A Decentralized Architecture for Multi-Robot Systems Based on the Null-Space-Behavioral Control with Application to Multi-Robot Border Patrolling

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1 DOI 1.17/s A Decentralized Architecture for Multi-Robot Systes Based on the Null-Space-Behavioral Control with Application to Multi-Robot Border Patrolling Alessandro Marino Lynne E. Parker Gianluca Antonelli Fabrizio Caccavale Received: 2 April 212 / Accepted: 11 Septeber 212 Springer Science+Business Media Dordrecht 212 Abstract This paper presents a control architecture for ulti-robot systes. The proposed architecture has been developed in the fraework of the Null-Space-based-Behavioral (NSB) control, a copetitive-collaborative behavior-based control approach. The standard NSB statically deterines a set of suitably defined eleentary The anuscript is based on three conference papers of the sae authors, naely, Marino et al. [27 29]. A. Marino (B) Dipartiento di Ingegneria Elettronica e Ingegneria Inforatica, Università degli Studi di Salerno, Via Ponte Don Melillo, 8484, Fisciano, SA, Italy e-ail: alarino@unisa.it L. E. Parker Departent of Electrical Engineering and Coputer Science, The University of Tennessee, 1122 Volunteer Blvd, Knoxville, TN , USA e-ail: leparker@utk.edu G. Antonelli DIEI - Dipartiento di Ingegneria Elettrica e dell Inforazione, Università di Cassino e del Lazio Meridionale, Via G. Di Biasio 43, 343, Cassino, FR, Italy e-ail: antonelli@unicas.it F. Caccavale Scuola di Ingegneria, Università degli Studi della Basilicata, Viale dell Ateneo Lucano 1, 851, Potenza, Italy e-ail: fabrizio.caccavale@unibas.it tasks (behaviors) and their priorities, i.e., they cannot be dynaically changed according to ission requireents and environental constraints. In this paper, a three layer architecture has been designed in order to avoid such a drawback. The single robotic unit (agent) perforing the ission is placed on the lower layer. In the iddle layer, suitably defined eleentary behaviors are defined; these eleentary behaviors are then cobined, via the NSB approach, in ore coplex actions. The upper layer is a Supervisor in charge of dynaically selecting the proper action to be executed. As further contribution, the architecture has been applied to the ulti-robot border patrolling ission to generate a decentralized, deterinistic and non-counicative solution that is robust to faults, and prevents collisions, even in the case of high robot density. Finally, the siulations on a tea coposed by a large nuber of robots, and experients on a real setup, coposed by three Pioneer-3DX robots, are provided. Keywords Behavioral control Null-space based behavioral approach Multi-robot systes Swar robotics Border patrol 1 Introduction Collaborative ulti-robot teas have great potential to add capabilities and iniize risks,

2 especially in the security doain. In fact, robots are increasingly used in perforing patrolling, surveillance and ilitary tasks. Today, such robots are not able to carry out a ission on their own, due to liited autonoy; hence, ost of the are reotely controlled by huan operators. This is due also to the risks connected to robots failures in highly dynaic scenarios. Of course, ulti-robot systes require a coordination echanis to accoplish the ission. Although several paradigs have been developed in the last decades, behavior-based robotics has been proven to be a successful technique [9]. Arbitration echaniss are usually adopted for selection of active behaviors on the basis of ission and syste requireents. An exaple is the subsuption architecture, in which a priority is assigned to each behavior, and behaviors with higher priorities are allowed to override the output of behaviors with lower priority [9]. However, ultiple non-conflicting behaviors cannot be activated siultaneously. Coand fusion echaniss try to establish a sort of cooperation between behaviors. For exaple, the otor schea allows the output of ultiple behaviors to be cobined [7]. However, it suffers fro the proble of local inia and coand averaging without explicit handling of conflicting behaviors. The traditional NSB approach requires the definition of a set of eleentary behaviors [4]. The ission achieveent is obtained by properly cobining the eleentary behaviors via the nullspace projection echanis. Thus, the NSB can be defined as a copetitivecooperative approach, that overcoes the disadvantages of the above approaches, allows the activation of several behaviors at once and properly handles the conflicts aong the. A coparison of the NSB approach with the other paradigs cited above can be found in Antonelli et al. [5]. However, the behaviors and their priorities are statically deterined, i.e., they cannot be changed dynaically according to ission requireents and environent constraints. Hence, the standard NSB approach can be effectively applied only to relatively siple issions. Thus, it is worth further extending this echanis to handle dynaic changes of behaviors and their priorities. In this paper, the NSB approach for ultirobot systes has been extended with respect to previous published papers. Naely, a ission whose coplexity cannot be effectively handled by the standard NSB approach is first decoposed into several sub-issions (or sub-goals). Each sub-ission requires the activation of ultiple behaviors, each characterized by its priority, and their cobination according to the Null-Space-Behavioral approach. Such a cobination of behaviors is called action. Finally, a higher level (i.e., the Supervisor) is needed to dynaically select the action to be activated. In addition, the classic NSB has a centralized structure, i.e., a central coputing unit or a leader agent is in charge of collecting the syste s state and calculating the agents otion coands. Here, a different perspective is used. Naely, a copletely decentralized architecture is proposed to overcoe this liitation. The proposed architecture has been applied to the ulti-robot patrolling ission. The overall patrolling architecture in the NSB fraework is able to perfor the ission in very critical conditions and under strong requireents (see Section 3.1). In detail, a suitable set of eleentary behaviors is defined, on the basis of typical patrolling ission requireents. Then, these behaviors are coposed, via NSB, into ore eaningful and coplex actions, which represent given sub-goals. Once the set of actions is defined, the Supervisor selects the action to be perfored by each robot in order to achieve ission goals. The proposed control architecture can be adopted by ulti-robot systes to perfor different classes of issions, by properly forulating the set of behaviors and actions. For the sake of clarity, in this paper the designed procedure has been presented by direct application to the patrolling ission that is a challenging scenario that helps to understand the ain features of the approach. The paper has been organized as follows. In Section 2, the contributions of the paper are strengthened and suarized, while in Section 3,

