A New Version of the Economic Metaphor of Politics for the Coalition Formation of a Robot Colony based on the Opponent Strategy

A New Version of the Economic Metaphor of Politics for the Coalition Formation of a Robot Colony based on the Opponent Strategy
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   1    Abstract  The variation version of the Economic Metaphor of Italian Politics [3] [4] [5] [6] [10], an architecture that loosely takes inspiration from the political organizations of democratic governments, following the example of Italian government, and providing a solution for the coordination of a spare colony of robots, is competent to allow the coordination of the behaviors of a team of four robots in order to play soccer in the robocup competition. The development of an evolution of Economic Metaphor of  Italian Politics is now outlined. This new approach proposes a mechanism to make a new coalition caused by the failure of the government strategy and by a general inefficiency of the whole colony during the reaching of the mission targets, such as goals scored, faults committed and other soccer  parameters (game evolution, score, time left, past team coalition performances). The main characteristic of the  frameworks proposed lies in its dynamic reconfigurability in order to adapt the robot colony behaviors to high dynamic environmental changes choosing from time to time the best coalition capable to apply the most suitable soccer strategy, (from an extreme offensive to a total defensive), for the current game situation. To validate the effectiveness of our approach we have realized a framework based on the  MissionLab robot simulation software developed at the  Mobile Robot Lab of the Georgia Institute of Technology and we have transferred this framework inside the OPEN-R environment of the team of four Sony Aibo Ers-7 Robots. I.   I NTRODUCTION   The problem of the coordination of a robot team for complex tasks in dynamic and not predictable environments has been studied in the literature by many researchers [10] [11] [13] [14] [15] [16]. A Robots agency can be efficiently used for many difficult tasks, because it can complete an assigned task more rapidly than a single agent by separating the task into sub-tasks and executing them simultaneously. Two main methods have been proposed in the literature: the first is the centralized approach while the second is the distributed approach [2] [9]. If we suppose to use the second approach, we need to decide how we can make the robots able to get organized and, moreover, how can they reproduce this organization during the time? In this report, we describe a method for coordinating a team of robots involved in playing soccer, a domain where the dynamic nature plays a key role,  based upon a metaphor of politics, using economic methods for coalitions regeneration. A robots agency playing soccer, needs a high level mechanism of coordination among the components of the team, in order to solve difficult problems as, for example, the ball passing among such as the robots of the team. In this paper we varied E-MIP architecture [3] [4] [5] [6], an hybrid and dynamic architecture to coordinate a robot team that we have been developing in the last years, introducing a new economic-based approach for the regeneration of the coalition according to the current trend of the team during the match, and to the performance obtained under the previous strategies applied by the various governments, allowing each robot to dynamically choose the  best one. Our economic approach took inspiration from the works of many researchers, like [1] [8]. The proposed solution is an hybrid since it adopts one centralized, but at the same time distributed method among the government members, deliberative planner and several agents with reactive and deliberative capabilities. A.   Previous Work Many researchers have developed locally reactive,  behavior-based systems to carry out simple tasks; a large number of these simple systems have been extended to more complex task domain. Arkin et al. [8] present a flexible,  behavior-based, software architecture for combining deliberation and reactivity. Parker [2] introduces a temporal division of tasks to allow f ault-tolerant multi-robot cooperation. A particular quotation must be dedicated to economic approaches for assigning tasks in a multi-robot team: developed a distributed market-based architecture, in which self-interested agents can compete for task assignment through revenue-cost models, so that maximizing individual A New Version of the Economic Metaphor of Politics for the Coalition Formation of a Robot Colony based on the Opponent Strategy Antonio Chella †, Rosario Sorbello †, Giacomo Grecomoro, Vito Pellegrino Dipartimento di Ingegneria Informatica Università di Palermo – Italy † chella@unipa.it sorbello_rosario@unipa.it Keywords : robot colony, multiagent system, coalition formation, opponent strategy, recognition   MMAR2006 12th IEEE International Conference on28 - 31 August 2006 Mi dzyzdroje, PolandMethods and Models in Automation and Roboticsę IEEE Conference Number: 11624  609   2 profit has the effect of moving the team toward the globally optimal solution. Toledo et al. [1] developed a framework in which robots cooperate signing contracts, which they can drop at any moment, paying a penalty, if in the current situation the conditions of a contract are no more favourable. II.   