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Thinking as One: Coordination of Multiple Mobile Robots by Shared Representations Ashley Tews and Gordon Wyeth Computer Science and Electrical Engineering Department University of Queensland Brisbane, Australia. environment states, this is difficult when the objects in the environment are dynamic.

Abstract This paper addresses issues in developing a coordination system for mobile robots in a hostile environment. Sharing a common representation of the environment improves the ability to plan future environment states. It is difficult to make plans in hostile environments, and a robust method must be used if coordination is required between the robots to carry out their goals. The Multi-Agent Planning System (MAPS) is described that addresses these issues. Performance is examined in the highly dynamic robot soccer environment and demonstrates MAPS as a viable method of providing robot coordination.

1

Introduction

When multiple mobile robots are expected to cooperate, they should work together towards a common goal without interfering with each other physically. There are many issues about the environment, goals, and robot architecture that need to be addressed before efficient coordination can be achieved. Dynamic, hostile environments require robust coordination strategies to be developed for the common goal of the robot team to be achieved. Robots need to avoid other robots (whether friendly or hostile), and ensure the individual sub-goals of members of the team are complementary. Possibly the most important determining factor for the robot’s effectiveness is the ability to acquire information with regard to the environment. Information may be acquired through sensors or by communication with other robots. The information needs to be sufficient not to confuse environment states, and not overwhelming in terms of processing required to make sense of it. If the robots need to communicate information between each other, the robots clearly need to represent the information in the same fashion and from the same reference frame. The ability to represent information in a similar fashion is also important for the mechanism that plans robot actions. Better coordination of actions relies on the decisions to be made on a common representation of the environment state. Since planning involves considering future

MAPS (Multi-Agent Planning System) addresses the issues of finding complementary sub-goals for multiple mobile robots in dynamic environments. It analyses the environment and remodels it using potential fields to provide an abstracted virtual environment. Sub-goals are extracted from this information and provided to the navigation module as a "plan-by-communication" [1]. The use of potential fields is important in MAPS to model not only the physical environment, but also abstract features such as the effect that objects have on the environment. The resulting system produces robust, emergent coordination between robots in highly dynamic test environments. The system has been extensively tested in a hostile and highly dynamic domain: robot soccer. Robot soccer provides a challenging testing ground for multi-robot coordination since it resembles human soccer where the best teams have good coordination strategies rather than just talented players. The next section discusses the impact of environment information gathering and how it affects coordination. It provides a rationale for the methods used by MAPS. Section 3 discusses how MAPS addresses these issues and how they are applied. Section 4 outlines the robotic soccer environment and MAPS’ application to it. Section 5 discusses the evaluation of MAPS in terms of criteria and methods used. Section 6 provides a discussion on why MAPS works. Section 7 provides a summary of the key features of the paper. Section 8 provides a future direction for improving MAPS.

2

Analysis of Robot Coordination in Dynamic Environments

The effectiveness of robot coordination is dependent upon appropriate modelling of the environment and competent selection of robot sub-goals. Robots need to have good mechanisms for both and the impact of appropriate and inappropriate models and selection mechanisms is analysed below.

2.1

Environment Modelling for Coordination

There is a vast amount of information about the environment that can be used by robots to select sub-goals for coordinated activity. Depending on what information is used and how it is processed affects the robot’s performance. The information can be completely based on local sensors, communicated from other robots, or provided from external sources. Having local sensors as the only input for the robot can create problems for coordination between robots. One robot will perceive the world differently from the next. It becomes difficult for one robot to predict the behaviour of another when the world is being analysed from such conflicting views. This can result in conflicting sub-goals being selected by the robots. Communication can be used to supplement information by transmission of the proposed actions of other robots. Protocols and arbitration mechanisms must then be adopted between communicating entities, which adds complexities and can degrade the system. It is generally argued that communication can add unacceptable delays in information gathering and should be kept minimal ([3], [7], [9]). Another view of communication is to share information about the environment. If the robots share representation frameworks, and each broadcasts their locally sensed information in a globally understood reference frame, all robots will build the same representation of the world. An alternative is to provide offboard sensor information to the robots that transmits information about the environment to them. Based on this shared representation all robots can produce sub-goals with knowledge of the sub-goals that will be chosen by other team members. It may not always be possible to implement a global world model, but where possible the shared representation is the key to good coordination. Whichever method is used for determining environment information, it must be provided accurately and consistently as demanded by the changes in the environment. There can therefore be a tradeoff between the amount of information provided by the sensing mechanism and the processing time required before it can be used by the robots. The key issue is that better coordination and robot interaction is achieved with the more common information robots share about the environment.