3 an overview of the patrolling ission is carried out and the ain assuptions and requireents are deterined. A description of the designed architecture is given in Section 4. A short review of the NSB approach together with the definition of the eleentary behaviors and actions is given in Section 5. The supervisor in charge of selecting the proper action to execute is described in Section 6. Siulations and experiental results are presented in Sections 8 and 9. Finally, conclusions are drawn in Section 1. 2 Main Contributions and Novelty The contribution of the paper ais to be twofold. First, a fraework has been designed that allows handling coplex issions by eans of a threelayered architecture. This objective is achieved thanks to the use of the NSB in the iddle layer, that allows building a set of well-structured behaviors and actions, whose output is fully predictable. Moreover, the NSB fraework allows the designer to focus on the design of the top level rather than on the low level effects. Second, the feasibility of the approach has been deonstrated by showing a practical exaple of how the proposed architecture can be used to accoplish the patrolling task. In addition, experients have been run on a real setup coposed by three fully autonoous vehicles. 3 The Patrolling Mission: Main Requireents and Assuptions As stated above, the ission to accoplish is the surveillance of a given area, i.e., a border or any ilitary and civil facility. An early exaple of a robotic surveillance syste is the Mobile Detection Assessent and Response Syste- Exterior (MDARS-E) [19] whose goal is to provide ultiple obile platfors that perfor rando patrols within assigned areas of warehouses. Sandia National Laboratories has developed the Surveillance And Reconnaissance Ground Equipent (SARGE) robotic vehicle for the US Departent of Defense [35]. SARGE is a teleoperated robot for battlefield surveillance applications without coputing power, aied at supporting autonoous navigation or vision processing. Recently, coercial border patrol applications have been proposed as well, such as Guardiu [21] and the unanned autonoous speed boat Protector anufactured by Ltd [36]. Perieter surveillance algoriths for the basis for effective execution of onitoring tasks in a nuber of applications fields, e.g., onitoring of oil spills [15], containant clouds, algae bloo [8], forest fires [12] and border security [23]. In Machado et al. [26], an analysis of the ain patrolling task issues and soe ulti-agent-based solutions are presented. Several features (agent type, agent counication, coordination schee, agent perception and decision-aking) are evaluated by using different criteria. In Kingston et al. [25], a decentralized solution to the ulti-robot perieter surveillance is presented, where changes of both the shape of the perieter and the nuber of robots are taken into account; oreover, critical coordination inforation is exchanged to optiize soe perforance index. In Agon et al. [1], the authors analyze non-deterinistic paths for a group of hoogeneous obile robots patrolling a frontier, under the assuption of a hostile agent trying to enter the area, where the latter has full knowledge of the algorith. In this paper, a linear border to be patrolled was considered. The border ay be any iaginary (like in the case of aerial vehicles as in [25]) or real line surrounding strategical facilities or even countries borders. In a real ission scenario, the first task the vehicles have to be able to perfor is to get to the border itself fro, for exaple, a base station. After the border has been reached, the vehicles have to ove along the border while keeping staying on the border. In addition, static or dynaic obstacles need to be considered. Obstacles can be represented by other teaates or natural obstacles close to the border. Finally, the case of a friend vehicles that try to enter the border can be of interest. A friend vehicle

4 is any agent that is allowed entering the area to be patrolled and that has not to be stopped by patrolling vehicles. In the following, the ain requireents and assuptions related to the border patrolling ission are listed. 3.1 Requireents A patrolling ission requires a high degree of autonoy and robustness. Several aspects and constraints ight affect the ission achieveents, e.g., occurrence of robot faults, large nuber of patrolling robots, presence of friends or intruders interfering with patrolling robots, liited counication range and coputational capabilities. For these reasons, the following requireents need to be et. Requireent 1: Decentralization The control architecture needs to be fully decentralized, i.e., there is not a central unit in charge of coputing the patrolling robots otion coands, by gathering inforation fro the. Requireent 2: Counication Explicit counication between patrolling robots is forbidden. This requireent is devoted to supply ore robustness to the control architecture as well as to enhance security, since, in certain applications, encryption of counications would be needed, at the expense of an increased software coplexity. Moreover, in soe scenarios (e.g., underwater environents and/or wide areas to be patrolled) reliable counications could be not available. Moreover, even in the case that explicit counications can be assued, the gathered data ay require significant tie to transit (e.g., coplete video footage). Of course, this requireent is not independent fro the previous one, since, without any for of counication, a centralized architecture cannot be ipleented. Requireent 3: Collision avoidance It is obvious to require that each patrolling robot ust avoid collisions with other teaates, friends or intruders, even in the case of a large nuber of robots. In addition, in the case of a large nuber of robots, interference phenoena ust be avoided, i.e., the adoption of a large nuber of patrolling robots ust not lead to ission failure or other unexpected and undesired events. Requireent 4: Robustness Patrolling issions are usually perfored in challenging environents. Hence, it is andatory to deal with robot faults, by providing a suitable degree of tolerance to faults of the single agents in the patrolling tea. More generally, sudden changes in the nuber of patrolling robots (due, e.g., to an increase of the available robots or failures of single robots) ust be taken into account. Requireent 5: Coputational burden Usually, in ulti-robot systes, relatively siple robots are eployed to achieve a given ission. Thus, the coputational burden of the control algoriths versus the available coputational power of the single robotic units ust be taken into account. 3.2 Assuptions The following assuptions are adopted to develop the proposed solution to the ulti-robot border patrolling proble, according to the above defined requireents. Assuption 1: Border geoetry The general perieter surveillance proble is reduced to the linear surveillance proble, by assuing that the perieter to be onitored is hoeoorphic to a line, and thus it can be represented as a single path between two points. In addition, closed perieters are allowed. Assuption 2: Visibility range It is assued that each robot has a liited visibility range, where it recognizes the presence of other agents and detects the border. For the sake of siplicity, the visibility area is odeled as a circle around the robot. This is not an unrealistic assuption, since it well approxiates the case of pan-tiltzoo caera sensors, laser range finders or onidirectional caeras. Assuption 3: Localization capabilities It is assued that each robot is able to localize itself in the environent and knows a local (i.e.,

