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Design of a Computer Aided Tele-Operation Plan in the Presence of Uncertainties
Copyright e IFAC Integrated Systems Engineering. Badc:n-Baden. Gennany. 1994
DESIGN OF A COMPUTER AIDED TELEOPERA TION PLAN IN THE PRESENCE OF UNCERTAINTIES S. MARIER. A. EL MHAMEDI* and Z. BINDER Laboratoir~ d'Automatiqu~ d~ Gr~nob/~.
ENS/EG. B.P. 46. 38402 St-Manin-d·Her~s. FRANCE Strasbourg. ENSAlS. 24 Bd d~ la Victoir~. 67084 Strasbourg.
·Laboratoir~ d~ R~ch~rch~ ~n Productiqu~ d~
FRANCE Group~
Cooperation
HommelMachin~
GR
AUlOmatiqu~
CNRS
AbstracL Most of the time. a particular Computer Aided Teleoperation (CAT) mission can be performed by several routings. The problem is then to choose the best one available. The choice is linked with routing quantification difficulties due to the presence of uncertainties. This paper aims at modeling and evaluating the various routings of a pre-established mission. To reach this goal. the Generalized Stochastic Petri Nets (GSPN) are used. Some numerical results. illustrating the measurable performances by the GSPN-model. are also presented. Key Words. Teleoperation. Activity planning. Modeling. Generalized Stochastic Petri nets. Performance evaluation.
I. INTRODUCTION
through a man-machine collaboration. The implication of a man induces the duration uncertainty since the man can execute the same activity in a variable time from one day to another. incident occurrence. An incident can occur at any moment during the unfolding of a mission. Its occurrence is then completely random, sequence uncertainty. Three types of activity performing mode can be used in CAT: manual, semi-automatic and automatic. The choice between these modes can meet a certain criterion linked with a particular situation. it remains however unpredictable from one man to another. A routing modeling and evaluation not taking these uncertainties into account will generate a large gap between the initial activity plan and the "real" unfolding of the mission. CAT research works rarely treat this kind of problem, but some approaches developed in industrial engineering can be applied easily. The approach proposed in this paper is inspired. more specifically, from those developed in the manufacturing shop planning field (El Mhamedi et al.. 1991).
Computer Aided Teleoperation (CAT) is in general "the remote execution of a manual work not feasible directly" (Vertut et al.. 1984). More specifically. a control operator moves a slave arm, situated in a hostile environment (slave universe), by means of a master arm, situated in a normal environment (master universe) . A supervIsion operator, helped by a servomechanism, a computer and videos, assists the control operator in his task. CAT is used above all in nuclear industry. in radioactive environment, in submarine environment and in space to make repairs and maintenance operations. A CAT mission is an activity sequence performed from a master universe that aims at transforming a slave universe from an initial state to a final state. according to a pre-established goal. It is worth noting that to perform a particular mission. several activity sequences are possible (each possible sequence will be called here a routing) . Consequently, the problem consists in choosing the best one. This selection problem is linked with routing quantification difficulties due to the presence of uncertainties. More specifically, the CAT plan has to take into account: duration uncertainty. In most cases. an activity is performed by an operator or
Some works. more specific to the CAT domain. consider the mode choice problem from an on-line viewpoint (Jolly et al.. 1991). The authors propose a supervisor integrated decision function based on fuzzy logic. Other works allow the routing
225
generation using a Coloured Petri Net (CPN) model (Ouali et aI. , 1992). This CPN-model is concerned by the CAT specificities, namely the mission activities taxonomy, the mode choices and the incident recovery procedures.
Most of the time. it will represent a slave arm movement or an operator mental activity . Note here that the same mission splitting is introduced by Castillo Castaneda (1991) by the words : mission. stages. simple tasks and elementary tasks.
This paper aims at modeling and evaluating the various routings of a pre-established CAT mission. To reach this goal, a modeling technique, allowing uncertainties to be taken into account, will be used : the Generalized Stochastic Petri Nets (GSPN). This modeling tool used in an uncenain context shows some advantages such as compatibility, flexibility, aggregation and synchronization. GSPN will not be presented here. Readers that want to know more about them can refer to Marsan er al. (1984) and Natkin (1985). The next section of this paper presents the design of a CAT plan. In section 3, the method for obtaining the performance evaluation is briefly described. Finally, section 4 shows some performance examples.
