A METHODOLOGY TO IMPLEMENT SUBSUMPTION ARCHITECTURE BASEDON DISCRETE EVENT SYSTEMS FORMALISM

Phillipe Cardoso Santos∗, Elyson Adan Nunes Carvalho∗, Lucas Molina∗, EduardoOliveira Freire∗

∗Federal University of SergipeSao Cristovao, Sergipe, Brazil

Emails: phillipe@gprufs.org, ecarvalho@ufs.br, lmolina@ufs.br, efreire@ufs.br

Abstract— This paper presents a methodology to implement subsumption architecture based on discrete eventsystems (DES) formalism. For this, two automata models are presented so that all behaviors can be modeledeasily, even for complex tasks. It also allows the inclusion of new behaviors on the system without changingthe ones previously modeled. This method is tested in real experiments for three behavior layers with a pioneer3-DX mobile robot and results show it as a feasible and efficient approach.

Keywords— Mobile robot, subsumption architecture, discrete event systems, automata

1 INTRODUCTION

In robotics, decision-making and execution is animportant aspect used by the system to achieve itsobjective. In mobile robotics, the specific aspectdirectly linked to robust mobility is navigationcompetence (Siegwart and Nourbakhsh, 2004),which can be described as the process to deter-mine an adequate and secure path from the startpoint to the goal point, considering the pieces ofinformation available to the robot (Ranganathanand Koenig, 2003).

In this context, navigation architectures areresearched in order to solve the problem ofdecision-making by the robot. A robot architec-ture defines how is organized the task of gener-ating action through perception (Russell et al.,2003).

In navigation area is common to divide a com-plex task (global task) in some simple tasks (sub-tasks), which are performed through independentnavigation systems called behaviors (Arkin, 1998).Then, the problem stands in how to coordinatethese behaviors.

One of the most important and refereedtheory in this area is the subsumption archi-tecture, also known as behavior-based control,developed by Brooks in 1986 (Brooks, 1986).This theory started reactive navigation architec-ture when Brooks tried to solve deliberative ap-proaches problems for dynamic and unknown en-vironments.

In his work, Brooks created a set of behaviorsorganized in layers to accomplish tasks. Thesebehaviors are triggered by stimuli from sensor re-sponses. Each behavior accepts suppression andinhibition signals, where a suppression signal over-rides normal input signal and the inhibiting sig-nal inhibits completely the output. These signalsallow behaviors overlap, so that the system canproduce a coherent behavior.

In addition, many behaviors can be triggered

simultaneously, being necessary a mechanism ofchoice that selects the corresponding action. Forthis, behavioral modules are arranged in layers ina hierarchy called subsumption, in which the lowerlayers are inhibited by the higher ones. Subsump-tion architecture idea is showed in Figure 1.

Figure 1: Layered behavior with higher levels sub-suming the roles of lower level layers.

Almost 30 years has passed and Brooks’ workis still cited by many authors, what shows the im-portance of this navigation architecture to mobilerobotics. However, this is also a reflex of someproblems found in this approach, such as the be-haviors design for complex tasks becomes compli-cated; the appearance of situations where an im-passe occurs and two or more process are unableto continue their execution; and the way how be-haviors are encapsulated in finite state machines,which makes some intern states unaccessible tocontrol layers. Furthermore, a formal descriptionto implement these finite state machines is neces-sary in order to demonstrate its correctness.

Examples of such formalisms can be seen in(Amir and Maynard-Zhang, 2004), where a logicalframework is used to implement subsumption ar-chitecture and (Baader et al., 1998) which uses anautomata theoretic approach to reduce the prob-lem into a language problem.

In this paper is proposed a methodology fordesigning subsumption architecture based on Dis-crete Event Systems (DES) formalism. This ap-proach allowed modeling different behaviors eas-

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ily, even for complex tasks, and it also allowed theinclusion of new behaviors on the system withoutchanging the ones previously modeled. Addition-ally, an automaton model was created, so that allnew behavior can be modeled with the same pat-tern.

In order to demonstrate the methodology fea-sibility, real experiments were performed for threebehavior layers with a pioneer 3-DX mobile robot.

This paper is structured as follows. In sectionII is present a brief review about subsumption ar-chitecture. In section III the proposed methodol-ogy is presented. Results are presented in sectionIV and conclusions in section V.

2 Background

In 1986, Ronald Brooks designed a control ar-chitecture based on behaviors which tackles thecontrol problem by thinking of it as a numberof horizontally arranged layers. In the light ofthis decomposing method, a control system canbe divided into a group of sub-systems, whichare able to implement one behavior independently(Yongjie et al., 2006). This control method,named subsumption architecture, is very used inrobotics for many different applications, such asintelligent cars, multiple robots (Nagata et al.,2013), aerial robotics and even underwater vehi-cles (Godin et al., 2010).