5 liited to its visibility range) geoetric description of the border (or is able to locally estiate the geoetry of the border). Localization and, in general, Siultaneous Localization and Mapping (SLAM) [38] are well-established probles in the literature and will be not addressed in this paper. Indeed, each robot needs to estiate only its position with respect to the border and other agents that are in its visibility range. How this goal is achieved highly depends on the available sensors and the practical goals to be faced. A notable exaple is given in Brueer et al. [1], where a swar is able to locate and surround a water spill using social potential fields ipleented via IR, chirps and light sensing; oreover, in Clarka and Fierro [15], caeras are used to locate the perieter of the area to patrol. Finally, it assued that each robot is able to follow the border [4]. Assuption 4: Safety area Each robot ust be characterized by its own safety area, in which other agents are not allowed to enter. The safety area is a circle around the robot (saller than the visibility area). Such an assuption is necessary to eet the collision avoidance requireent, particularly in the case of teas coposed by a large nuber of robots, where conflicts and interferences ay arise. Assuptions 5: Awareness Each robot does not know the exact nuber of patrolling robots. However, it is aware of the existence of other agents (other patrolling robots, friends or intruders). As described in the following, the awareness assuption will be iplicitly taken into account by properly defining the eleentary behaviors. 4 Control Architecture 4.1 Paradig By taking into account the requireents defined in Section 3.1, an approach belonging to the swar robotics class has been adopted. In swar robotics (see Dorigo and Sahin [16] for a survey and Dudek et al. [17] for a taxonoy), the achieveent of the ission is the result of the cooperation of independent agents foring the swar. The swar intelligence ais at developing robust task solving by iniizing the coplexity of the individual units; its central idea is to distribute the control over a group of nuerous inialist robots rather than gathering and redistributing inforation with the help of a central unit. There are two ain advantages of this approach: first, scalability fro a few to thousands of units, second, increased syste robustness, not only through unit redundancy but also through the unit siple design. In this approach, the overall behavior is generally eergent, i.e., each unit does not have a global cognition of the assigned ission and reacts to external stiuli via siple behaviors, where, in general, the stiuli-behaviors couples are organized in such a way that the cooperation iplicitly arises fro the interaction aong robots and with the environent. Moreover, this approach is clearly odular, since new eergent behaviors at the swar level can be obtained and, in general, ore coplex issions could be accoplished by properly defining new behaviors at the level of the single unit. There are, of course, soe drawbacks connected to this approach. Naely, foral ethods are still not available that can generate (starting fro a suitable description of the overall ission) a set of stiuli-behaviors couples, whose interaction leads to task accoplishent. This is true especially in the presence of dynaically changing environents. 4.2 Outline of the Control Architecture Since the approach is copletely decentralized and disallows any for of counication, the control architecture described in the following ust refer to the single robot in the patrolling tea. As it can be seen in Fig. 1, the control architecture is coposed by three layers. Starting fro the top layer, they are the Supervisor Level, the Action Level and the Robot Level. The first two levels are abstract levels. In particular, the Action Level, described in detail in Section 5, defines the set of actions the robot can undertake. Clearly, the set of actions depends on the ission to be achieved, involving different skills. As already stated, this eans that the architecture does

