Petri Net Plans. 1 Introduction. Vittorio Amos Ziparo 1 and Luca Iocchi 2

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1 Fourth International Worksho on Modelling of Objects, Comonents, and Agents (MOCA'06), 2006 Petri Net Plans Vittorio Amos Ziaro 1 and Luca Iocchi 2 1 Diartimento di Informatica e Sistemistica, Università di Roma La Saienza, ziaro@dis.uniroma1.it 2 Diartimento di Informatica e Sistemistica, Università di Roma La Saienza, iocchi@dis.uniroma1.it Summary. In this aer we resent a novel reresentation framework based on Petri Nets for describing robot and multi-robot behaviors. The Petri Net Plan (PNP) formalism allows for high level descrition of comlex action interactions that are necessary in rogramming cognitive robots: non-instantaneous actions, sensing and conditional actions, action failures, concurrent actions, interruts, action synchronization in a multi-agent context. We show how this framework is caable of describing effective lans for robotic agents which inhabit a dynamic, artially observable and unredictable environment. The roosed framework has been imlemented and successfully deloyed on actual robotic teams in different alication scenarios. 1 Introduction High level rogramming of mobile robots is very imortant for develoing comlex and reliable robotic alications. In this aer we resent a framework based on Petri nets that has been used for describing high level robot and multi-robot behaviors. The roosed framework has been used for describing effective lans for robotic agents which inhabit dynamic, artially observable and unredictable environments, and exerimented in different alication scenarios, including robotic soccer and rescue cometitions. Our cognitive robots are based on a heterogeneous hybrid architecture. These kind of architectures are caable of integrating reactiveness and roactiveness. In articular, they are structured in two layers: a deliberative and an oerational one. The former maintains a high level reresentation of the environment which is used to choose actions; the latter maintains a low level reresentation which is used to evaluate conditions and to execute basic behaviors (which we call actions). Hybrid architectures can further be classified based on how the knowledge is reresented. A hybrid architecture may be homogeneous if the knowledge is reresented in the same way both at the deliberative level and the oerational one, heterogeneous otherwise. Our aroach follows the heterogeneous one where the deliberative layer is obtained by secifying high level lans (in fact, the Petri Net Plans that we are describing

2 2 Vittorio Amos Ziaro and Luca Iocchi in this aer), while the oerative level maintains numeric information about the state of the robots, integrating different techniques (such as robabilistic localization, dynamic control, etc.). The objective of this aer is to describe a novel reresentation framework for high level robot and multi-robot behaviors, its imlementation on actual mobile robots, and our exerience using such a framework. The roosed framework, called Petri Net Plans (PNP), is based on Petri nets [Mur89], a grahical modeling language for dynamic systems. Our modeling language is one of the many extensions to transition grahs existing in literature. As a difference with such other aroaches, e.g. XABSL [LBBJ04], we clearly distinguish action secification and imlementation, obtaining a framework which ermits easier debugging: first, the semantic is well defined and easily verifiable by automated verification rograms; second, we have a high granularity of actions which are groued by functional roerties and hysical resources used. Moreover, we rovide a rich set of oerators for handling comlex behaviors. There exist other languages caable of handling synchronization constraints (e.g., [SA98, PDPW, Fir89]) or knowledge acquisition (e.g., [GL86, Kon97]), but not many which can handle both. One such language is ConGolog [DLL00] which extends Golog for handling concurrent execution but fails in modeling reactive behaviors. For this reason, Golog was further extended introducing interruts. The resulting language is called RGolog [Rei01]. Our formalism is very rich and includes all of the above mentioned features. It differs from these languages mainly in the way in which the knowledge of the agent is used to reresent the roerties in the environment and in the higher efficiency of lan execution, due to the absence of comutational exensive reasoning rocedures during this rocess. More detailed analysis and comarison with these languages are given in Section 7. The roosed framework has been imlemented and used to control robotic systems in three domains: (i) the RoboCu 4Legged soccer cometitions [IN04], (ii) the RoboCu Rescue cometitions, and (iii) a multi robot foraging testbed for task assignment exeriments based on a token assing aroach [FINZ06]. The remainder of the aer is structured as follows: we first define the syntax for our language using Petri nets in terms of oerators (i.e., actions) and ossible interactions among them. Two tyes of models for non-instantaneous actions are given: 1. ordinary non-instantaneous actions, which allow comlex constructs for action synchronization and failure recovery. 2. sensing non-instantaneous actions, which allow for dynamically sensing roerties at execution time and thus for knowledge acquisition. We then rovide a set of oerators for handling concurrency, conditionals and iterations. In order to give a clear oerational semantics to our modeling language we rovide an execution algorithm. After defining what is a correct execution for a lan, we roof that, if a correct execution is ossible, then the algorithm will achieve it. The extension of the framework to deal with Multi-Agent lanning in rovided in Section 5.