2.2. Model construction Respecting the mission splitting. the model is developed from the modeling levels represented in Fig. 2. In this figure , by the words mission. operation. task or action. the place-transition set will represent respectively the unfolding and the end of the considered event. In the most abstract level (level 1). a CAT mission is symbolized simply by a place and a transition. At the second level. the mission is viewed like an operations set beginning with the unfolding of the first operation and finishing with the end of the last one. At the third level. an operation is composed of a succession of tasks feasible under different alternatives. At the last level, a task is formed by a succession of actions feasible. this time, under different modes.
2. DESIGN OF THE CAT PLAN The construction of the GSPN plan is inspired from the CPN-model mentioned above and by the mission splitting described below (see Fig. 1).
Taskl Task2
Task 0
~()-1- . ~Q-1I
Fig. 1. The mission splitting LEVEL 4 2.1 . Mission splittin2 Act. I
A mission is split into several operations. The operation is characterized by the existence of several strategies and alternatives. and by the existence of incident recovery procedures (Gravez, 1991). An operation. carried out under any alternatives. is then split into tasks. Each task can include up to three performing modes: the automatic mode. the semi-automatic mode and the manual mode. The task. carried out under a panicular mode, is in turn split into actions. The action is the smallest mission splitting unit.
Act. 2
It- ..~ Act. 2
Act. s
n-..~
Act. 2
Fig. 2. The modeling levels
226
P34: To take out the drill + to leave the tool P35: To determine the drilling point + To acquire the initial drilling position P36: To drill P37 : Incident recovery: to free the drill + To come back on the drilling axis + To finish the drilling P38: To take out the drill + to leave the tool P40: To put down the tool task initialization ; mode choice
2.3. Modeling of the drilling operation by GSPN Depending on the chosen alternative. the DRILLING operation can regroup up to four tasks: To grasp the tool. To determine the drilling coordinates. To drill and To put down the tool. The to drill task model is detailed in Fig. 3. The same representation logic is shown in Fig. 4 with the drilling operation model (Fig. 3 is a part of Fig. 4). This last model includes two types of places. one arriving on a immediate transition (symbolized by a bar) and another one going to an exponentially distributed timed transition (symbolized by a rectangle). The first one represents the choice between several possible alternatives or modes (through random switches) and/or the beginning or the finishing of a task. The second regroups. for simplicity's sake. a sequence of feasible actions without interruption. Compared to Fig. 2. the operation model is situated between the third and the fourth modeling level. This compromise allows the incidents to be taken into account. The rate of each timed transition will represent a performing duration inverse of an action sequence. an incident occurrence frequency or a validation rate. The removable loop. linking the end of the operation to the start. allows the transient and the steady state to exist together in the same model. Finally. it is worth noting that the model exhibits all the sequences of possible actions able to perform the drilling operation. Faced with the large number of places and transitions. this paper will be limited to the evaluation of an operation, knowing that a mission is a succession of operations.
ii) Exponential transitions: e31 : end of P31 e36: end of P35 e32: drill blocking e37: drill blocking e33: end ofP33 e38: end ofP37 e34: end of P32 e39: end of P36 (without blocking) (without blocking) e35: end of P34 e311: end of P38 iii) Immediate transitions: i31: automatic mode choice i32: semi-automatic mode choice Fig. 3. The to drill task model
Semi-Auto. Mode
/'
i) Places: P30: To drill task initialization; mode choice P31 : To determine the drilling point + To do the pre-hole + To acquire the initial drilling position P32: To drill P33: Incident recovery: to free the drill + To come back on the drilling axis + To finish the drilling
I L ____ _ Fig. 4. The drilling operation model
227
the tool" task performing mean duration (exponentially distributed) is of 100 sec. Note that all computations were performed on Matlab.
3. PERFORMANCE EVALUATION To evaluate the model performances, we have used the method developed by Marsan er af. (1984). It consists, through different manipulations, in transforming the GSPN model of Fig. 4 into a Markov Chain. Once this MC is obtained, it can be transcribed into a probability matrix P. From this matrix p, results in transient and steady state are computed. In transient state. the matrix P has to be changed into a transition rate matrix Q, by:
Q =(P-I)I~t
Table 2 Minimum case PI=I P2=O Table 3 Maximum case SI=O·5 s2=O·5
(I)
By extracting the fundamental mattix (-F-l) from the Q, the mean absorption time by the ergodic state (operation end) can be obtained. In steady state, the power method is used to find the continuous time occurrence probabilities of the tangible states (Stewart, 1992):
4. 1. General results Fig. 5 proposes performances in transient state: the mean completion time to achieve the operation for the minimal, mean and maximal cases. The minimal case represents the mean completion time under an "optimistic" behaviour, i.e. that no breakdown and no "unvalidation" problems occur during the mission. The mean case shows the mean behaviour of the operation; usual breakdown and validation rates. Finally, the maximal case forms a "pessimistic" prediction of the unfolding of the operation; bad breakdown and validation rates. Those performances aim to help the operator "in-line", informing him of the temporal consequences of the offered options. For example in Fig. 5, the semi-automatic alternative choice .(bar chart left-hand side) proposed larger time variations than the manual alternative choice (right-hand side): the manual alternative is less risky.