6 Fig. 1 Sketch of the control architecture not depend on the particular ission, but can be applied to different issions by properly defining the action set. Once the actions have been defined, each robot chooses the proper action to perfor, according to its internal state and environental inforation. To this ai, a Supervisor needs to be designed. Finally, the Robot Level coprises the coputing hardware/software and the echanical features of the single robot; the structure of this layer depends on the adopted robotic platfor and is priarily concerned with the available sensors and actuators. A description of the platfor used to test the proposed approach is given in Section 9. Inthe following, the architecture will be detailed with reference to the patrolling ission 5 Behaviors and Actions In this section, the set of behaviors required by the patrolling ission is defined. Then, these behaviors are cobined into ore coplex and eaningful actions by eans of the Null-Spacebased-Behavioral (NSB) approach. 5.1 Review of the NSB Approach A coplex ission for a robotic syste can be encoded via different basic tasks (behaviors) to be properly cobined to achieve ission goals. As already stated, the NSB approach can be defined as a copetitive-cooperative approach, trying to overcoe the disadvantages of arbitration and coand fusion approaches; it is based on the task-priority control approach for robotic anipulators [32]; it has been experientally copared to the layered-control syste and otor-schea control in the case of a wheeled obile robot [5], and successfully applied to control of a platoon of ground vehicles [6]. Let us consider the task function σ R which is the atheatical representation of a generic task to be achieved by a robotic syste. It is assued that σ = σ ( p) R, (1) where p R n is a vector describing the syste configuration (e.g., in case of a tea of robots, p is the vector containing the positions of all the vehicles) and is the diension of the task space. Assuing that σ is a differentiable function, it is useful to consider the relationship between the first derivatives of σ and p σ = σ ( p) p ṗ = J( p)v, (2) where J R n is the task Jacobian atrix. Equations 1 and 2 represent the so-called direct task odel of the syste, i.e., the equations needed to copute the value of the task function, σ, given the syste configuration, p. The inverse task odel proble is defined as the deterination of the desired syste s configuration, p d, corresponding to a desired task function, σ d. It can be easily recognized that the inverse task odel proble is of the utost iportance, since, by eans of the desired task function, the desired high level aggregate behavior of the syste is specified, while the corresponding desired configuration represents the set of coands to be delivered to the actuators. A possible solution to the inverse task odel proble can be sought at the differential level, by inverting the (locally linear) apping (Eq. 2); this solution has been widely studied in robotics (see, e.g., [37] for a tutorial). A typical requireent is to pursue iniunor velocity in a closed loop version, leading to v d = J ( σ d + σ ), (3) where J = J T ( JJ T) 1 is the pseudo-inverse of the Jacobian atrix, is a suitable positive-

7 definite atrix gain and σ = σ d σ is the task error. It can be easily shown that Eq. 3 leads to the following asyptotically stable error syste σ + σ =. (4) When dealing with coplex issions, several tasks need to be handled. If N tasks (encoded by functions σ d,1,...,σ d,n ) are considered, the NSB solution to the task cobination can be forulated in a recursive way, by coputing the series of velocity vectors as follows ( ) v d,i = J i σ d,i + σ i i = 1, 2, N, (5) v (i) = v d,i + N s,i v (i+1), where J i is the i-th task Jacobian, v (N+1) =, v d = v (1) and the atrix N s,i = I J s,i JT s,i is a projector onto the null-space of J s,i (i.e., its coluns for a basis of the null space of J s,i ). The atrix J s,i is obtained by stacking the atrices J k with k = 1, 2,, i. In the case of two tasks σ 1 R 1 and σ 2 R 2, as will be the case in this paper, Eq. 5 becoes v d,1 = J ( ) 1 σ d,1 + σ 1 v d,2 = J ( ) 2 σ d,2 + σ 2 v d = v d,1 + N 1 v d,2. (6) In su, the coanded velocities corresponding to a lower priority task are projected onto the null-space of the iediately higher priority task; then, eventually conflicting velocity coponents are cut off before being added to the higher priority task velocity coponents. In this way, lower priority behaviors are executed only in their coponents not affecting higher priority behaviors. Convergence to zero of task errors can be guaranteed for properly defined tasks [3]. On the other hand, a differentiable analytic expression of the defined behaviors is required, so as to copute the required Jacobian atrices. 5.2 Eleentary Behaviors and Actions In the case of the border patrolling of a linear border, a set of eleentary behaviors is defined: Reach Frontier Patrol Frontier Clockwise Patrol Frontier Counter-Clockwise Teaate Avoidance Friend Avoidance whose seantics and analytical expressions are given in Appendix A.1. As otivated above, it is appropriate to copose the eleentary behaviors into ore coplex behaviors; the latter are soeties defined as behavior sets in the literature. Siilar to the concept of behavior set, here a higher abstraction layer is introduced: the action. Anactionisgiven by the proper coposition, achieved via NSB, of several eleentary behaviors and represents a acroscopic attitude of the robotic syste. Only one single action can be active at once. For the specific case of the border patrolling task, the following set of actions is obtained by cobining the eleentary behaviors defined above: Action Reach Frontier Action Keep Going Action Patrol Clockwise Action Patrol Counter-Clockwise Action Teaate Avoidance Action Friend Avoidance According to the definitions in Appendix A.2, each action is given by eleentary behaviors arranged in priority; e.g., the Reach Frontier action properly cobines the eleentary behaviors Reach Frontier and Teaate Avoidance, depending on the sensed presence of other patrolling robots in the visibility range and the distance fro the border. It is worth noticing that such actions require that each robot is able to recognize other agents and their nature (friends or teaates). 5.3 Behaviors Copatibility In the NSB fraework it is possible to define conditions for behavior copatibility [3], allowing