3 Petri Net Plans 3 Imlementation issues are rovided in Section 6, while Section 7 contains a discussion about advantages and difficulties in using such a method on our mobile robotic teams, as well as comarison with other aroaches. Finally, we conclude the aer by illustrating ossible future work. 2 Petri Nets Petri nets are a grahical and mathematical modeling tool [... ] for describing and studying information rocessing systems that are characterized as being concurrent, asynchronous, distributed, arallel, nondeterministic, and/or stochastic.[mur89] (a) (b) (c) Fig. 1. (a) A lace. (b) A Transition. (c) A Place with one token. Petri nets, as a modeling language, grahically deict the structure of a distributed system as a directed, weighted and biartite grah. As such, a Petri net has two tyes of nodes connected by directed weighted arcs (if not labeled we assume a weight of one). The first tye is called lace (Fig. 1a) and may contain zero or more tokens (Fig. 1c). The number of tokens in each lace (i.e. marking) denotes the state of the system. The other tye of nodes, called transitions (Fig. 1b), reresent the events modeled by the system. Transitions can consume or roduce tokens from laces according to the rules defining the dynamic behavior of the Petri net (i.e. the firing rule). More formally, a Petri net can be defined as a tule where: P N =< P, T, F, W, M 0 > P = { 1, 2,..., m } is a finite set of laces. T = {t 1, t 2,..., t n } is a finite set of transitions. F (P T ) (T P ) is a set of edges. W : F {1, 2, 3,...} is a weight function and w(n s, n d ) denotes the weight of the edge from n s to n d. M 0 : P {0, 1, 2, 3,...} is the initial marking. P T and P T = Petri nets are used to model comlex systems that can be described in terms of states and their changes. We can define the state changing behavior (i.e. the marking evolution) in a Petri net by the following firing rule:

4 4 Vittorio Amos Ziaro and Luca Iocchi 1. A transition t is enabled, if each inut lace i (i.e. ( i, t) F ) is marked with at least w( i, t) tokens. 2. An enabled transition may or may not fire, deending on whether related event occurs or not. 3. If an enabled transition t fires, w( i, t) tokens are removed for each inut lace i and w(t, o ) are added to each outut lace o such that (t, o ) F. There exists another tye of arc called inhibitor arc. This arc is reresented as a dashed segment with a small circle (Fig. 7). This connects a lace to a transition and enables it when there are no tokens in the lace. Obviously no tokens are moved when the transition fires. Petri Nets with inhibitor arcs are called Extended Petri Nets. The use of this connector enables the net to test for the zero and gives to these nets the same modelling ower as Turing machines [Pet81]. 3 Plan Reresentation Programming high level behaviors for a mobile robot executing comlex tasks in dynamic, artially observable ad unredictable environments requires a owerful descrition language. The reference scenario in this aer is the cognitive control of a four-legged robot (AIBO) involved in robotic soccer. Such comlex scenario requires to deal with noninstantaneous actions, sensing and conditional actions, action failures. Moreover, since the AIBO robot can indeendently move its legs and its head execution of concurrent actions is also needed. In this section we formally introduce a modeling language for describing robotic behaviors based on Petri nets. The roosed language allows for secifying lans, called Petri Net Plans (PNP), describing comlex behaviors of a mobile robot. These lans are defined by combining different kinds of actions (ordinary actions and sensing actions) using control structures, such as if-then-else, while, concurrent execution and interruts. A Petri Net Plan is a Petri net < P, T, F, W, M 0 > with the following characteristics. 1. Places i reresent the execution hases of actions; each action α is described by a lace corresonding to its initiation (we call it initial lace of α), one corresonding to its execution (we call it execution lace of α), and one corresonding to its termination (we call it termination lace of α); 2. Transitions t i reresent events and are groued in different categories: action starting transitions, action terminating transitions, action interruts and control transitions (i.e. transitions that are art of an oerator). Transitions may be labeled with conditions that control their firing. 3. w(f i, f j ) = 1, for each (f i, f j ) F. 4. M 0 is the initial marking reresenting a descrition of the initial state of the robot.

5 Petri Net Plans 5 In the following we will focus on the structure of a PNP (i.e. considering only the terms < P, T, F >). A Petri Net Plan is formally defined by a set of elementary structures (i.e. noaction, ordinary action, sensing action) and constructs for combining PNP (i.e. sequences, loos, concurrent execution, interruts). Elementary structures. Elementary PNPs are defined as follows: 1. no-action is a PNP defined by a single lace and no transitions, i.e. < { 0 },, > (see Fig.1a), where 0 is both an initial and a terminating lace. Fig. 2. An ordinary non-instantaneous action. 2. ordinary-action is a PNP defined by 3 laces and 2 transitions (see Fig. 2): < { i, o, e }, {t s, t e }, {( i, t s ), (t s, e ), ( e, t e ), (t e, o )}} > where: i is the initial lace. o is the terminating lace. e is the execution lace. t s the transition starting the action. t e the transition terminating the action. In order to model those actions which may be considered instantaneous, we introduce the instantaneous variant of the above PNP: < { i, o }, {t a }, {( i, t a ), (t a, o )}} > where t a is the transition reresenting the event of executing an instantaneous action. 3. sensing-action is a PNP defined by laces and transitions as described in Fig. 3: < { i, e, ot, of }, {t s, t et, t ef }, {( i, t s ), (t s, e ), ( e, t et ), ( e, t ef ), (t et, ot ), (t ef, of )} > where transitions and laces are the same of the revious examle excet for: t et and t ef are, resectively, the transitions ending the action when the sensed roerty is true and when it is false. of and of are, resectively, the laces terminating the the action when the sensed roerty is true and when it is false.