(2)
For further details about the performance evaluation, the readers can refer to Viswanadham et al. (1988).
4. PERFORMANCE EXAMPLES In order to illustrate by numerical results some measurable performances, indicative data from the "Commissariat a l'Energie Atomique de France" (CEA, 1991) were used. Those data concerned the duration measurements of the tasks performed by two different control operators. The tables below (see tables 1-2-3) exhibit the numerical values of the parameters used in the drilling operation model of Fig. 4.
ALlFRNA11VES SEX:
s2=O·7 s3=O·2 s4=O·8 Pl=O·75 P2=O·25 gl=O·7 g2=O·3 (lI=O·01 (l2=O·1 (l3=O·03
04=0·1 (l5=O·125 %=0.017 A.--o.015 Jl=O.2 ~ 1=0.2 ~2=O·015 ~3=O·012 . ~4=O·013
SFMI-AlITO
~,---------------------------~
Table 1 Mean case A=O.5 B=O.5 ai=O·2 bi=O·25 ci=O·5 di=O·5 fi::O· 2 q=\),5 T2=O.5 SI =0.3
A.=O.03
S3=O·5 S4=O·5
300
P2=O·017 P3=O·033 P4=O·25 P5=O·067 P6=O·017 P7=O·067 01=0·014 02=0·047 K=O.OO6
200
100
Cl MINI
~I =0.25
•
MEAN
•
MAXI
Fig. 5. Mean completion time Parameters A, B, ai, bi, ci, di, fi and gi represent random switches, i. e. the occurrence probability of each option. The A. parameters and the associations Mi, P2s I, P6S3 symbolize breakdown rates and the association J.1P2, a validation rate. Finally, the other parameters represent distributed duration inverses. For example, by the 0,01 value, parameter (ll means that the "to grasp manually
Fig. 6 and 7 show some steady state results computed from the occurrence probabilities. The first one presents the operators occupation, i.e. the time proportion spent by the operators in each task making up the operation. It can be noted that the operators perform the to grasp/to put down and the to drill tasks for more than 85% of their time. The
228
relative importance of the to grasp/to put down tasks make us think that there is some problems while performing them. Fig. 7 represents the mode utilization or in other words, the time proportion spent to carry out a task under a specific mode . Assuming that the manual mode is theoretically the slowest one, it is not surprising to see that it uses 67% of the operator's time.
ALTERN A11VE5 SEC SEMI.AurO _ _ _ _ _ MANUAL -UMI..,.....;._.....;.;;;.;..;;.....
.;.;.:..:..:.:::.=:....--, r--
-
,.... 200_
_
L.-
I
1......
Auto $enu-auto Manual
Cl
1..1..
.....
Modes Auto Semi-auto Manual
Operator J
•
OperatorM
Fig. 8. Mean completion time In Table 4, some significant differences between the operators on the to grasp/to put down and to drill tasks can be seen. On the contrary, Table 5 presents a relative uniformity on the mode utilization. Table 4 Qperator occupation Fig. 6. Operator's occupation Tasks To gr.ffo put down To drill To del. the coord
Operator M 51.45% 34.01% 14,54%
Operator J 38.69% 47.85% 13,45%
Table 5 Mode utilization Modes Automatic Semi-Automatic Manual
Operator J 11 .53% 19.79% 68,57%
Operator M 12,57% 23.54% 63,89%
5. CONCLUSION The GSPN-model of a mission allows various aspects of uncertainties to be taken into account by integrating into the same model the duration uncertainty, the incident occurrence and the sequence uncertainty. Moreover, this model offers the possibility to reduce the mission complexity by the use of modeling levels.
Fig. 7. Mode utilization
4.2. Individual results Through Markov Chains, the GSPN-model measures the performances analytically in transient and steady state. In transient state. the minimum. mean and maximum mean completion times were computed. The goal of this time bracket was to show the consequences of the different structural choices (mode choice, alternative choice) offered to the operator during a mission performing. This online decision aid aspect can be very useful when perturbations occur. In the steady state, various performances can be computed. in addition to ones computed in this paper. These performances could help to detect some problems in the unfolding of a
Fig. 8 and tables 4-5 propose some results computed for two different operators: operator J and M. The parameters of the drilling operation model were also extracted from CEA (1991) and appear in the appendix. Fig. 8 shows a comparison between the two operators for the mean completion times. On the bar chart right-hand side (manual alternative side), an important operator influence on the times can be noted. Consequently, this aspect should not be neglected while designing the mission plan.