The advantages of subsumption architecturestands on the way it decomposes the system into aseries of units vertically; it also eliminates the bot-tleneck, which occurs when sensors data must befused with data from other sensors. Instead, con-trol behaviors receive sensory data that is relevantonly to their particular decision-making needs(Yongjie et al., 2006). Furthermore, all of themodules in subsumption can function independentof any other module in the system, introducingan increase in processing speed and improving ro-bustness (Turner et al., 2013).

However, this hierarchically layered struc-ture has some limitation which are described in(Yongjie et al., 2006) on the following items:

• In order to make a most proper decision, itneeds to weight many factors in the selectionof control commands. It is sometimes unaptfor behavior of high level to inhibit that oflower level, which will miss all information ofthe inhibited layers;

• Another problem is encapsulating behaviorswithin a set of finite state machines, whichmake the internal state of these behaviors in-accessible to control layers. The designer ofeach layer cannot think out what other lay-ers will do and he cannot forecast the rela-tionship between his layer and other layerseither. As a result, once a new behavior layer

is added, other layer need to adjust accord-ingly;

• Although subsumption architecture raises theresponse speed of the system, its behavior de-sign is comparatively simple, and short fornecessary competence of reasoning and co-ordination. On average, it can get satisfy-ing results for some simple tasks, but for amore complicated one, the limitation of lack-ing planning ability emerged clearly.

Many different methodologies were used toimplement subsumption architecture in order tomake it more robust. Connell (Connell, 1992)combined subsumption with a servo-control layerand a symbolic layer in a way that allows theadvantages of each technique. Yongjie (Yongjieet al., 2006) proposed a hybrid architecture basedon subsumption and a behavior based planningprocess. Antonelli (Antonelli et al., 2008) pre-sented a technique called Null-Space Based Be-havioral (NSB) to deal with relative priority ofeach task. Turner (Turner et al., 2013) imple-mented subsumption architecture by using ModelDriving Development (MDD) and modeled behav-iors through finite state machines.

In order to keep improving the method ro-bustness and also facilitate its design, this paperproposes a methodology based on Discrete EventSystems (DES), modeling behaviors as automata.The idea is presented in the following section.

3 The Proposed Methodology

The proposed methodology consists in modelingeach layer as an automaton which contains theactivation of the controller for that subsystem anda switching rule to enable or not the activation oflower layers behaviors.

The switching rule used depends on whetherthe behavior goal is being achieved and how longit can be disturbed. In other words, if the be-havior goal of a high priority layer is not beingperformed correctly, it is not interesting for thesystem enabling the activation of a different con-troller from a lower layer, even if a necessity for itsactivation arises. This controller would probablydisturb more the goal achievement, once it mayhave a different objective.

Nevertheless, if the behavior goal of a highpriority layer is being performed correctly and anecessity to activate a behavior from a lower layerarises, its activation can be allowed since it doesnot disturb significantly higher priority objectives.Hence, disturbance is allowed only during a shorttime τ to not compromise the system. Right afterτ , the system checks if the higher behavior goal isstill being performed correctly in order to continueallowing lower behaviors to be used or not.

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Hence, a temporal checking is done based ona time τ in order to assure the hierarchy accom-plishment. This time is defined by the designerand it must be done carefully, because this pa-rameter represents how flexible is the system inrelation to disturbance from lower priority behav-iors.

This approach is an hierarchical cascade sys-tem where higher priority goals are desirable evenif lower ones do not be achieved. And it can bemore robust if the highest priority controller isglobally asymptotically stable, because the pro-posed methodology makes the system always re-turn to it after a short time τ , trying to lead themain objective to be accomplished.

Once the switching rule was defined, behav-iors were modeled based on Discrete Event Sys-tems formalism as automata. This approachavoided the requirement of modeling complex be-haviors, thereby providing a foundation to makeit by modeling small parts of the overall de-sired behavior and composing them through paral-lel automata composition (Cassandras and Lafor-tune, 2009).

Additionally, two automata models are pro-posed in order to design behaviors simply and eas-ily. The first model is for the highest priority be-havior and the other for all the lower behaviors,even new ones which may be still added to thesystem.

These automata models and a result of paral-lel operation are presented in next section.

3.1 Behavior automata models

The system modeling for this approach starts inthe highest layer, where the most desirable behav-ior must be. This layer is designed based on theevents defined at table 1 and the automaton canbe seen at Figure 2.

