, function θsj and θsj · ARR1j Generation and regroup Coriolis, centrifugal and gravitational forces applied at each joint. It includes also the unmodeled The first ARRj corresponds to those generated from the j th electromechanical system where its bond graph model dynamics and other unknown external disturbances. in derivative causality (see Fig. 11). In this model, the C After a concatenation of the different bond graph models, element is already in integral causality, because the system the global model of the j th electromechanical system is is sub-determined with the actual configuration. So, the deduced in Fig. 10. The measured and estimated states dualization of the sensors is possible in this case because are shown by detectors element Df : θ˙sj and Df ∗ : θ˙ej the initial conditions of this electromechanical system are deduced from derivation of the articular joint positions. supposed known, and then the C element can be presented in integral causality.
Fig. 10.
jth Global bond graph model of the electromechanical system
4. FAULT DETECTION AND ISOLATION ALGORITHM In this section, a model based Fault Detection & Isolation algorithm (F DI) (Staroswiecki and Comtet-Varga (2001),
142
Fig. 11.
jth Global bond graph model of the electromechanical system in derivative causality
The constitutive relations of the junctions 11 , 12 01 and 13 are given by the following equations: e2 = e0 − e1 − e3 ;
(10)
e15 = e4 − e5 + e6 − e7 − e8 ;
(11)
e11 = e12 + e14 + e16 − e13 − e28
(13)
f10 = f8 − f9 ;
(12)
Two structurally independent ARRj of the j th electromechanical system can be generated from equations 11 and 12 after eliminating the unknown variables. This elimination process is achieved by following the causal paths from unknown to known variables on the bond graph model.
d θ˙sj d Jsj . + fsj .θ˙sj − Nj .w j +ϕj ARR2j : N j . dt dt +K j . Nj .θ˙sj −θ˙ ej = 0
Once the list of possible ARRj is generated, the Fault Signature Matrix (F SM ) can be built by deducing the signature of the system components on each ARRj . Note that each component in the physical system can be represented by one or more variables in the ARRsj . In addition, From equation 11, the unknown variables are given by the in the residuals’ F SM are represented instead of ARR, following relations: where each residual rkj is a numerical evaluation of an ARRkj . The corresponding residuals r1j and r2j of ARR1j e = 0; 15 and ARR2j (j ∈ [1; 2]) are given by the following relations: d d e5 = Jej . (f5 ) = Jej . θ˙ej ; dt dt Lj .Jej d2 ˙ Lj Jsj d2 ˙ e6 = wj ; θej + θsj . . . r = 1 (14) j kej dt2 kej Nj dt2 e7 = fej .f7 = fej .θ˙ej ; ! Re .Je Lj .fej d ˙ dθ˙sj 1 e11 θej + + j j . ˙ fsj .θsj − Nj .wj + Jsj . k k dt e8 = e10 = N = N e e j j dt j j Rej .Jsj Lj ..fsj Re ..fej d ˙ + θsj + kej + j + . .θ˙ej Nj .kej Nj .kej dt kej From the junction 11 the following equations are deduced: Re Re ..fsj ˙ .θsj − U0j − 2. j .wj ; + j df3 N .k kej j ej e3 = U 0j −e2 −e1 = U 0j −Rej .f 3 −Lj . ; dt ˙ d θsj 1 d .e4 f3 = + fsj .θ˙sj − Nj .wj + ϕj r2j = Nj . Jsj . kej dt dt then + Kj . Nj .θ˙sj − θ˙ej Re Lj de4 e3 = U 0j − j .e4 − . = k ej .f 4 = k ej .θ˙ej (15) kej kej dt From equations 14 and 15 the following ARR1j is deduced: The corresponding F SM of the system under study is given in Fig 12. Rej d ˙ ˙ ˙ ARR1j : k ej .θej −U 0j + . Jej . θej −wj +f ej .θej kej dt D I r r r r r r r r r r r r 1 d ˙ + θsj fsj .θ˙sj − Nj .wj + Jsj . 1 0 1 1 0 0 0 0 0 0 0 0 0 0 2 Actuator 1 Nj dt 1 0 1 1 0 0 0 0 0 0 0 0 0 0 2 Lj d d ˙ 1 0 0 0 1 1 0 0 0 0 0 0 0 0 2 + . θej Jej . Actuator 2 kej dt dt 1 0 0 0 1 1 0 0 0 0 0 0 0 0 2 1 d 1 0 0 0 0 0 1 1 0 0 0 0 0 0 2 −wj + fej .θ˙ej + fsj .θ˙ sj − Nj .w j +J sj . θ˙sj =0 Actuator 3 Nj dt 1 0 0 0 0 0 1 1 0 0 0 0 0 0 2 b