229
mission or to control some specific variables (e.g. the work load of the operators. the resources efficiency).
Stewart. W.J. (1992). An introduction to the numerical solution of Markov chains. Dept. of Computer Science. N. Carolina State University. Raleigh, N. Carolina. USA. Vertut. J. and P. Coiffet (1984). Les robots. Teleoperation. Hermes. Paris. Viswanadham. N. and Y. Narahari (1988). Stochastic Petri net models for performance evaluation of automated manufacturing systems. Inform. Decision Technol.. Vol. 14. pp. 12S-142.
To continue in this work. a validation campaign is in progress. It will allow a comparison between the GSPN-model results and the real performances of a mission. Moreover. it will be possible to check the hypothesis about the exponential probability function behaviour. Eventually. other Petri nets. allowing the use of every probability function. will have to be considered like modeling tools. The Extended Stochastic Petri Net (Dugan et aJ.. 1984) and the Extended Time Petri Net (Roux et al.. 1987; Juanole et al.. 1989) provide some interesting examples on this subject.
APPENDIX
:rabIc 6 Qpm,1W: 1 A=O.5 B=O.5 ai=O·2 bi=O·25 Ci=O.5 di=O·5 fi=O·2 q=O.5 f2=O.5 s}=O.3
6. REFERENCES Castillo Castaneda. E. (1991). Le planning des taches dans le domaine de la teleoperation. Rapport de DEA. Institut National Polytechnique de Grenoble. LAG. Grenob1e. CEA. (1991). Mesure de la duree des taches de pe~age. Note interne du CEA. Dugan. J.B .• K.S. Trivedi • R.M. Geist and V.F. Nicola (1984). Extended Stochastic Petri Nets: Applications and Analysis. Performance '84. pp. S07-S19. El Mhamedi. A .• S. Bouchardy and Z. Binder (1991). Conduite Hierarchisee d'un atelier de fabrication de moules. 3eme Congres international de Genie industriel. Tours. France. 20-22 mars Gravez. P. (1991). Description de la manip. de per~age effectuee au cours de la campagne d'essais Triton. Note interne du CEA. Jolly. D .• A.M. Desodt and F. Wawak (1991). Choix de modes de conduite en teleoperation. La Revue d'Automatique et de Productique Appliquee. Vol. 4. No. 4. pp. 43S-44S. Juanole. G .• and J.L. Roux (1989). On the pertinence of the extended time Petri net model for analyzing communication activities. IEEE. pp. 230-239. Marsan. M.A .• G. Balbo and G. Conte (1984). A class of Generalized Stochastic Petri nets for the performance evaluation of multiprocessor systems. ACM Trans. Comput. Sys. 2 (2). pp. 93-122. Natkin. S. (198S). Reseaux de Petri. Stochastiques: theorie et application. These de doctorat. Universite Pierre et Marie Curie. Ouali. M.S., A. El Mhamedi and Z. Binder (1992). Task scheduling approach in computer aided remote operation based on decision aids. Human Decision Making and Manual Control, Valenciennes. France. Roux, J.L.. and G. Juanole (1987). Functional and Performance Analysis using Extended Time Petri Nets. IEEE, pp. 14-23.
s2=O·7 s3=O·2 54=0.8 Pl=O·7S P2=O.2S gl=O·7 g2=O·3 a}=O.0l2 a2=O·1 a3=O·03
J..I.=O.2 PI =0.2 P2=O·01S P3=O·012 P4=O.013 Pl=O·2S
P2=O·0l7 P3=O·033 P4=O.2S P5=O·052 p6=O.013 p7=O.OS2 01=0·014 02=0·047 1C=O.OO5
liable ZQgcratw: M A=O.5 B=O.5 ai=O·2 bi=O·2S ci=O.5 di=O.5 fi=O·2 q=O.S f2=O.S s]=O.3
230
S2=O·7 S3=O·2 54=0·8 Pl=O·7S P2=O.2S gl=O·7 g2=O·3 al=O·OO8 a2=O·1 a~=O.03
J..I.=O.2 PI =0.2 P2=O·OlS P3=O·0l2 P4=O.013 p]=O.2S
P2=O·017 P3=O·033 P4=O.2S P5=O·067 P6=O·0l7 P7=O·067 01=0·013 02=0·047 1C=O.009
DESIGN OF A COMPUTER AIDED TELEOPERA TION PLAN IN THE PRESENCE OF UNCERTAINTIES S. MARIER. A. EL MHAMEDI* and Z. BINDER Laboratoir~ d'Automatiqu~ d~ Gr~nob/~.