8 the robot to properly handle conflicts aong different behaviors (algorithic singularities). Issues related to singularities are deeply discussed in Chiaverini [14], where a singularity-robust taskpriority strategy, in the case of two tasks, is derived. According to this technique, a secondary task is fulfilled if it does not conflict with a higher level task, while it is released in the case it is conflicting. The ore general case of copatibility of three or ore tasks handled in the NSB fraework has been discussed in Antonelli [3], by resorting to a Lyapunov-based analysis. A straightforward application of the results of the above entioned papers guarantees proper definition of all the actions used in this paper; in particular, collisions between robots and between robots and obstacles are avoided. Copatibility of the behaviors cobined in actions is discussed in the Appendix. actions to be perfored can be easily apped to situations. To build a Finite State Autoata, two sets ust be deterined: the sets of the states the agent can be in, the sets of causes forcing the agent to change its state. The structure of the supervisor that selects the proper action is shown in Fig. 2. As it can be seen, the supervisory layer is arranged in a hierarchical way, by defining three levels. At the top level two scenarios have been identified. The first one corresponds to the situation where a friend agent is in the safety area 6 The Supervisor The set of actions defines the robot s skills needed to react to situations encountered in the environent. Hence, each robot has to be equipped with a Supervisor that is in charge of selecting the action to be executed, according to the robot s internal state and/or external stiuli. According to the assuptions and requireents defined in Section 3, the Supervisor of each robot decides the next action to be perfored, based only on locally available inforation. Although several paradigs ight be used, two appealing tools for the design of the Supervisor are represented by Finite State Autoata and Fuzzy Logic Engines. The Finite State Autoata Supervisor [27] will be described in the following, while details on the Fuzzy Logic Supervisor can be found in Marino et al. [29]. A coprehensive description of hierarchical state achines and of their properties is carried out in Alur and Yannakakis [2]. Finite state achine action selection echaniss assue that [11]: there are only a liited nuber of salient situations the agent can find itself in, these situations are utually exclusive, Fig. 2 Sketch of the supervisor

9 of the patrolling robot. In the second scenario no friend agents are in the visibility area of patrolling agents. The second level defines four acro-states: MS, for the first scenario, MS1, MS2 and MS3 for the second scenario. At each tie instant the robot can be in one of the acro-states. In acro-state MS, Action Avoid Friend is active. On the other hand, if no friend agents are present (second scenario), one of the states MS1, MS2 or MS3 is active. In the acro-state MS1, the robot tries to reach the border (and, at the sae tie, avoid the teaates). In the acro-state MS2 the robot behaves as if it is patrolling the border (while avoiding teaates); however, in this state, the robot still cannot be considered as perforing the patrolling ission. In the acrostate MS3, the robot perfors the patrolling ission and does not allow robots approaching the border to influence its otion. The reason for the distinction between acrostates MS2 and MS3 is that, in the case of a large nuber of patrolling robots, interference between robots can be effectively counteracted. In fact, when a robot is in the acro-state MS3, it cannot be influenced by other teaates that are not in the sae acro-state; the avoidance of other teaates that are in the acro-state MS3 is achieved by activating Action Patrol Clockwise and/or Action Patrol Counter-Clockwise. In detail, the supervisor acts as described in the following. Scenario 1 One or ore friend agents are in the safety area of the robot Macro-State MS: Action Avoid Friend is active Scenario 2 No friend agents are in the safety area of the robot Macro-State MS1: The distance between the robot and the border is larger than the Visibility Range if no teaate is in the safety area then Action Reach Frontier is active, if one or ore teaates are in the safety area then Action Avoid Teaate is active. Macro-State MS2: The distance between the robot and the border is saller than the Visibility Range and larger than a given threshold, ζ FS if no teaate is in the safety area then Action Keep Going is active, if one or ore teaates are in the safety area then Action Avoid Teaate is active. Macro-State MS3: The distance between the robot and the border is saller than a given threshold, ζ FS if no teaate is in the visibility range then Action Keep Going is active, if there is a teaate on the left then Action Patrol Clockwise is active, if there is a teaate on the right then Action Patrol Counter-Clockwise is active. Finally, it is worth noticing that, when the syste has enough degrees of obility, a ore advanced Supervisor could be designed to further cobine, via NSB, the actions outputs in order to achieve ore sub-goals at once. For instance, when a Fuzzy Logic Supervisor is used, several actions can fire at once with different degrees of activation. These can be used as priority of the fired actions in the NSB approach. 7Analysis The FSA has been designed according to guidelines described in Murphy [31, pp ]. The ain properties that have been considered and checked are the consistency and copleteness [33]. Naely, a FSA is said to be consistent if only a single transition rule can be enabled at the sae tie for all the states. By considering the structure of the supervisor, it can be verified that this property holds. Proposition 7.1 The FSA shown in Fig. 2 is consistent.

10 Proof Since the supervisor is arranged in a hierarchal way with three levels (Fig. 2), with scenarios at the top layer, acro tasks in the iddle layer and actions at the lowest layer, it is required to prove that in each tie instant: 1. only one scenario can be active, 2. for each scenario, only one acro task can be active, 3. for each acro-task, only one action can be active. 1) Consistency of the Scenario Layer With regards to the scenarios, the following transition has been defined: C: there is a friend in the safety area of the considered robot; this condition, essentially, identifies two situations depending on whether a friend vehicle is close or not to the given patrolling vehicle. Since the two conditions are utually exclusive, it is obvious that only one scenario can be active at a tie. 2) Consistency of the Macro-Task Layer With regards to the acro-tasks, there is only a acro-task in the first scenario (MS), thus, no conflict occurs in this scenario. With regards to the second scenario, the following transitions for the acro-tasks (MS1, MS2, MS3) have been defined: C1: the distance fro the border is saller than the visibility range, C2: the distance fro the border is saller than the threshold ζ FS defined in Section 6. Fro each of the considered acro-tasks, only one output transition is defined, thus, conflicts cannot occur. 3) Consistency of the Actions Layer In the case of the actions in each acrostate, the following situations have to be considered: the acro-state MS is active. In this case, only the action Action Avoid Friend can be active; the acro-state MS1 is active. Two actions ight be active (Action Reach Frontier and Action Avoid Teaate). Only one transition rule, naely c1, is present; this eans that conflicts do not arise; the acro-state MS2 is active. Two actions ight be active (Action Keep Going and Action Avoid Teaate). Also in this case, only one transition, naely c1, is present; thus, any conflict is avoided; the acro-state MS3 is active. Three actions ight be active (Action Keep Going, Action Patrol Clockwise and Action Patrol Counter-Clockwise). Three transition rules are present, naely c2, c3, c4. Because c2 and c3 cannot both be true at sae tie, the following cobinations are aditted: c2 c3 c4=!c2!c this iplies that only one transition rule is active at a tie. In addition, each action is characterized by only one output transition. Thus the consistency is proved. Moreover, a FSA is said to be coplete [33] if it operates correctly for all possible input/ state sequences. Proposition 7.2 The FSA shown in Fig. 2, cobined with the behavior-action level and the properties of the NSB approach, is coplete. Proof Copleteness can be inferred fro the ain NSB properties. In the environental odel that has been considered, in each tie instant the inputs a vehicle takes into account are the distance fro the border, the distance fro the friend vehicles and the distance fro teaates or other obstacles. Based on the acro state MSi (i=,1,2,3), any sequence of the considered inputs is adissible for the designed FSA.