2.2

Planning

Planning is important when the tasks, goals and the environment require some prediction of future environment states. Prediction of the future allows selection of robot actions that will modify the current environment state in order to progress it towards the predicted future [1]. The

more dynamic the environment, however, the more unpredictable the future becomes. So there is a tradeoff between the amount of time to plan ahead and the accuracy of the prediction. Environments such as robotic soccer are highly dynamic and plans need to change quickly. The effectiveness of the plan depends on the speed, predictability of environmental objects, and totality of environment information which depends on the sensor selection and processing. Apart from the timeliness and completeness of environment information, the planning mechanism for each robot must also be based on the same information if coordination is to result. It can exist as a single centralised entity which each robot has access to, or can exist independently on each robot. If the robots need to coordinate their tasks, they need to have agreement and consistency in their decision-making mechanisms. This can most easily be achieved if the decisions are based on the same environment information.

2.3

MAPS as a Solution

MAPS uses globally shared information to determine the current state of the environment. The environment is remodelled to an abstracted virtual space to include intangible features of the environment as well, such as the predicted effect of an object based on its current state. From this abstracted virtual space, which MAPS models with potential fields, robot sub-goals are determined by evaluation of the influences of the various features of the problem domain. Since MAPS uses the same environment information for all robots, it can better coordinate their actions. Each robot perceives the identical information from its own perspective, and can make judgements about its role in the solution of the problem. Importantly it can also evaluate the actions of its team members in achieving the common system goal.

3

Applying MAPS

MAPS observes the environment and processes it as a set of tangible and intangible features rather than as a complex whole. Object locations, system goals, and robot intentions are examples of useful features. It models these features in the same space, and the resulting abstraction is examined to determine what the robots should do next. MAPS uses potential fields that can provide a full model of the existing environment, model predicted or projected features and provide a search space for solutions. Potential fields have been used in a variety of robot applications such as robot motor schemas in navigation [2], obstacle avoidance ([5], [10]) and action maps for soccer robot movements [8]. The concept behind their use revolves around creating a virtual map of the physical

environment such that features of the physical map are represented by regions of attraction and repulsion in the virtual map. Figure 1 shows an example of how dynamic obstacles can be represented by potential fields. Notice that the obstacles are represented as oblong shapes. This is to provide a region of influence that these objects have in the direction they are moving. By itself, this field can be used to model the future as well as the present.

current time interval. Typically, evaluations are carried out many times a second since the intended environment is extremely dynamic and opportunities don’t exist for long.

Figure 1. Modelling dynamic obstacles in a potential field. The projected regions indicate likely influence in the future.

4.1

Below are examples of how MAPS models environment features as potential fields. Object Regions (Physical feature) These feature fields represent the presence of obstacles or targets in the abstracted environment. They are relatively small in area and represent locations and motion of objects as demonstrated in figure 1. Base Field (Physical feature) The base field feature is a representation of the physical field and can contain biases towards the specific areas in the environment depending on the system goal. Clear Path To Object (Abstract feature) This is a function applied to the physical attributes of the environment to bias locations that are not occluded by any of the field objects from the robot's current location. It is convenient for moving the robots so they are within ‘sight’ of one another. Distance From Current Position (Abstract feature) This is a distance function that provides a bias towards locations that are close to the robot’s current position. A bias towards local moves is beneficial as the robot may receive new directives before any gross movement can be completed due to the nature of the environment. It also provides better predictability in the short term planning mechanism of MAPS. Combinations of these features are superimposed to create a working field. The working field is an abstract and more suitable representation of the real world, allowing informed decisions to be made. The process is applied systematically by each robot in the environment and provides directives staying true to the overall system goal, but evaluated at the

4

Testbed

Robot soccer provides a dynamic, challenging environment for multi-robot coordination. It also adds complexity in the sense that there is competition between the mobile agents in the environment. The coordination system must be robust if it is to be effective since the opposition can have a variety of strategies with which it must contend. This makes the environment hostile and consequently emphasises the importance of planning and coordination between the agents. An overview of the robot soccer environment is provided below.

The Robotic Soccer Environment

The RoboCup robotic soccer competition is designed to promote research in the domains of robot design and artificial intelligence. The structure of the environment and the robots is determined by an international committee of artificial intelligence and robotic researchers, around the structure of normal soccer [6]. The environment described in this section conforms to the small sized league. In particular, this section describes the RoboRoos soccer system which participated in RoboCup '99 in Stockholm during August 1999 [11]. The soccer system uses a global camera which provides images to interpreting software that produces the locations and heading of objects on the field. MAPS uses this information to model the environment and produce directives for the robots. The directives and environment information are transmitted to the robots.

4.2

MAPS Implementation

This section details how MAPS is applied to the soccer robot environment. It exists at two levels; the high level control algorithm, and the potential field construction algorithms. The high level control algorithm is shown below (Algorithm 1) with the potential field constructions termed [PF]. The priority in robot soccer is controlling the ball. As such, MAPS determines which robot is in the best position to control the ball. The robot is considered as the ‘kicking’ robot. MAPS creates a potential field to determine where the robot should kick the ball and sends this directive and the kick coordinates. All other robots are sent directives to go to locations that assist by offering opportunities for passes, or that provide defence against attacking robots.