6 6 Vittorio Amos Ziaro and Luca Iocchi Fig. 3. An non-instantaneous sensing action. As for the ordinary-action, we define the instantaneous variant of the sensingaction as: < { i, ot, of }, {t et, t ef }, {( i, t et ), ( i, t ef ), (t et, ot ), (t ef, of )} >. Oerators. Elementary PNPs can be combined by using the oerators sequence, conditional, loos, concurrent execution and interruts. Fig. 4. Sequence of two PNPs. The sequence of two PNPs is defined as follows: given two PNPs Γ 1 =< P 1, T 1, F 1 >, Γ 2 =< P 2, T 2, F 2 > and two laces o1 P 1 and i2 P 2, such that o1 is a terminating state for an action α 1 in Γ 1 and i2 is an initial state for an action α 2 in Γ 2, a new PNP Γ =< P, T, F > is obtained by joining the laces o1 and i2 as follows: (i) P 2 = P 2 \{ i2 }, is the set of laces excluding i2, (ii) τ( i2 ) = {t i ( i2, t i ) F 2 } is the set of transitions following the lace i2, (iii) F 2 = F 2 \{( i2, t ) t τ( i2 )} is the set of edges of Γ 2 excluding the ones coming from i2, (iv) F 1 = F 1 {( o1, t ) t τ( i2 )} is the set of edges of Γ 1 augmented

7 Petri Net Plans 7 by those obtained connecting the lace o1 to the successors of i2, (v) P = P 1 P 2, T = T 1 T 2, F = F 1 F 2, is the union of the sets after the above modifications. The above formulation actually allows for merging two PNPs choosing a terminating lace for an action, an initial lace for another action and join the two nets making such laces to be the same. A grahical reresentation of this oerator is given in Figure 4. i t s1 e1 t e1 o1 t s e t e f t e t o t o f t s 2 t s 3 e2 e3 t e2 t e3 o 2 o3 Fig. 5. Conditional structure. Conditional structures are imlemented though sensing actions: given a sensing action α, three PNPs Γ 1, Γ 2, Γ 3, and three laces: o1 a terminating lace in Γ 1, and

8 8 Vittorio Amos Ziaro and Luca Iocchi i2, i3 initial laces in Γ 2, Γ 3, a new PNP Γ is obtained by joining the initial lace of the sensing action α with o1 and the two terminating laces for α with i2 and i3. The joining oeration is similar to the one described for the sequence oerator and, for maintaining an easy notation, we resent it here only in grahical form in Figure 5. Fig. 6. An indefinite iteration which executes the PNP Γ 1 while the sensed roerty is true. Loo structures are also imlemented through sensing actions: given a sensing action α, two PNPs Γ 1, Γ 2, and three laces: o1 a terminating lace in Γ 1, i1 an initial lace in Γ 1, i2 an initial laces in Γ 2, a new PNP is obtained by joining the initial lace of the action α with t1 and the two terminating laces for α with i1 and i2. The grahical reresentation of this oerator is given in Figure 6. Fig. 7. A definite iteration which executes the PNP Γ 1 n + 1 times. Adding to this structure a control lace marked with n tokens (Fig. 7), we obtain a definite iteration oerator. In this way we can execute n + 1 times a given net. Concurrent execution is defined by adding new transitions and edges: given three PNPs Γ 1, Γ 2, Γ 3, a terminating lace o1 in Γ 1, and two initial laces i2, i3, re-

9 Petri Net Plans 9 Fig. 8. (a) The fork structure. (b) The join structure. Fig. 9. Interrut structure where ossibly Γ 1 is interruted and then Γ 2 executed.