ENS/EG. B.P. 46. 38402 St-Manin-d·Her~s. FRANCE Strasbourg. ENSAlS. 24 Bd d~ la Victoir~. 67084 Strasbourg.
·Laboratoir~ d~ R~ch~rch~ ~n Productiqu~ d~
FRANCE Group~
Cooperation
HommelMachin~
GR
AUlOmatiqu~
CNRS
AbstracL Most of the time. a particular Computer Aided Teleoperation (CAT) mission can be performed by several routings. The problem is then to choose the best one available. The choice is linked with routing quantification difficulties due to the presence of uncertainties. This paper aims at modeling and evaluating the various routings of a pre-established mission. To reach this goal. the Generalized Stochastic Petri Nets (GSPN) are used. Some numerical results. illustrating the measurable performances by the GSPN-model. are also presented. Key Words. Teleoperation. Activity planning. Modeling. Generalized Stochastic Petri nets. Performance evaluation.
I. INTRODUCTION
through a man-machine collaboration. The implication of a man induces the duration uncertainty since the man can execute the same activity in a variable time from one day to another. incident occurrence. An incident can occur at any moment during the unfolding of a mission. Its occurrence is then completely random, sequence uncertainty. Three types of activity performing mode can be used in CAT: manual, semi-automatic and automatic. The choice between these modes can meet a certain criterion linked with a particular situation. it remains however unpredictable from one man to another. A routing modeling and evaluation not taking these uncertainties into account will generate a large gap between the initial activity plan and the "real" unfolding of the mission. CAT research works rarely treat this kind of problem, but some approaches developed in industrial engineering can be applied easily. The approach proposed in this paper is inspired. more specifically, from those developed in the manufacturing shop planning field (El Mhamedi et al.. 1991).
Computer Aided Teleoperation (CAT) is in general "the remote execution of a manual work not feasible directly" (Vertut et al.. 1984). More specifically. a control operator moves a slave arm, situated in a hostile environment (slave universe), by means of a master arm, situated in a normal environment (master universe) . A supervIsion operator, helped by a servomechanism, a computer and videos, assists the control operator in his task. CAT is used above all in nuclear industry. in radioactive environment, in submarine environment and in space to make repairs and maintenance operations. A CAT mission is an activity sequence performed from a master universe that aims at transforming a slave universe from an initial state to a final state. according to a pre-established goal. It is worth noting that to perform a particular mission. several activity sequences are possible (each possible sequence will be called here a routing) . Consequently, the problem consists in choosing the best one. This selection problem is linked with routing quantification difficulties due to the presence of uncertainties. More specifically, the CAT plan has to take into account: duration uncertainty. In most cases. an activity is performed by an operator or
Some works. more specific to the CAT domain. consider the mode choice problem from an on-line viewpoint (Jolly et al.. 1991). The authors propose a supervisor integrated decision function based on fuzzy logic. Other works allow the routing
225
generation using a Coloured Petri Net (CPN) model (Ouali et aI. , 1992). This CPN-model is concerned by the CAT specificities, namely the mission activities taxonomy, the mode choices and the incident recovery procedures.
Most of the time. it will represent a slave arm movement or an operator mental activity . Note here that the same mission splitting is introduced by Castillo Castaneda (1991) by the words : mission. stages. simple tasks and elementary tasks.
This paper aims at modeling and evaluating the various routings of a pre-established CAT mission. To reach this goal, a modeling technique, allowing uncertainties to be taken into account, will be used : the Generalized Stochastic Petri Nets (GSPN). This modeling tool used in an uncenain context shows some advantages such as compatibility, flexibility, aggregation and synchronization. GSPN will not be presented here. Readers that want to know more about them can refer to Marsan er al. (1984) and Natkin (1985). The next section of this paper presents the design of a CAT plan. In section 3, the method for obtaining the performance evaluation is briefly described. Finally, section 4 shows some performance examples.
2.2. Model construction Respecting the mission splitting. the model is developed from the modeling levels represented in Fig. 2. In this figure , by the words mission. operation. task or action. the place-transition set will represent respectively the unfolding and the end of the considered event. In the most abstract level (level 1). a CAT mission is symbolized simply by a place and a transition. At the second level. the mission is viewed like an operations set beginning with the unfolding of the first operation and finishing with the end of the last one. At the third level. an operation is composed of a succession of tasks feasible under different alternatives. At the last level, a task is formed by a succession of actions feasible. this time, under different modes.