11 In fact, any sequence of the following situations is adissible: a friend is in the visibility area. In this case, the acro state MS is active and then the Action Avoid Friend. As stated in Section A.2.5, this action guarantees that no collision between friends occurs; no friend and no obstacle is in the visibility area. In this case, either the vehicle is in the acro states MS1 or MS2. Thanks to the Action Reach Frontier (see Section A.2.1) it is ensured that the vehicle gets to the border and starts the patrolling ission; an obstacle is in the visibility area. In this case, the robot is either in the acro state MS1 or MS2.TheAction Avoid Teaate in Section A.2.4 guarantees that no collision occurs, since the collision avoidance has the highest priority task in the NSB sense. Thus copleteness is proven. 7.1 Advantage of the use of NSB The considered task priority algorith guarantees that the higher priority tasks are not affected by the lower ones. For the generic task, in fact, it has been deonstrated that its error converges to zero within the null-space of the higher ones and it is not affected by the lower ones [5]. The actions used in this paper are properly defined as discussed in the Appendix; in addition, tuning of the feedback gains is extreely siplified with respect to cooperative behavioral approaches. In fact, the NSB decouples the tasks spaces, eaning that the paraeter tuning can be done for each task independently fro the reaining ones and independently fro its priority. This property is a significant advantage with respect to any cooperative behavior approach. In fact, the coupling aong the tasks/behavior is done by selecting the priority, thus at a higher level, and not by selecting the gains. In su, in the case of one robot, the FSA ensures the robot reaches the border and starts the patrolling ission (in acro-state MS3). In fact, whatever is the starting acro-state, since Reach Frontier is always the priary behavior (in the absence of obstacles or other teaates), the robot is forced to reach the border (i.e., the FSA is in the acro-state MS3). In the case of ultiple robots (but in the absence of friends), thetransitiontowardsms3 occurs if there is enough space along the border to let the robot stay on it. The behavior of robots left out of the border (whose supervisor is in acro-states MS1 or MS2), thanks to the distinction between acrostate MS2 and MS3, do not affect the patrolling robots. In the presence of friend vehicles and independently fro the other conditions, the acrostate MS becoes active. In this case, the Reach Frontier Behavior is not the priary behavior; hence, the robot reaches the border only after the friend vehicles have crossed it (the behaviors coposing Action Avoid Friend are not copatible [3]). 8 Siulations Several siulations, perfored in the presence of both closed and open borders with different sizes and shapes, have been carried out by using both Matlab [3] and Player/Stage [39] environents. A video of the siulation can be downloaded at the footnote link Siulations in the Presence of a Large Nuber of Robots In order to test the approach in the presence of a large nuber of robots in the tea, a free environent with a closed border has been considered in a nuerical siulation. The tea is coposed by 6 robots, with visibility and safety areas equal to 2. The atrix gains in Eqs of Appendix A.1 have been chosen 1 A video of the siulation is available at: unicas.it/lai/robotica/video/sipatrolling.avi.

12 Fig. 3 Saple fraes at different tie instants of robots perforing a patrolling ission without friend agents [] 2 1 tie =.4s [] 2 1 tie = 4s [] [] tie = 7s 2 1 tie = 25s [] [] [] [] 1 2 as λ rf = 5I, λ cw = 8I, λ ccw = 8I, λ ta = 1I and λ fa = 1I. The gains have been selected by setting the desired velocities to be assued when approaching and patrolling the border, as well as when escaping fro teaate and friend agents. Friend vehicles are not present in this siulation. Figure 3 shows the robot positions at four different tie instants. Robots are represented by green points surrounded by their visibility ranges; the continuous blue line represents the closed border to be patrolled. As it can be seen, the task is executed in four different phases (each corresponding to a frae in Fig. 3): in the first phase, all robots are trying to reach the border, while avoiding teaates; in the second phase, soe robots reach the border and start patrolling the border; in the third phase, ost of the robots are patrolling the border, in the fourth phase, the robots reach the axiu density along the border, and the patrolling robots are not affected by other agents trying to reach the border. It is useful to reark that a swar approach should also prevent robot collisions in critical conditions like this one. To this ai, in Fig. 4 (top), the tie history of the iniu value of the distances aong all possible robot pairs is depicted, i.e.: d r,in (t) = [] [] in p i,r (t) p j,r (t), (7) i = ji, j N r 5 5 Miniu distance between robots [s] Coverage Index Fig. 4 Top: tie history of iniu of distances between all possible robot pairs. The dashed line represents the radius of the safety area. Botto: tie history of the coverage index over tie 15 [s]