10 10 Vittorio Amos Ziaro and Luca Iocchi sectively in Γ 2, Γ 3, a new PNP is obtained by adding one transitions t fork and three edges ( o1, t fork ), (t fork, i2 ), (t fork, i3 ) to the union of the sets secifying Γ 1, Γ 2, Γ 3. The grahical reresentation of this oerator is given in Figure 8(a). In a similar way we can define an oerator to join concurrent execution: given three PNPs Γ 1, Γ 2, Γ 3, an initial lace i1 in Γ 1, and two terminating laces o2, o3, resectively in Γ 2, Γ 3, a new PNP is obtained by adding one transitions t join and three edges ( o2, t join ), ( o3, t join ), (t join, i1 ) to the union of the sets secifying Γ 1, Γ 2, Γ 3. The grahical reresentation of this oerator is given in Figure 8(b). Interrut constructs are defined by adding a new transition and edges to the execution lace of an action: given two PNPs Γ 1, Γ 2, an execution lace e1 in Γ 1, an initial lace i2 in Γ 2, a new PNP is obtained by adding a new transition t interr and new edges ( e1, t interr ), (t interr, i2 ) to the union of the sets secifying Γ 1, Γ 2. The grahical reresentation of this oerator is given in Figure 9. Labeling transitions. In order to secify external events occurring during task execution, we define a labeling mechanism for transitions in the net. In articular, all transitions may be labeled with conditions which must be verified in order to be fired when enabled. A condition φ on the transition t is denoted with t.φ. If no condition is secified for a transition, we will assume that it is the condition T rue. Sometimes it is useful to set such condition to F alse in the ending transitions to model non-terminating actions. These are usually suorting actions (see for examle, the action texttttrackball in the following examle) that are executed concurrently with a main action that actually determines lan transitions. 3.1 Examle: A simle Robocu 4Legged Striker We will show a simle lan for a Robocu 4Legged Striker. The following examle consists of a model for a robot which must seek for the ball and eventually reach it. We have the following rimitive behaviors: 1. aroachball which is a behavior for aroaching the ball controlling the leg actuators. This action is modeled as a non-instantaneous action. 2. trackball which is a behavior for tracking the movement of the ball with the camera ositioned on the robot s head. This action is modeled as a noninstantaneous action. 3. seekball which is a behavior for seeking the ball modeled as a non-instantaneous action. In Figure 10 we show a lan for this task. The robot seeks for the ball which we assume is not seen. When it finds it, the current state will move to the one where the ball is seen. In this case, the robot will concurrently move the legs to aroach the ball and track its osition with the camera ositioned on the head. When the robot is sufficiently near to the ball, the actions aroachball and trackball will terminate their execution at the same time thus reaching the goal state.

11 Petri Net Plans 11 Fig. 10. A simle attacker from the Robocu Soccer domain. Moreover, if while aroaching the ball the robot looses visual contact with the ball, an interrut will trigger the system to abort the current actions and move to the state where the ball is not seen. This loo will continue until the robot reaches the ball. 4 Plan Semantics In this section we rovide an oerational semantics for the execution of PNPs and we resent an algorithm that correctly executes a PNP, in the sense that it correctly erforms transitions reaching a final state according with the occurrence of external events. The state of an agent during the execution of a PNP is given by its marking. Transitions between the agent states are thus modelled by transitions in the PNP, i.e. by evolution of its markings. We thus give the definitions for executable transitions of a PNP, that allows for defining the notion of execution of a PNP and of correct execution of a PNP.

12 12 Vittorio Amos Ziaro and Luca Iocchi During the execution of a lan, and thus during the transitions we are defining, we assume that the robot is rovided with a set of functions that are able to evaluate its internal state. These functions are used to evaluate the conditions labelling the transitions of the PNP and thus determine when and how it is ossible to erform such transitions. Definition 1. Possible Transitions in a PNP. Given two markings M i, M i+1, a transition from M i to M i+1 is ossible iff t T, such that (i) P, s.t. (, t) F, then M i ( ) > 0; (ii) M i+1 ( ) = M i ( ) 1 for each P, s.t. (, t) F ; (iii) M i+1 ( ) = 1 for each P, s.t. (t, ) F. A ossible transition from M i to M i+1 is denoted by M i M i+1. Definition 2. Executable transition in a PNP. Given two markings M i, M i+1 and a situation at time τ, a transition from M i to M i+1 in the situation τ is executable iff t T, such that a transition from M i to M i+1 is ossible and the event condition φ labelling the transition t (denoted with t.φ) is verified in situation τ. An executable transition from M i to M i+1 in situation τ is denoted by M i τ M i+1. In order to secify the desired states for the system, we introduce the set GoalMarkings(P ) which is a roer subset of the ossible markings that a given PNP P may reach. Definition 3. Executable PNP. A PNP P is executable iff it exists a finite sequence of markings {M 0,..., M n }, such that M 0 is the initial marking, M n is a goal marking (i.e. M n GoalMarkings(P )) and M i M i+1, for each i = 0,..., n 1. Definition 4. Correct execution of a PNP. An executable PNP P can be correctly executed iff there exist a finite sequence of situations {τ 0,..., τ n 1 } and a finite sequence of markings {M 0,..., M n }, such that M 0 is the initial marking, M n is a goal marking (i.e. M n GoalMarkings(P )) and M i τi M i+1, for each i = 0,..., n PNP Execution Algorithm Algorithm 1, resented above, correctly executes a PNP. The algorithm comutes a sequence of transitions {M 0,..., M n } that evolve the system from the initial marking (i.e. M 0 ) to a goal marking (i.e. M n GoalMarkings), according with the sequence of situations {τ 0,..., τ n 1 } occurring in the environment. At each ste it checks if each transition t T can be fired (Algorithm 1, line 4). This requires to verify that: i) the transition is enabled and ii) in the current situation τ current the event condition t.φ (usually a roositional formula) of the transition t is true. The evaluation of a condition (Algorithm 1, line 4) is erformed by activating a corresonding function that evaluates the roerty from the internal state of the robot.