2. DESIGN OF THE CAT PLAN The construction of the GSPN plan is inspired from the CPN-model mentioned above and by the mission splitting described below (see Fig. 1).
Taskl Task2
Task 0
~()-1- . ~Q-1I
Fig. 1. The mission splitting LEVEL 4 2.1 . Mission splittin2 Act. I
A mission is split into several operations. The operation is characterized by the existence of several strategies and alternatives. and by the existence of incident recovery procedures (Gravez, 1991). An operation. carried out under any alternatives. is then split into tasks. Each task can include up to three performing modes: the automatic mode. the semi-automatic mode and the manual mode. The task. carried out under a panicular mode, is in turn split into actions. The action is the smallest mission splitting unit.
Act. 2
It- ..~ Act. 2
Act. s
n-..~
Act. 2
Fig. 2. The modeling levels
226
P34: To take out the drill + to leave the tool P35: To determine the drilling point + To acquire the initial drilling position P36: To drill P37 : Incident recovery: to free the drill + To come back on the drilling axis + To finish the drilling P38: To take out the drill + to leave the tool P40: To put down the tool task initialization ; mode choice
2.3. Modeling of the drilling operation by GSPN Depending on the chosen alternative. the DRILLING operation can regroup up to four tasks: To grasp the tool. To determine the drilling coordinates. To drill and To put down the tool. The to drill task model is detailed in Fig. 3. The same representation logic is shown in Fig. 4 with the drilling operation model (Fig. 3 is a part of Fig. 4). This last model includes two types of places. one arriving on a immediate transition (symbolized by a bar) and another one going to an exponentially distributed timed transition (symbolized by a rectangle). The first one represents the choice between several possible alternatives or modes (through random switches) and/or the beginning or the finishing of a task. The second regroups. for simplicity's sake. a sequence of feasible actions without interruption. Compared to Fig. 2. the operation model is situated between the third and the fourth modeling level. This compromise allows the incidents to be taken into account. The rate of each timed transition will represent a performing duration inverse of an action sequence. an incident occurrence frequency or a validation rate. The removable loop. linking the end of the operation to the start. allows the transient and the steady state to exist together in the same model. Finally. it is worth noting that the model exhibits all the sequences of possible actions able to perform the drilling operation. Faced with the large number of places and transitions. this paper will be limited to the evaluation of an operation, knowing that a mission is a succession of operations.
ii) Exponential transitions: e31 : end of P31 e36: end of P35 e32: drill blocking e37: drill blocking e33: end ofP33 e38: end ofP37 e34: end of P32 e39: end of P36 (without blocking) (without blocking) e35: end of P34 e311: end of P38 iii) Immediate transitions: i31: automatic mode choice i32: semi-automatic mode choice Fig. 3. The to drill task model
Semi-Auto. Mode
/'
i) Places: P30: To drill task initialization; mode choice P31 : To determine the drilling point + To do the pre-hole + To acquire the initial drilling position P32: To drill P33: Incident recovery: to free the drill + To come back on the drilling axis + To finish the drilling
I L ____ _ Fig. 4. The drilling operation model
227
the tool" task performing mean duration (exponentially distributed) is of 100 sec. Note that all computations were performed on Matlab.
3. PERFORMANCE EVALUATION To evaluate the model performances, we have used the method developed by Marsan er af. (1984). It consists, through different manipulations, in transforming the GSPN model of Fig. 4 into a Markov Chain. Once this MC is obtained, it can be transcribed into a probability matrix P. From this matrix p, results in transient and steady state are computed. In transient state. the matrix P has to be changed into a transition rate matrix Q, by:
Q =(P-I)I~t
Table 2 Minimum case PI=I P2=O Table 3 Maximum case SI=O·5 s2=O·5
(I)
By extracting the fundamental mattix (-F-l) from the Q, the mean absorption time by the ergodic state (operation end) can be obtained. In steady state, the power method is used to find the continuous time occurrence probabilities of the tangible states (Stewart, 1992):
4. 1. General results Fig. 5 proposes performances in transient state: the mean completion time to achieve the operation for the minimal, mean and maximal cases. The minimal case represents the mean completion time under an "optimistic" behaviour, i.e. that no breakdown and no "unvalidation" problems occur during the mission. The mean case shows the mean behaviour of the operation; usual breakdown and validation rates. Finally, the maximal case forms a "pessimistic" prediction of the unfolding of the operation; bad breakdown and validation rates. Those performances aim to help the operator "in-line", informing him of the temporal consequences of the offered options. For example in Fig. 5, the semi-automatic alternative choice .(bar chart left-hand side) proposed larger time variations than the manual alternative choice (right-hand side): the manual alternative is less risky.