13 J Intell Robot Syst 2 2 tie = Fig. 5 Saple fraes at different tie instants of robots perforing a patrolling ission with friend agents. Dashed vehicles are the friend agents tie = tie = tie = different phases (each corresponding to a frae in the figure) are the following: in the first phase, robots are randoly distributed and try to reach the border, while avoiding other teaates; MiniuDist [] where pi,r (t) is the position of the i-th robot at instant t, and Nr is the set of patrolling robots. As it can be seen in Fig. 4 (top), even in the case of a large nuber of robots, collisions are avoided. Moreover, the structure of the supervisor avoids interference between robots. In fact, the fourth frae in Fig. 3 shows that robots still approaching the border do not affect the otion of robots already perforing the patrolling ission (i.e., robots in the acro-state MS3). In Fig. 4 (botto), the tie history of a coverage index of the border (defined as the ratio between the portion of border that is in the visibility area of the patrolling robots and the overall length of the border) is shown. As it can be seen, it onotonically approaches the axiu value [s] MiniuDistFriend 7 6 Siulations showing the approach perforance in the presence of 1 friend agents (trying to enter the border) are carried out. The tea is coposed by 6 robots with visibility and safety areas equal to 2. The gains are the sae as in the previous siulations. Figure 5 shows the robot positions at different tie instants. As in the previous case, the 5 4 [] 8.2 Siulations in the Presence of Friend Vehicles [s] Fig. 6 Top: tie history of iniu of distances between all possible robot pairs. The dashed line represents the radius of the safety area. Botto: tie history of the iniu of distances between all robot-friend pairs

14 1 CoverageIndex 1 CoverageIndex.8.8 [] Fig. 7 Tie history of the coverage index over tie in the presence of several friend vehicles [s] [] [s] Fig. 9 Tie history of the coverage index over tie in the case of several faults in the second phase, soe robots have reached the border and start to perfor the patrolling ission, activating Action Keep Going and Action Patrol Clockwise (or Patrol Counterclockwise); in the third phase, friend agents, represented by cross arkers surrounded by their safety areas (dash-dot circles), start to approach the border and cross it, without any collision with patrolling robots; in the fourth phase, friends gain the center of the bordered zone; in this situation, patrolling robots are no longer affected by friends otion. In Fig. 6 (top), the tie history of the iniu value of the distances aong all the possible robot pairs, coputed according to Eq. 7,isdepicted. In Fig. 6 (botto), the iniu distance over tie of all the possible robot-friend pairs is shown, i.e.: d f,in (t) = in p i,r (t) p j, f (t), (8) i N r, j N f where p j, f (t) is the position of j-th friend agent at the tie instant t and N f is the set of friend agents. Friend agents cross the border between 15 s and 24 s; even during border crossing the safety distance (dashed line) is not violated. Thus, the proposed architecture is capable of avoiding collisions, and the ission is safely accoplished. In Fig. 7, the tie history of the coverage index is shown. Again, since interference situations do not occur, the coverage index onotonically approaches 1; the index decreases only when friends cross the border. 8.3 Siulations in the Presence of Friend Vehicles and Multiple Sudden Faults In this siulation case study, the initial conditions and the paraeter values are the sae as in the previous one. In addition, robot failures occur. Naely, 5 % of the initial patrolling robots suddenly fail. As in the previous siulations, at the beginning, robots are randoly distributed and reach a final configuration corresponding to the fourth fraes of Figs. 3 and 5. Starting fro this configuration, Fig. 8 (left) shows the configuration of robots iediately after the occurrence of the faults. The second frae shows that the Fig. 8 In the left frae, several robots fail. In the right frae, the reaining robots autoatically redistribute around the border tie = tie =

15 Fig. 1 The experiental setup at the Distributed Intelligence Laboratory of University of Tennessee. Left: a Pioneer-3DX obile robot. Right: the tea used in the experients surviving robots redistribute along the border after the failures, thus keeping the ission objective. In Fig. 9, the tie history of the coverage index is shown. Initially, the index alost reaches the value 1; at 15.5 s, when 5 % of the robots suddenly fail, the reaining robots redistribute to axiize the coverage index. 8.4 Discussion The nuerical siulations have been designed in order to stress the algorith in severe tests. Dozens of different case studies with different siulation paraeters such as, e.g., the nuber of robots, the visibility range, the robot speed, etc., have been run. The results show that, even in the presence of a large nuber of robots, collisions and interference between robots are avoided. The results confir that the approach is capable of achieving nearly optial values of the adopted perforance indexes. The presence of a generic nuber of friend robots in a cloud configuration is also handled in a proper way, while ensuring satisfactory perforance. Finally, siultaneous faults of several robots affect significantly the perforance only during a transient phase; the expected values for the given nuber of working robots are then proptly reached. 9 Experients The proposed control architecture has been ipleented on an experiental setup coposed of three Pioneer-3DX obile robots (Fig. 1), available at the Distributed Intelligence Laboratory of University of Tennessee. Videos about the experients can be downloaded at the footnote links. 2 The Pioneer-3DX robot has a aluinu body with.165 diaeter. This differential drive platfor is nonholonoic and can rotate in place by oving both wheels, or it can swing around a stationary wheel on a circle of.32 radius. A rear castor balances the robot. In addition to otor encoders, the robot base includes eight ultrasonic transducers (range-finding sonar) arranged to provide a 18- degree forward coverage at a sapling rate of 25 Hz. The coputational board includes a 32-bit RISC-based controller running Linux. Additional hardware includes ethernet counication, a Wi-Fi radio turret for reote control, a Pan-Tilt- Zoo color caera and a laser rangefinder. Since the orientation θ of the robot is not of interest and our ai is not to solve the control proble for non-holonoic systes, the following direct task odel has been considered p b = [ ẋb ẏ b ] = [ cos(θ) b sin(θ) sin(θ) +b cos(θ) ][ ] v, (9) ω where p b is a point whose distance fro the wheels axis is equal to b. Taking into account the velocities generated by the control algorith, the diensions and the axiu linear and angular velocities of the Pioneer-3DX robots, b has 2 The videos of the experients on an open and closed border are available at: video/expopenborder.avi and robotica/video/expclosedborder.avi.