b
11
21
12
22
13
23
14
24
15
15
16
16
2 e4 Actuator 4 2 s4
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2 e5 Actuator 5 2 s5
1
0
0
0
0
0
0
0
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0
1
1
0
0
1
0
0
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2 e6 Actuator 6 2 s
1
0
0
0
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0
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1
1
0
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0
0
0
0
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0
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1
1
e1 s1
e2 s2
e3 s3
The second ARRj can be deduced from equation 12, where the following system is obtained: f = N j .f 11 = N j .θ˙sj , 10 f8 = f 15 = θ˙ej , (16) 1 d (e9 ) 1 d f9 = . = .N j . (e12 + e14 + e16 − e13 ) Kj dt Kj dt where:
e13 = N j .wj ; e12 = f sj .f 12 = f sj .θ˙sj ; d (f14 ) d ˙ e = J . = J . θsj ; 14 s s j j dt dt e16 = 0; e27 = ϕj
(17)
· ARR2j Generation
The second ARRj is then deduced by replacing the unknown variables of equations 16 and 12 by their expressions in 17:
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6
Fig. 12.
Fault signature matrix of the manipulator robot system.
In this table 12, the rows represent the components signatures and the columns are respectively the fault detectability Db , the fault isolability Ib , and the twelve residuals r1j and r2j . A ‘1’ value on respectively Db and Ib columns means that faults on the corresponding components are detectable and isolable. The presence of ‘1’ value on the residual columns shows the influence of the corresponding component on the residual dynamics. In this application, the F SM helps to detect and to distinguish the presence of eventual obstacles, which lock the normal operating of the actuator.
5. EXPERIMENTAL RESULTS In this section, experimental results have been done on the IRB140 robot while following the planned trajectory of Fig. 3.Numerical values of the actuators parameters used for the online simulation are not given because the constraints of pages number. Fig. 13 shows the identified controls inputs of actuators models during normal operating. In this case the time domain variation of the angular joint positions and the whole residuals are represented successively by Fig. 14 and Fig. 15. It is noticed that the residuals still equal to 0 while there is no collision detection with the robot. By repeating the experiment after introducing a static obstacles on the first and the second D.O.F , the residuals r21 and r22 are sensitive to external collision (see Fig. 16) because it locks the normal motion of the appropriate actuated axis. Then the articular positions are given by Fig. 17. The virtual simulator Fig. 18 shows the variation state of the residuals two residuals in collision situation.
Fig. 13.
Control Input of Actuators 1 to 6
Fig. 16.
Residuals in collision situation
Fig. 17.
Articular positions in collision situation
Fig. 18.
Online collision detection on the real robot from a virtual simulator.
REFERENCES
Fig. 14.
Articular variables in normal operating
Fig. 15.
Residuals in normal operating
6. CONCLUSION In this work, a virtual simulator of an industrial robot is developed in order to make online supervision for possible collisions detection. The real and virtual systems are operating in parallel, while a model based F DI algorithm in running in real-time. This practical approach can help the user to avoid accidental situations without been closer to the system and by using a soft solution. The validation of the method is done after system modelling validation and online experiments.
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