T HEORETICAL B ACKGROUNG   The E-MIP framework considers a colony composed of H robots and M political parties, with  H  M  ≤  to guarantee the  presence of at least one robot for every party. Within this framework a set of political issues is associated with every robot, which may express, for example, the individual’s attitude towards risk, its dependence on reactive or deliberative behavior, its exploration proclivities, or interest in object recovery. The robots’ attitudes towards these issues are represented over the range [-1, 1], where 0 means don’t care, -1 absolutely not, and 1 absolutely yes. Let E={-1,0,1} be the set of issue values. Each party is represented by an ideal  prototypical robot, standing for the central positions with respect to the political issues that characterize the party. Each robot is identified by N features; for each robot i  and party j there is a vector of n issues:  Ri  I  , P j  I    ∈   n  E   where i  = 1…H; j = 1…M; P = party and R = robot; with n  E   we call the set of column n vectors whose components belong to E. As an example to describe our model, we consider 3 issues which are identified with the following terms and meanings: –   Welfare :  Energy of the robot    –   Defense :  Attitude towards risk    –   Labor :  Amount of work   Every issue is weighted by a non-negative coefficient (from 0 to + ∞ ), where the coefficient represents the intensity or the strength of the issue. Every robot i  R  and party  j P  is represented by a vector with n components:  Ri Rii  I S  R ⋅=  , P jP j j  I S P ⋅=  (1) where  Ri S   , P j S   are diagonal n × n matrixes containing the weights of the robots’ attitudes towards the issues and of the  parties issues respectively; i  R  and  j P  are representative of a robot and of a party in a multi-dimensional space .  A.   Voting Process The voting process consists of two steps. The first step is Cluster Identification, where classical clustering techniques can be applied to our problem for the identification of the membership groups. The literature provides several candidates; in particular we focus on Voronoi tessellation. In the E-MIP framework, the cluster identification step groups the robots of the colony on the basis of their party membership; this choice is based on the consideration that every robot maintains a political orientation depending on the closest aligned political party according to the issues. We remark that parties and robots live in the same space, named ROBOT ISSUES SPACE . We say that a robot i  R  “belongs” to the  party  j P  if the following condition is satisfied: { } k  ,ik  j ,i ji d mind P R =⇔∈  k = 1,2,…M (2) where k  ,i d   is the euclidean distance between the robot i  R  and the party k  P  in the ROBOT ISSUES SPACE. B.   Coalition Formation   The formation of a political coalition which constitutes the new government is made with the support of a 1-dimensional space, the POLITICAL IDEOLOGY SPACE that is represented on the real axis, so that the subsequent refinement of the position allowing replace of the robot itself to the right or to the left of the voted party’s position. A political mass  j ,i m  is associated with each robot i  and represents its weight within the voted party  j ; the calculation of this mass is based on the following function: ∑∑= ≠ k  j ,k ikj ,k   j ,i d d m   if   i voted for   j  , 0 otherwise  (3) where the index k includes all the robots of the colony which expressed a vote for the j party. This center of mass is obtained using an analogous form derived from classical physics: ( ) ∑∑⋅= i j ,iii j ,i  jCM  mr mr   (4) where the index i describes all the robots of the colony which voted j and subsequently i r  1  represents the position of the robot i in the POLITICAL IDEOLOGY SPACE  axis. C. Role Determination In our simulation, we choose the following government roles: Prime Minister PM), Minister of Defence (MD), Minister of Communications (MC), assigned n the basis of the following rules: the PM is chosen from the robots belonging to the winning party, while the MD and the MC are chosen among the robots belonging to the winning coalition which have not had previously a governative role. Representing respectively with ( ) PM k  r   , ( )  MDk  r   and ( ) CM k  r   the positions of the robots which satisfy these conditions, and with CM  r   the position of the center of mass of the winning party, the PM role is assigned to the robot i  closer to the CM  r   center of mass, the 610   3MD role is assigned to the robot i  positioned to the rightmost extremity of the coalition, and the MC role is assigned to the robot j positioned to the leftmost extremity of the coalition: ( ) CM PM k k PM ii  r r minr PM  R  −=⇔=  (5) ( ) CM  MDk k  MDii  r r maxr  MD R  −=⇔=  (6) ( ) CM  MC k k  MC  j j  r r minr  MC  R  −=⇔=  (7) 1  Let  x,y  be vectors in the Robot issues space. Then their squared Euclidean distance is given by ( ) ( )  y x y x y x  T 2 −−=−  Let ( ) ( )  x M  M  x f r   T  L R  −== , ( ) ( )  y M  M  y f s  T  L R  −==  be the  points of the POLITICAL IDEOLOGY SPACE axis in which  x  and  y  are mapped by  f . Then the distance between r and s on the POLITICAL IDEOLOGY SPACE axis is related to the difference vector  x-y  by: ( ) ( ) ( ) ( )  y x M  M  y M  M  x M  M sr   T  L RT  L RT  L R  −−=−−−=−   This formula relates r  ’s values with k  , j d   values.  