Table 1: Events description of the highest prioritylayer automaton

Events Descriptionn1 Necessity to activate controller 1nn1 Non necessity to activate controller 1Ac1 Activates controller 1r1 Switching rule being satisfiedEL2 Enable layer 2t Time τ achieved

In this automaton the system starts checkingthe necessity to activating controller 1. If nec-essary (event n1), controller 1 is activated(eventAc1) and then it is checked if the switching ruleis being satisfied . If the behavior goal for thislayer is being performed correctly (event r1), thesystem enables the second layer (event EL2) dur-

Figure 2: Highest priority layer automaton

ing the time τ . Right after τ (event t), the secondlayer must be disabled and the system return theinitial state H1. When there is no necessity toactivate controller 1 (event nn1),the marked stateH0 is selected, meaning the system main objectivewas achieved.

An important point to highlight is that en-abling the second layer does not mean the con-troller 2 will be activated. Its activation is set bythe next automaton presented in Figure 3, whichis designed based on the events of the table 2

Table 2: Events description of the second layerautomaton

Events DescriptionEL2 Enabling controller 2r2 Switching rule 2 satisfiedn2 Necessity to activate controller 2nn2 Non necessity to activate controller 2Ac2 Activate controller 2EL3 Enable layer 3t Time τ achievedt2 Time τ2 achieved

Figure 3: Second layer automaton

The second automaton is started enablinglayer 2 and then checks if its controller activa-tion is required. If there exists this requirement(event n2), controller 2 is activated (event Ac2),otherwise (event nn2), the system enables layer 3(event EL3), which is also enabled when controller2 is activated, but the switching rule for the sec-ond behavior is being satisfied. As in the highestlevel automaton, the third layer is enabled only

XXI Congresso Brasileiro de Automática - CBA2016 UFES, Vitória - ES, 3 a 7 de outubro

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during a certain time τ2 (event t2) or until thetime τ of the first behavior be achieved.

This approach considers that only one con-troller can be active, so activation of a controllermeans switch for it, deactivating all the others.

The design of all other layers will follow ex-actly the same model used for the second one, justincreasing some events to create a submission inrelation to all higher priority behaviors. The au-tomaton model to design any layer i is presentedin Figure 4.

Figure 4: Automaton model for any behavior iexcept the highest priority one

Once all layers are designed, the overall be-havior of the system is generated through paral-lel composition operation. An example with fourlayers is presented in Figure 5 to show how hardwould be design the whole model without doingit by parts. In this automaton is even difficult toidentify the four behavior layers, what shows theimportance of using the DES formalism.

The automata analysis in terms of accessi-bility and co-accessibility was done on softwareSupremica(Akesson et al., 2006) with a composi-tion up to ten behavior layers and no deadlocksor livelocks were found. A deadlock occur whenthe automaton reaches a state where no furtherevent can be executed and a livelock occurs whenthere is a set of states reachable from one an-other, but with no transition going out of the set(Cassandras and Lafortune, 2009). Hence, as atemporal switching rule is used, the system alwaysreturn to the main controller and possibly achieveits objective (marked state B3 on automaton Bindicates the main objective achievement).

3.2 Developed behaviors to methodology valida-tion

In order to test the proposed methodology, threebehaviors were developed to the robot: move togoal point, avoid contact with obstacles and cap-ture some artificial marks on the environment, or-ganized in this priority order.

For both move to goal point and capture ar-tificial marks behaviors, the goal position con-troller proposed by (Secchi, 1998) is used, a glob-ally asymptotically stable controller which makes

Figure 5: Automaton B: Overall behavior automa-ton with four behavior layers.

the robot goes from its position to a desired onebased on linear (V) and angular (W) velocities.

V = kvtanh(ρ)cos(α) (1)

W = kwα+ kvtanh(ρ)

ρtanh(ρ)cos(α) (2)

where kv and kw are positive constants, ρ is thedistance between the robot and the goal point andα is the robot orientation error in relation to thegoal position.

For the avoid contact with obstacles behavior,the controller proposed by (Freire et al., 2004) isused, which consists in keep linear velocity con-stant and control angular velocity based on a vir-tual point created opposite to the nearest obstaclefound.

V = k1 (3)

W = kw2α′ + kv2

tanh(ρ′)

ρ′tanh(ρ′)cos(α′) (4)

where k1, kw2 and kv2 are a positive constants,α′ is the robot orientation error in relation to thevirtual point, ρ′ is a fixed distance between therobot and the virtual point.