13 Petri Net Plans 13 Algorithm 1 PNP Execution Algorithm 1: CurrentMarking = InitialMarking 2: while CurrentMarking GoalMarkings do 3: for all t T do 4: if enabled(t) eval(t.φ) then 5: if t.hasaction() then 6: handleaction(t) 7: end if 8: CurrentMarking = fire(t) 9: end if 10: end for 11: end while Algorithm 2 The Action Handler rocedure handleaction(t ransition t) 1: CurrentAction = t.getaction() 2: if t.isstart() then 3: CurrentAction.start() 4: else if t.isend() then 5: CurrentAction.end() 6: else if t.isinterrut() then 7: CurrentAction.interrut() 8: end if Recall that we rely on a heterogeneous hybrid architecture (Section 1). This imlies that we reresent knowledge both at an oerational and deliberative level. In general, both reresentations of the knowledge are consistently maintained in a world model which summarizes the current state (e.g. current distance from the ball and reliability of the information). In our framework, the knowledge at the deliberative level is used to evaluate the event conditions in the PNPs. Each time we have to evaluate a condition guarding an enabled transition we query the world model in order to interret the roositions comosing it. For examle, if a condition to evaluate includes the roosition haveball, we will query the world model for the distance to the ball being smaller than a given small value. Thus, if the transition is executable and belongs to an action structure, the rocedure handleaction (Algorithm 2) takes care of aroriately activating or deactivating the related action. The details of how this is done deend on the actual imlementation of the system. Finally, the algorithm fires the firable transition t i udating the marking accordingly to the firing rule. The algorithm correctly executes a PNP if the sequence {τ 0,..., τ n 1 } allows for it, as shown by the following theorem. Theorem 1. If {τ 0,..., τ n 1 } is a finite sequence of situations such that a PNP can be correctly executed, then Algorithm 1 comutes a sequence of transitions

14 14 Vittorio Amos Ziaro and Luca Iocchi {M 0,..., M n }, such that M 0 is the initial marking, M n is a goal marking, and M i τi M i+1, for each i = 0,..., n 1. Proof. We want to rove that Algorithm 1 comutes a sequence of transitions {M 0,..., M n }, such that M 0 is the initial marking, M n is a goal marking, and M i τi M i+1, for each i = 0,..., n 1. Trivially the first marking M 0 is the initial marking (Algorithm 1, line 1). Furthermore, in order for the algorithm to halt, the final marking must be a goal marking (Algorithm 1, line 2). Thus, M n GoalMarkings. The transition from a marking M i to a marking M i+1 is obtained firing (Algorithm 1, line 8) a transition t i. A necessary condition for firing is that t i is enabled (Algorithm 1, line 4). If t i is enabled this means that each inut lace i (i.e. ( i, t) F ) is marked with at least w( i, t) tokens. Since we assume 0 w( i, t) 1 this imlies that P, s.t. (, t) F, then M i ( ) > 0. When an enabled transition t fires according to the firing rule, w( i, t) tokens are removed for each inut lace i and w(t, o ) are added to each outut lace o such that (t, o ) F. Thus given the assumtion that 0 w( i, t) 1, we have M i+1 ( ) = M i ( ) 1 for each P, s.t. (, t) F and M i+1 ( ) = 1 for each P, s.t. (t, ) F. Thus, each transition erformed by the algorithm is a ossible transition. Finally, the algorithm ensures executable transitions checking that t.φ is verified at the current situation τ before firing t (Algorithm 1, line 4). 5 Multi-Agent Plans Describing multi-agent lans has been considered either as lan sharing (or centralized lanning), where the objective is to distribute a global lan to agents executing them, or as lan merging, where individual lans are merged into a global lan (see [Dur99] for details). In our work we followed the centralized lanning aroach that has been easily imlemented in our formalism as described in this section. A Multi-Agent PNP, for agents {1,..., n}, can be defined as the union of n single agent PNPs enriched with synchronization constraints between actions of different robots. When writing a Multi-Agent lan, the syntax is not much different from the single robot case, excet that actions are labeled with a unique id for the robot. Given n single agent lans aroriately labeled {P NP i =< P i, T i, F i >}, the simlest way to define a Multi-Agent lan is: where: M P = n i=1 P i M T = n i=1 T i M P NP =< M P, M T, M F >