(2)
For further details about the performance evaluation, the readers can refer to Viswanadham et al. (1988).
4. PERFORMANCE EXAMPLES In order to illustrate by numerical results some measurable performances, indicative data from the "Commissariat a l'Energie Atomique de France" (CEA, 1991) were used. Those data concerned the duration measurements of the tasks performed by two different control operators. The tables below (see tables 1-2-3) exhibit the numerical values of the parameters used in the drilling operation model of Fig. 4.
ALlFRNA11VES SEX:
s2=O·7 s3=O·2 s4=O·8 Pl=O·75 P2=O·25 gl=O·7 g2=O·3 (lI=O·01 (l2=O·1 (l3=O·03
04=0·1 (l5=O·125 %=0.017 A.--o.015 Jl=O.2 ~ 1=0.2 ~2=O·015 ~3=O·012 . ~4=O·013
SFMI-AlITO
~,---------------------------~
Table 1 Mean case A=O.5 B=O.5 ai=O·2 bi=O·25 ci=O·5 di=O·5 fi::O· 2 q=\),5 T2=O.5 SI =0.3
A.=O.03
S3=O·5 S4=O·5
300
P2=O·017 P3=O·033 P4=O·25 P5=O·067 P6=O·017 P7=O·067 01=0·014 02=0·047 K=O.OO6
200
100
Cl MINI
~I =0.25
•
MEAN
•
MAXI
Fig. 5. Mean completion time Parameters A, B, ai, bi, ci, di, fi and gi represent random switches, i. e. the occurrence probability of each option. The A. parameters and the associations Mi, P2s I, P6S3 symbolize breakdown rates and the association J.1P2, a validation rate. Finally, the other parameters represent distributed duration inverses. For example, by the 0,01 value, parameter (ll means that the "to grasp manually
Fig. 6 and 7 show some steady state results computed from the occurrence probabilities. The first one presents the operators occupation, i.e. the time proportion spent by the operators in each task making up the operation. It can be noted that the operators perform the to grasp/to put down and the to drill tasks for more than 85% of their time. The
228
relative importance of the to grasp/to put down tasks make us think that there is some problems while performing them. Fig. 7 represents the mode utilization or in other words, the time proportion spent to carry out a task under a specific mode . Assuming that the manual mode is theoretically the slowest one, it is not surprising to see that it uses 67% of the operator's time.
ALTERN A11VE5 SEC SEMI.AurO _ _ _ _ _ MANUAL -UMI..,.....;._.....;.;;;.;..;;.....
.;.;.:..:..:.:::.=:....--, r--
-
,.... 200_
_
L.-
I
1......
Auto $enu-auto Manual
Cl
1..1..
.....
Modes Auto Semi-auto Manual
Operator J
•
OperatorM
Fig. 8. Mean completion time In Table 4, some significant differences between the operators on the to grasp/to put down and to drill tasks can be seen. On the contrary, Table 5 presents a relative uniformity on the mode utilization. Table 4 Qperator occupation Fig. 6. Operator's occupation Tasks To gr.ffo put down To drill To del. the coord
Operator M 51.45% 34.01% 14,54%
Operator J 38.69% 47.85% 13,45%
Table 5 Mode utilization Modes Automatic Semi-Automatic Manual
Operator J 11 .53% 19.79% 68,57%
Operator M 12,57% 23.54% 63,89%
5. CONCLUSION The GSPN-model of a mission allows various aspects of uncertainties to be taken into account by integrating into the same model the duration uncertainty, the incident occurrence and the sequence uncertainty. Moreover, this model offers the possibility to reduce the mission complexity by the use of modeling levels.
Fig. 7. Mode utilization
4.2. Individual results Through Markov Chains, the GSPN-model measures the performances analytically in transient and steady state. In transient state. the minimum. mean and maximum mean completion times were computed. The goal of this time bracket was to show the consequences of the different structural choices (mode choice, alternative choice) offered to the operator during a mission performing. This online decision aid aspect can be very useful when perturbations occur. In the steady state, various performances can be computed. in addition to ones computed in this paper. These performances could help to detect some problems in the unfolding of a
Fig. 8 and tables 4-5 propose some results computed for two different operators: operator J and M. The parameters of the drilling operation model were also extracted from CEA (1991) and appear in the appendix. Fig. 8 shows a comparison between the two operators for the mean completion times. On the bar chart right-hand side (manual alternative side), an important operator influence on the times can be noted. Consequently, this aspect should not be neglected while designing the mission plan.