D. Conduct Business The robots forming the new government produce behavior to achieve their common goals in agreement with the underlying political ideologies of their coalition. The political ideologies are represented by a strategy that the robots must adopt. In the E-MIP framework, two fundamental strategies are used: a leftist progressive (typically reactive) and a right-wing conservative (typically deliberative). In general, the government coalition is constituted by several parties for which these two strategies are the extremes of an overall methodology which changes its characteristics depending on the formation of the government. A right-center or left-center government will favor either a progressive or conservative strategy based on the weight given to the right or the left components during the formation of the government coalition.A strategy is characterized by a set of parameters which identify various aspects of the robot’s behavior; each  parameter has values along a continuous interval whose extremes (lower and upper) are associated with the left and right strategies. For every parameter s, for each of M parties there is an associated value so that  M  j21  s...s...ss  ≤≤≤≤≤  where j represents the generic party and 1 s ,  M  s  identifies the two extreme parties. The winning coalition is consist of '   M    parties with  M  M  '  ≤  The parameter c s  is only affected by the parties that form the coalition, where they act on the basis of their relative weight within the coalition. Its value is calculated as a weighed average of the parameters of the coalition parties: ∑ ⋅= k k k c  sas  (8) where k   refers to the parties which form the coalition. The k  a  weight associated with the k-th  party is obtained by taking into account the k  V   votes which it received with respect to the total votes of the coalition: ∑= h hk k  V V a  (9) Mini-Crisis . A mini-crisis is a mechanism which allows the  partial replacement of the government with new robots  belonging to the existing coalition and business is carried on using the same strategy. This mechanism eliminates the need for the election of a new government and works to solve inefficiencies like death, damage, or excessive loss of energy of any current government members, which would negatively affect the behavior of the entire colony. A robot fault/failure requires a change in the Roles Matrix; for instance if the elected robot i-th cannot cover its role k-th any longer, then the matrix element (k, i) is replaced with a zero value. A mini-crisis is generated when an operating parameter exceeds its limits as well, for instance when the Welfare (which could  provide information about the robots’ available energy), falls  below a critical threshold. A mini-crisis is not as critical as a full re-election that would stress the existing coalition, being the rejecting of the current strategy used, even if the overall colony behavior was acceptable. Re-election . The re-election mechanism allows the colony to either reconfirm the previous coalition or change it completely. A re-election is normally caused by the expiration of a fixed time assigned for the government to complete the entire mission ( TIME OUT ), or under exceptional circumstances for evident deficiencies in the performance of the colony (  NO CONFIDENCE ), that is not imputable to a single robot but rather to the governing strategy. For instance if mini-crises occur frequently then there is something wrong in the adopted  policy and a re-election needs to be conducted. III.   A PPLICATION TO A R OBOTIC S OCCER T EAM   In order to apply the E-MIP model to a robotic soccer match, we are going to use a team composed by four AIBO ERS-7 robots. The tests had we already carried out inside Mission Lab software [3] [5] [4] [10], were in fact concerned with missions of bombs searching and defusing. These tests  proved that the performances obtained by the colony were optimal, since the robots dynamically adapted their political  positions to the results of the mission, voting from time to time the coalition which granted the best results. The same model can be applied to a robotic soccer team. First, we need to change the issues of the robots; for this application, we selected the following ones (Fig 1,2): •   Attack , the attitude to attack; •   Protection , the attitude to defence; •   Aggressiveness , the attitude to commit faults. 611   4  Fig 1.  Progressive Government. Fig 2.  Conservative Government. IV.   C OORDINATION   The E-MIP is responsible for implementing a distributed coordination protocol for dynamic task assignment according to the current situation of the environment. We have experimented the adaption of the Economic Metaphor of Italian Politics (E-MIP) [10] carried out by each robot to the game of soccer, in such a way that every robot will be equipped with voting ability and express ) its political  preference (based on the evaluation of the actual situation on the field. The comparison among several preferences will carry to the election of a government, that will lay down the law for all the members of the team. For example, the head of the government will be able to decide the game strategy and give to the remaining robots orders like the passing of the ball. In the phase of re-election of the government one should keep into account efficiency of the previous governments so as to make the political preferences of every robot move in the successive elections. V.   C ASE S TUDY   In order to validate the architecture proposed, we modified and used it in a multi-robot application: Robocup Four Legged. Every issue is weighed through a non negative coefficient representing the intensity of the issue. The heterogeneity of the robots inside the colony is described by two functions, attitude to defend and to attack; for example one robot could  be more or less inclined to play the forward or defender role, while another one could be more or less inclined to kick the  ball in order to score a goal. Fig 3. The FSA adapted to Robocup domain. The architecture foresees at the highest level of abstraction the four macro-states showed in the figure 3, that will be explained in detail in the next sections. A.   