15 M F = n i=1 F i Petri Net Plans 15 Such a Multi-Agent lan consists simly of n indeendent lans. When dealing with Multi-Agent systems, the main issue is how to reresent the interactions among actions erformed by different agents (i.e. among lans). The Multi-Agent lan, as reviously defined, fails to cature such interactions and may result in the execution of conflicting actions. In articular, we want to be able to order actions across lans so that overall consistency is maintained and conflicting situations are avoided. For examle, consider two robots cooerating in a foraging task (see the Multi- Robot testbed in Section 6).They must at first hel each other to allow one of the robots to grab the object, then this robot can transort the object to a collect oint, while the suort of the second robot is not necessary anymore, and it should move away for not interfering with the first robot. Action synchronization is thus needed first for coordinating the grab action, then to communicate that the suorting robot is out of the way. In our aroach, we use action synchronization to avoid unsafe interactions. We will assume that the agents will be able to communicate through a reliable channel and thus to send and receive synchronization messages. The synchronization oerator is defined as follows where: i, j {1,..., n} i j SY NC =< { c }, {t ci, t cj }, {(t ci, c ), ( c, t cj )} > The synchronization oerator is used to add temoral constraints in the execution of the actions in a multi-agent lan. For examle, Figure 11 describes a constraint between the execution of two actions erformed by agents R1 and R2. The figure shows the reresentation of a constraint indicating that the action of agent R1 must start after the termination of the action of agent R2. While in Figure 12 we show how to reresent the simultaneous execution of two actions by two agents R1 and R2. Note that network delay may affect exact simultaneous starting of the two actions; however, the formalism ensures that the two actions will be generally executed at the same time by the two robots. Using the synchronization oerator, we can thus write Multi-Agent PNPs in which all the conflicts in the actions are solved. Moreover, given a Multi-Agent PNPs, we can automatically roduce the single-agent lans by isolating the ortion of the lans relative to each robot and relacing synchronization oerators with communication actions. In articular, the synchronized Single-Agent lan S P NP i = < S P i, S T i, S F i >, will be the minimal net such that: P i S P i T i S T i F i S F i (1)

16 (, t send(ti,t j)) S F i (t i, ) S F i (2) 16 Vittorio Amos Ziaro and Luca Iocchi t R2 e i R2 t R2 s e R2 o R2 c R1 R1 R1 t t R1 i s e e R1 o Fig. 11. Two actions of different agents which must be executed in sequence. t R2 e R2 i t R2 s e R2 t R2 e R2 o c c R1 t e R1 i t R1 s R1 e t R1 e R1 o Fig. 12. Two actions of two different robots which must start at the same time. t i T i M P ( t j T j i j (t i, ) M F (, t j ) M F ) S P i t send(ti,t j ) S T i

17 (t rec(ti,t j ), ) S F i (, t i ) S F i (3) Petri Net Plans 17 t i T i M P ( t j T j i j (t j, ) M F (, t i ) M F ) S P i t rec(ti,t j ) S T i Condition 1 states that the synchronized lan must include the original single agent one. Condition 2 and Condition 3 state resectively that action communication rimitives and message recetion events must be added to the lan. When the transition t send(ti,t j ) is enabled the agent i will fire it and thus erform an instantaneous action which sends a synchronization message relative to the transitions t i and t j to agent j. When agent j receives such a message will store it and fire t rec(ti,t j ) when enabled. R2 sendsync t R2 sendsync R2 i t R2 s e R2 t R2 e R2 o t R2 e t R2 recsync R2 recsync t R1 recsync R1 recsync R1 t e R1 i t R1 s R1 e t R1 e R1 o R1 sendsync t R1 sendsync Fig. 13. The single agent lans extracted from the Multi-Agent one in Fig. 12

18 18 Vittorio Amos Ziaro and Luca Iocchi An examle of such a rocess is shown in Figure 13. Here the Multi-Agent PNP of Figure 12 is divided in two PNPs for the two agents, and the synchronization oerator is relaced by Send and Receive actions. The synchronized single agent lans are then executed as shown in Section 4. The communication rimitives will guarantee the consistency of the distributed Multi-Agent lan. 6 Imlemented Systems The roosed framewok has been imlemented and used to control different robotic systems in different domains. A lan executor for our formalism has been imlemented with a set of tools for designing and debugging lans. Plans are executed also according to the events occurring in the environment and to the state of the robot, which reresents the agent s knowledge about the environment. During the execution of a PNP, the robot makes use of a set of functions that can access the internal state of the robot and return truth values about relevant roerties for the execution of the lan, and information about the state of knowledge about such roerties. For examle, the robot may use a function returning whether the osition of the ball is known (i.e. the ball is visible to the robot s sensors), and another function returning an evaluation of the fact that the ball is close enough to be kicked. Plans can be generated by an off-line lanner (currently without concurrency) or edited by hand. In the latter case we use an available oen-source grahical tool, Jar 3, which can generate an aroriate standard XML format (PNML). If transitions and laces are correctly labeled to meet the secification of the Petri Net Plan the PNML code is arsed to roduce executable reresentation on the robot (PET files). Moreover, Jar has been extended in order to debug lans on-line. During lan execution, the robot can roduce (or stream through a TCP/IP connection) a log containing the information regarding the deliberative rocess. This log can be arsed by our tool to view the evolution of the Petri Net Plans, allowing for easily identifying loos or wrong behaviors, and roviding a quick and user friendly lan debugging interface. The Petri Net Plans are used for designing the behaviors of the Robocu 4Legged team S.P.Q.R. Legged 4 since 2004 [IN04]. In this league, two teams of four autonomous Sony Aibo, lay a soccer match on a rectangular field with a set of landmarks in known ositions. The aroach has been successful in modeling behaviors in such a highly dynamic and noisy environment. The robots were able to handle reactively raid state changes while demonstrating a roactive behavior allowing for a good erformance in the cometitions. On the other hand, Petri Net Plans have been emloyed to design behaviors for quasi-static environments, where the focus is on information gathering. This is the 3 htt://jar.sourceforge.net/ 4 htt://sqr.dis.uniroma1.it/