229
mission or to control some specific variables (e.g. the work load of the operators. the resources efficiency).
Stewart. W.J. (1992). An introduction to the numerical solution of Markov chains. Dept. of Computer Science. N. Carolina State University. Raleigh, N. Carolina. USA. Vertut. J. and P. Coiffet (1984). Les robots. Teleoperation. Hermes. Paris. Viswanadham. N. and Y. Narahari (1988). Stochastic Petri net models for performance evaluation of automated manufacturing systems. Inform. Decision Technol.. Vol. 14. pp. 12S-142.
To continue in this work. a validation campaign is in progress. It will allow a comparison between the GSPN-model results and the real performances of a mission. Moreover. it will be possible to check the hypothesis about the exponential probability function behaviour. Eventually. other Petri nets. allowing the use of every probability function. will have to be considered like modeling tools. The Extended Stochastic Petri Net (Dugan et aJ.. 1984) and the Extended Time Petri Net (Roux et al.. 1987; Juanole et al.. 1989) provide some interesting examples on this subject.
APPENDIX
:rabIc 6 Qpm,1W: 1 A=O.5 B=O.5 ai=O·2 bi=O·25 Ci=O.5 di=O·5 fi=O·2 q=O.5 f2=O.5 s}=O.3
6. REFERENCES Castillo Castaneda. E. (1991). Le planning des taches dans le domaine de la teleoperation. Rapport de DEA. Institut National Polytechnique de Grenoble. LAG. Grenob1e. CEA. (1991). Mesure de la duree des taches de pe~age. Note interne du CEA. Dugan. J.B .• K.S. Trivedi • R.M. Geist and V.F. Nicola (1984). Extended Stochastic Petri Nets: Applications and Analysis. Performance '84. pp. S07-S19. El Mhamedi. A .• S. Bouchardy and Z. Binder (1991). Conduite Hierarchisee d'un atelier de fabrication de moules. 3eme Congres international de Genie industriel. Tours. France. 20-22 mars Gravez. P. (1991). Description de la manip. de per~age effectuee au cours de la campagne d'essais Triton. Note interne du CEA. Jolly. D .• A.M. Desodt and F. Wawak (1991). Choix de modes de conduite en teleoperation. La Revue d'Automatique et de Productique Appliquee. Vol. 4. No. 4. pp. 43S-44S. Juanole. G .• and J.L. Roux (1989). On the pertinence of the extended time Petri net model for analyzing communication activities. IEEE. pp. 230-239. Marsan. M.A .• G. Balbo and G. Conte (1984). A class of Generalized Stochastic Petri nets for the performance evaluation of multiprocessor systems. ACM Trans. Comput. Sys. 2 (2). pp. 93-122. Natkin. S. (198S). Reseaux de Petri. Stochastiques: theorie et application. These de doctorat. Universite Pierre et Marie Curie. Ouali. M.S., A. El Mhamedi and Z. Binder (1992). Task scheduling approach in computer aided remote operation based on decision aids. Human Decision Making and Manual Control, Valenciennes. France. Roux, J.L.. and G. Juanole (1987). Functional and Performance Analysis using Extended Time Petri Nets. IEEE, pp. 14-23.
s2=O·7 s3=O·2 54=0.8 Pl=O·7S P2=O.2S gl=O·7 g2=O·3 a}=O.0l2 a2=O·1 a3=O·03
J..I.=O.2 PI =0.2 P2=O·01S P3=O·012 P4=O.013 Pl=O·2S
P2=O·0l7 P3=O·033 P4=O.2S P5=O·052 p6=O.013 p7=O.OS2 01=0·014 02=0·047 1C=O.OO5
liable ZQgcratw: M A=O.5 B=O.5 ai=O·2 bi=O·2S ci=O.5 di=O.5 fi=O·2 q=O.S f2=O.S s]=O.3
230
S2=O·7 S3=O·2 54=0·8 Pl=O·7S P2=O.2S gl=O·7 g2=O·3 al=O·OO8 a2=O·1 a~=O.03
J..I.=O.2 PI =0.2 P2=O·OlS P3=O·0l2 P4=O.013 p]=O.2S
P2=O·017 P3=O·033 P4=O.2S P5=O·067 P6=O·0l7 P7=O·067 01=0·013 02=0·047 1C=O.009