Election This first state can be divided into sub-states, each one representing a different phase of the entire process; we will describe these states below: 1)   Voting Process Each robot is able to know always its absolute position inside the game field, and to communicate its position to the other members of the team. Each agent is also qualified to calculate the ball and the opponent positions inside the soccer pitch. Fig 4. The Election Phase.  2)   Government Formation The new government will be formed by the winning political  party, that is the most voted one. B.   Determining Roles The PM role is then assigned to the robot closest to the winner  political party, the MD role is assigned to the robot of the Winner Political Party Election Strategy Replacment   Role Player DeterminationTeam Strategy Selection   Opponent Team Strategy Recognition   612   5second political party and the MC role to the third political  party . C.   Conduct Business The robots forming the new government will adopt a behavior in the mission’s management according to the strategy of the winning political party. They are 4 and the choice of the strategy determines also the formation of the members of the team in the soccer field, and each has its own strategy decided by the Prime Minister: •   P1 Strategy (Extreme Progressive) → We have 3 forwards and 0 defenders (Breaking down the opponent area); •   P2 Strategy  (Offensive) →   We have 2 forwards and 1 defenders (Forward passing of the ball); with one of the forwards with the role of supporter in order to pass the ball; •   P3 Strategy  (Defensive)   → We have 1 forward and 2 defenders (Protection of the goal keeper Area); •   P4 Strategy  (Extreme Conservative)   → We have 0 forwards and 3 defenders (Total protection of the goal keeper Area). Fig 5. The 4 Possible Government’s Strategy. This last state is responsible for the effective updating of the  political orientation of the robots in the robot issues space. The robots will use the value of the function Y to update their  position, approaching or rejecting the running government  proportionally to their satisfaction or dissatisfaction degree. VI.   T HE O PPONENT T EAM S TRATEGY R ECOGNITION   In the following paragraph we will explain the choice that allows the realization of the behaviour module for the Dinfobot Sicilia project. The power of this architecture, that consists in the division of the generic problem of playing a soccer game into smaller different problems, depends on this division, that allows the various teams’ components to carry out a job in an independent way. The method we used to detect the opponent strategy consists in identifying the zones most frequently occupied by the opponent robots and the ball shifting from the beginning of the match. From the collected data it is possible to predict the zones that will be occupied by the opponent. The study of the opponent strategy is applied into the context of the E-MIP architecture which determinates the way the different political parties are organized to create government coalitions. Using the political concept with the E-MIP architecture, it is possible to adapt the dynamic strategy to every situation. The goal of this study is to improve the  performances of a robotic team by supplying an adequate reaction to the different opponent tactics. In fact, an excellent robotic soccer team has to change its strategy depending on the opponent team‘s behaviour. The E-MIP adapted to the coordination of a soccer robots’ team will care about the opponents’ playing strategy optimizing the services and the strategy dynamism. Fig 6. The FSA of the new E-MIP’s version.   The new version of the E-MIP architecture is characterized by a  Finite State Automation (FSA) . It is different from the  previous architecture, in fact a new state regarding the estimation of the opponent strategy has been introduced. The figure 6 illustrates the new state inserted in the E-MIP architecture, called “Opponent Policy Estimation”. The  process starts with the election step, followed by the determination of the roles and the creation of the policy. The conduct business state is influenced by the state responsible of the estimation of the opponent strategy; the process then continues as in the previous version of E-MIP. A.   The Determination of the Opponent’s Strategy In order to the opponent game strategy it is necessary to have a robot store, a lot of information and use it at the same time. So a new role in the E-MIP architecture has been inserted: the Super Minister’s role. It is responsible of inspecting the behaviour of the opponent team with its companions’ help. The robots can communicate among themselves and every field player has dynamic role, except the goalie that has a fixed role, for this reason, the role of Super Minister is assigned to him, in fact he can receive and send messages to the companions of his team without any  problems. The goalie, in fact, has a better view of the soccer field and positions of the robots. The other robots have the task to supply the Super Minister, with all the information useful to determine the opponent strategy as: •   The position of the opponent robots; •   The position of the ball at t time; •   The current robots’ position; •   The current ball’s position. 613
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