19 Petri Net Plans 19 case of the Real Robot Rescue cometitions where the goal is to exlore and seek for victims in an unstructured environment (i.e a disaster scenario like a building after an earthquake). The S.P.Q.R. Real Rescue team 5 adots the Petri Net Plans since 2005 to control their rescue robots. The use of Petri Net Plans to model urban search and rescue scenarios has been one of the toics of the ractical sessions at the Rescue Robotics Cam 6. Finally, we used the Petri Net Plans to design a set of exeriments for a task assignment technique based on token assing 7 [FINZ06]. Our alication scenario was formed by a set of robots that need to erform a synchronized oeration on a set of similar objects scattered in the environment. In order to achieve such a comlex foraging task it is necessary to be able to synchronize actions across lans as shown in Section 5. In articular, we imlemented the communication through TCP/IP triggering events based on recetion of aroriate sync messages. 7 Discussion The exerience in using Petri Net Plans for rogramming our robots has been very effective, roviding for many advantages over other techniques, as well as some difficulties that we have dealt with. In this section we want to analyze the main advantages and ossible drawbacks of this formalism. The main advantage of the Petri Net Plan framework is the clear definition of the modeling language and of its semantics in terms of Petri nets. We have chosen to adot the Extended Petri nets because it is the simlest model necessary to secify the constructs we needed to model. Moreover, if the definite oerator is not used, PNPs are a subset of the basic Petri nets. Using such a model, rather than one of its many extensions, guarantees us the ossibility to use standard tools to evaluate roerties of the nets such us liveness and reachability of the goal states. The gain in using Petri nets is that we have a formal method to distinguish action imlementation and secification. Moreover, the grahical reresentation of Petri nets allows for an easy understanding and debugging of the lans which seeds u the develoment rocess. High exressiveness of PNPs thus allows for effectively caturing and dealing with most of the situations encountered when designing autonomous robots. On the other hand, such high exressiveness is also a limitation when designer is interested in using lan generation techniques. Therefore, it is necessary for the user to manually write the lans for the agents or enhance automatically generated lans for handling concurrency. Although we rovide an oerational semantics for our lans, in order to have a clear secification of the behavior of the robots during execution, it may still be 5 htt://sied.dis.uniroma1.it/ 6 htt://sied.dis.uniroma1.it/cam/ 7 A video of the exeriment is available at: htt:// farinell/video/cooforaging-commentary.wmv

20 20 Vittorio Amos Ziaro and Luca Iocchi very difficult to debug lans when their size grows and the deendency across them becomes very comlex. This is esecially true for Multi-Agent lans. At the moment we rely on the user to design correct lans and to solve related roblems. The roblem of lan correctness is a common roblem in behavior design and has been addressed in the literature in different ways. In articular, we can roughly categorize related aroaches in three main classes. 1. Hand-written behaviors directly coded in robot rogram. In this case there is no exlicit reresentation of actions and lans. It is thus very difficult to design, write and debug lans. 2. Hand-written behaviors using behavior oriented languages (e.g. Xabsl [LBBJ04] and Colbert [Kon97]). These languages consist of behavioral routines, but, although a framework for designing lans is defined, there is no formal secification and thus it is not ossible to verify roerties of these rograms/behaviors. 3. Logic-based rogramming (e.g. Golog [Rei01]). These are declarative languages with reasoning abilities. In articular, in these frameworks behaviors are secified in a high level rogramming language based on some formal system (e.g. Situation Calculus). Such rograms allow not to secify all the details of the rogram which are comuted by a reasoning system. The main drawback of such aroaches is that they are comutationally very exensive and are inadequate to control very comlex real time systems. Our aroach lies between the second and the third category. On the one hand, as for other behavior oriented languages, we rovide for an efficient framework for designing, writing, executing, and debugging lans, which exlicitly reresents actions and lans. On the other hand, as in logic based rogramming, we rovide a formal secification of our lans which allows for imlementing reasoning and verification rocedures. In fact, we are working on integrating formal action secification in the PNP in order to verify roerties of lans such as correctness and termination. Our formalism differs from Golog language also in the reresentation of the roerties in the environment. In PNP it is ossible to model only the knowledge (or the absence of knowledge) of the agent about the environment, while it is not ossible to model what is actually true in the environment. In other words, the agent acts only on the basis of what it knows about the environment: knowledge is acquired either by direct ercetion (i.e., analysis of sensor data) or by the assumtion that the effects of an action hold when this action has been correctly executed. To this end we make exlicit use of sensing actions (or knowledge roducing actions), as in [SL93, DGINR97]. 8 Conclusions and Future work In this aer we have resented a modeling language to design deliberative layers of agents/robots based on a heterogeneous hybrid architecture which inhabit a dynamic, artially observable and unredictable environment.