Based on these behaviors and their respectivecontrollers, experiments were performed in ordervalidate the methodology. Implementation detailsand results are presented in section 4.

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4 Results

Experiments were performed with a pioneer 3-DXrobot in different environments and the main ob-jective was to move the robot from an initial pointto a goal point. However, obstacles were placed onthe environment and the robot should avoid themsince this process does not make the robot deviatetoo much from the main objective. Furthermore,some artificial marks were spread out on the envi-ronment before the experiments starts and it wasconsidered the robot could detect marks in a dis-tance less than 200cm and should get them if itdoes not make the robot collide with obstacles orgo too far from the goal point.

Position and orientation of the robot are mea-sured based on pioneer 3-DX ’s odometry and ob-stacles are detected based on its ultrasonic sen-sors. Moreover, no previous knowledge about theenvironment was used in the system besides thegoal point and artificial marks coordinates, fea-turing a purely reactive navigation.

In relation to enable or not lower layers, theproposed methodology analysis the distance fromthe robot to the goal position and the angle be-tween them to the highest priority behavior. So,the switching for other controllers is allowed dur-ing a time τ = 4s, if this distance and this angledecreased in relation to the last time a switchedoccurred. The value of τ was arbitrarily chosen.

For the second layer, third layer is enabledduring a time τ2 = 1s if the robot is in distancehigher than 70 cm in relation to the obstacle.

Considering these attributions, three experi-ments are presented in order to illustrate the pro-posed methodology.

The first experiment was performed on a sim-ple environment with one box as obstacle, and fourmarks represented by red and green points. Theresult, based on pioneer odometry, is presentedin Figure 6a and it is possible to see that bothfirst and second objective were accomplished suc-cessfully, as long as the robot achieved the goalpoint with no collision. The third objective waspartially accomplished because one mark was toofar from the robot, so it was not detected, and theother was too close to the obstacle, so priority wasgiven to avoid collision.

For the second experiment, a similar environ-ment was used, but with lots of artificial marksplaced in order to persuade the robot to moveaway from the goal point. The result presentedin Figure 6b shows the robot moving away to themain objective to get the marks. However, whenit goes too far, the switching rule forces the mainbehavior to be active and the robot moves to thegoal point.

For the third experiment, obstacles were ar-ranged to test a situation where avoiding obstaclesbehavior leads the robot too far to the goal point.

In this case, the time τ = 4s gave enough flexi-bility to the system to overcome the obstacle andaccomplish both first and second objectives, as itis presented in Figure 6c. This time could be in-creased or decreased depending on the expectationof obstacle challenge and the desired flexibility interms of main objective deviation.

Obstacles including local minima were notused on the experiments as long as it would re-quire a more robust controller, which is not thisresearch focus. The controllers switching along allexperiments are presented in Figure 7.

(a) (b)

(c)

Figure 6: Robot navigation for the 3 experiments.a) Experiment 1. b) Experiment 2. c) Experiment3. Different colors were used to indicate whichbehavior was active: red - go to goal position,blue - avoid obstacles and green - capture marks.

Contr

olle

rsC

ontr

olle

rsC

ontr

olle

rs

Time in seconds

Experiment 1

Experiment 2

Experiment 3Time in seconds

Time in seconds

Figure 7: Controllers switching during the exper-iments. In this graphic controller 1 is responsiblefor the main objective, controller 2 to avoid ob-stacles and 3 to capture marks.

5 Conclusion

In this paper a methodology to implement sub-sumption architecture through discrete event sys-tems formalism is proposed and experimentally

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tested. This theory enabled modeling differentbehaviors and their interaction in a simple andformal way, since the overall behavior was mod-eled by parts. Furthermore, two automata modelswere developed, one to design the highest prioritylayer and the other to design all the others, eventhe ones which will still be added to the system.

Addition of new behaviors is an importantfeature of the proposed methodology, as long asthe overall behavior is generated through parallelautomata composition between the layers. Hence,adding a layer on the system just means to per-form this operation, with no need to change thebehaviors previously modeled.

Results also showed the switching rule used toenable or not activation of lower layers only duringan arbitrary time τ as a feasible solution on whichthe designer can choose how long the high prioritygoals can be disturbed by lower ones.

Furthermore, the use of a formalism to imple-ment the finite state machines allowed an analysisof system correctness with no deadlocks or live-locks found on the experiments performed on soft-ware Supremica. This analysis may be extended infuture works to prove, theoretically, that the com-position will never present deadlocks or livelocksfor an arbitrary number of layers. The develop-ment of a method to choose the best value τ willalso be investigated.

6 Acknowledgment

The authors would like to thanks CAPES for thefinancial support.

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