16 been chosen equal to.1. This value prevents saturation of the actuators and ensures a control point located inside the robot chassis. The Player/Stage environent [39] has been used to ipleent the proposed architecture. Player/Stage is based on a client-server paradig; it provides a set of tools to siulate the syste (Stage), as well as the software priitives for counicating with the robotics hardware (Player). In Fig. 11 (left) a portion of the patrolled area is shown, together with its representation in Player/Stage (right); in addition, an open (top) and closed (botto) borders have been considered. The blue line represents the border, the red, green and cyan polygons represent the robots, together with their visibility ranges (assued to be equal to the corresponding safety areas). The open border (top) is 1 long; the closed border (botto), coposed by segents joined by arcs, has an overall length of 51. The results in the following refer to the closed border; nevertheless, siilar results have been obtained for the open border. The robots know the exact description of the border and they approach it at a speed of.3 /s (λ rf =.3), patrol at a speed of.35 /s (λ cw = λ ccw =.35) and escape other teaates at a speed of.3 /s (λ ta =.3). Localization in the environent is achieved via a pre-built ap and a localization driver based on an adaptive particle filter [2], available within the Player software. The visibility range and safety area are equal to 2.5, the threshold value ζ FS for the transition between acro-states MS2 and MS3 is.6. Moreover, if a robot is in the patrolling state, every 3 s it can decide to invert its otion direction or to keep going in the sae one, according to a rando variable. Figure 12 (top) shows the tie history of the distance fro the border for the three robots. In noral operating conditions (i.e., in the absence of faults), the utual distances are within.1, this value is acceptable for the experiental conditions and assued requireents. Moreover, peaks are reached during rotation oveents due to sensor noise and, above all, to the neglected robot dynaics in the control law. When a fault occurs to robot nuber 2, after 28 in fro the ission start, the robot is anually driven far fro the border and is reactivated at inute 41. Two faults occur to robot nuber 3, after 15 and 33 in fro the ission start. As can be noticed in Fig. 12, thanks to the decentralized Fig. 11 Left: a portion of the environent. Right: environent representation in Player/Stage, the path and the three patrolling robots

17 Tracking error of the border t [in].4 Robot t [in].4 Robot t [in] Distance between consectuvise robot Desired value Rob.1 and Rob.2 Rob.2 and Rob.3 Rob.1 and Rob.3 Width of Safety area Robot1 only by battery life. The achieved results clearly show that the proposed approach is also practically viable. According to Chevaleyre [13], at each tie instant, the distance between two consecutive robots should be one third of the overall border length; oreover, all robots should ove in the sae direction. On the contrary, according to Agon et al. [1], robots should ove synchronously but in a nondeterinistic way, so as to axiize the probability of intercepting an intruder. Both cases require a centralized supervisor or inforation exchanges between robots, so it is straightforward to iagine that the proposed approach can be characterized by better perforance only by increasing the nuber of vehicles or by reoving soe constraints t [in] Fig. 12 Top: distance fro the border. Botto: distance between two consecutive robots structure of the control law, faults do not affect the overall behavior of the swar. For the sake of clarity, it is worth showing the tie history of the distance between two consecutive robots (Fig. 12, (botto)). 9.1 Discussion In addition to intensive tests based on nuerical siulation, the approach has been also validated by perforing experients with 3 robots. The experients, even if involving a liited nuber of robots, have been conducted without particular shortcuts (e.g., an ad-hoc localization ethod). The faults have been eulated by turning on/off the robots during the patrolling of the reaining ones. The experients duration has been liited 1 Conclusion A higher layer above the traditional Null-Space- Behavioral (NSB) approach has been designed. At the basis of the developed architecture, there is the concept of action, obtained by cobining eleentary behaviors in the NSB fraework. Once the set of actions has been defined, a Supervisor can be designed that chooses the action to be executed. The developed architecture has been applied to the challenging border patrolling ission. To this ai, a set of constraints and requireents have been forulated and the ission achieved thanks to the designed architecture. The algorith is fully scalable; the coputational load, in fact, is siply independent of the nuber of robots as no counication occurs between robots and the control strategy of each robot does not depend on the nuber of robots. The robustness, in a wide sense, has been designed by avoiding the need for a central coputational unit or dead-lock counication aong the robots. This intrinsic robustness of the approach has been confired by siulation and experiental results. Future work will be devoted to the application of the developed architecture to different issions, e.g., coverage and flocking, by properly redefining the behavior and action sets. Moreover, it would be of utost iportance to test the approach by adopting different classes of vehicles (e.g., unanned

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