21 Petri Net Plans 21 As already mentioned, this modelling tool has been deely tested and imlemented in different scenarios. We can thus enforce the adequacy of the aroach based on exerimental evidence. In articular, we have seen that the high flexibility of the language, the modular develoment and the easy to use tools hel the user in the design task and our many students that used the tool to write, execute and debug comlex behaviors quickly and with a small effort. The most critical roblem we faced when secifying PNPs was to define a semantics in order for the user to have a clear secification of the behavior of the robots during execution. This roblem was solved by defining an oerational semantics and roving the correctness of its execution. Nevertheless, it may still be the case that conflicts arise when executing arallel lans. As future work, we are lanning to imlement verification and lan assistant tools in order to guarantee the safeness of lans. In order to do this, we will need to rovide a formal descrition of actions using some action secification language. In articular, we are studying a more formal relationshi between the resented modelling language and logic-based formalisms for reasoning about actions (such as, ConGolog [DLL00]). In this direction, we are currently investigating a ossible extension of a formalism for reasoning about actions based on Descrition Logic [BCM + 03], that has been reviously used for generating high-level rograms for mobile robots [INR00, ILNR04, INR04]. References [BCM + 03] Franz Baader, Diego Calvanese, Deborah L. McGuinness, Daniele Nardi, and Peter F. Patel-Schneider, editors. The Descrition Logic Handbook: Theory, Imlementation, and Alications. Cambridge University Press, [DGINR97] Giusee De Giacomo, Luca Iocchi, Daniele Nardi, and Riccardo Rosati. Planning with sensing for a mobile robot. In Proc. of 4th Euroean Conference on Planning (ECP 97), [DLL00] G. DeGiacomo, Y. Leserance, and H. J. Levesque. Congolog, a concurrent rogramming language based on the situation calculus. Artificial Intelligence, 121(1-2): , [Dur99] Edmund H. Durfee. Distributed roblem solving and lanning. In G. Weiss, editor, Multiagent Systems: A Modern Aroach to Distributed Artificial Intelligence, ages MIT Press, [FINZ06] [Fir89] [GL86] [ILNR04] A. Farinelli, L. Iocchi, D. Nardi, and V. A. Ziaro. Assignment of dynamically erceived tasks by token assing in multi-robot systems. Proceedings of the IEEE, Secial issue on Multi-Robot Systems, To aear. R. James Firby. Adative Execution in Comlex Dynamic Worlds. PhD thesis, Yale, M. P. Georgeff and A. L. Lansky. Procedural knowledge. In Proceedings of the IEEE Secial Issue on Knowledge Reresentation, volume 74, ages , L. Iocchi, T. Lukasiewicz, D. Nardi, and R. Rosati. Reasoning about actions with sensing under qualitative and robabilistic uncertainty. In Proc. of 16th Euroean Conference on Artificial Intelligence (ECAI 04), ages , Sain, 2004.

22 22 Vittorio Amos Ziaro and Luca Iocchi [IN04] Luca Iocchi and Daniele Nardi. SPQR-Legged Team In RoboCu 2004: Robot Soccer World Cu VIII. Sringer-Verlag, [INR00] L. Iocchi, D. Nardi, and R. Rosati. Planning with sensing, concurrency, and exogenous events: logical framework and imlementation. In Proc. of KR 2000, [INR04] L. Iocchi, D. Nardi, and R. Rosati. Strong cyclic lanning with incomlete information and sensing. In Proc. of 4th Int. Worksho on Planning and Scheduling for Sace, Darmstadt, Germany, [Kon97] K. Konolige. COLBERT: A language for reactive control in sahira. Lecture Notes in Comuter Science, 1303:31 50, [LBBJ04] Martin Ltzsch, Joscha Bach, Hans-Dieter Burkhard, and Matthias Jngel. Designing agent behavior with the extensible agent behavior secification language XABSL. In Daniel Polani, Brett Browning, and Andrea Bonarini, editors, RoboCu 2003: Robot Soccer World Cu VII, volume 3020 of Lecture Notes in Artificial Intelligence, ages , Padova, Italy, Sringer. [Mur89] T. Murata. Petri nets: Proerties, analysis and alications. Proceedings of the IEEE, 77(4): , [PDPW] Barney Pell, Gregory A. Dorais, Christian Plaunt, and Richard Washington. The remote agent executive: Caabilities to suort integrated robotic agents. [Pet81] James Lyle Peterson. Petri Net Theory and the Modeling of Systems. Prentice Hall PTR, Uer Saddle River, NJ, USA, [Rei01] R. Reiter. Knowledge in action: Logical foundations for describing and imlementing dynamical systems. MIT Press, [SA98] Reid Simmons and D. Afelbaum. A task descrition language for robot control. In Proceedings Conference on Intelligent Robotics and Systems, October [SL93] Richard Scherl and Hector J. Levesque. The frame roblem and knowledge roducing actions. In Proc. of AAAI-93, ages , 1993.