Update field object coordinates from vision system for each robot if the robot is best to kick the ball Build a “kick to” working field [PF] Send “kick to” command to robot Send “kick to“ coordinates to robot else if we are in control of the ball Build an attacking “go to” field [PF] else Build a defensive “go to” field [PF] Send “go to” command to robot Send “go to” coordinates to robot end end Algorithm 1. MAPS high level control

As can be seen from the high level controlling algorithm, three potential fields are used to determine locations for actions. These are the kicking, attacking and defending potential fields. Each of these consists of a weighted set of environment features that highlight locations that enable better coordination between the robots. To demonstrate how the fields are modelled, the kicking potential field algorithm is presented below. for each robot on the field Add the Object Region for that robot Apply Clear Path To Object (ball) Add Basefield Add the Distance From Current Position of the ball Add in small bias to old coordinates Select lowest valued coordinate on field Algorithm 2. Kicking Potential Field Generation

Each robot is represented on the potential field by an object region similar to figure 1. From this, the clear paths from the ball’s location are added so the ball won’t be kicked into a player. The basefield is modelled as a ramp towards the opposition goal, and is added to this combination to bias locations closer to the goal. The distance from the ball’s current position is added so the kicking robot won’t try to kick the ball too far. This results in smaller, controlled kicks towards team-mates or into open spaces. The last kicking destination persists so it will be stable for a slightly extended period of time, increasing the probability that the ball will be kicked, rather than the robot constantly repositioning itself in response to small deviations to the kicking location. An example of a kicking potential field taken from the real environment is provided below (Figure 2).

5

MAPS Evaluation

Structured testing can be carried out by playing two identical teams against one another that vary only in the algorithms the two teams use for multi-robot coordination. The team with the better coordination in this case, should produce better play, and therefore, show a marked

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Figure 2. An example of the kicking potential field. Robots are located at the crosses and represented by the dark regions, with locations behind them occluded by the clear path to object (ball) function. The ball is the white circle with the kicking robot at the black cross. The light regions indicate two possible passes, with another close option being a shot to the upper corner of the goal.

improvement in gameplay and the final score. This is achievable in simulation where identical robots are available. The simulation developed for the RoboRoos system is of sufficient fidelity for debugging of even lowlevel navigation and kicking routines, and produces results similar to the real robots. Nevertheless, there is no substitute for testing with real robots. The number of real robots available is limited to a single team, so a supplementary testing strategy is adopted. Here the robots play against a stationary opposition using different multi-robot coordination systems for comparison

5.1

Comparative Algorithms

The tests are performed against two comparative algorithms. The first algorithm is termed greedy and resembles young children playing soccer. It operates by a basic rule: If you are closest behind the ball kick it towards the goal, or else try to get closest behind the ball. This method is expected to show that all robots will be impeding each other and therefore, a slower game, with less goals. The second algorithm, termed dumb plan, consists of quartering the environment and giving each field robot a quarter of responsibility. The rules for this algorithm are: if the ball is in your quarter, go to it and kick it towards the goal, or else maintain your home position. This algorithm should show better performance than greedy since the robots will not impede one another.

5.2

Simulation Test 1

Below (Table 1) are the results of playing MAPS against the greedy and dumb plan algorithms for 23 minutes of play each. Neither team played with a goal keeper.

Opposition

Impede

Attack

Shots

Goals

Greedy

16-6

18%

3-18

4-12

Dumb Plan

0–4

27%

8-15

5-10

exchanging roles when required and passing to team-mates when they were in a better position to score.

Table 1. Results of MAPS versus the test algorithms. Results are listed as opposition - MAPS.

The Impede column represents the number of times a robot impeded another in carrying out its task. The Attack column shows the percentage of time the ball was in the opposition’s attacking half. Shots represents the total number of shots at the goal mouth, while Goals is the number of successful goals. The results show that MAPS performed better in general field play, and towards the system goal of scoring. The greedy algorithm had an expected high rate of robots impeding each other which held them up while they were trying to free themselves. This resulted in better attacking and goal scoring opportunities since MAPS had the robots positioned around the field to take advantage of the greedy robots impeding each other. Dumb plan never had the problem of impeding robots since they were always spatially dislocated from each other. As a result of the same positions being maintained, there was no coordination or passing between robots and only one attacking robot against the coordinated defence of the MAPS robots.

5.3

Simulation Test 2

This test is a comparison of each algorithm playing against stationary opposition. The opposition was placed as shown in figure 3 which was chosen to represent a good defence as well as providing up front robots to possibly rebound balls into the goal. Home

Opposition

The results are shown in Table 2. Once again, greedy had the biggest problem with impeding robots which also lead to more own goals. There was a long time between successive plays due to the time taken to unwind from a locked robot situation once the ball had moved away. MAPS provided a good flowing play with the robots

Impede

Attack

Shots

OG

Goals

MAPS

2

87%

12

1

13

Greedy

17

67%

9

3

7

Dumb Plan

1

86%

16

1

7

Table 2. Results of different algorithms against stationary opposition in simulation.

5.4

Real Robot Results

Table 2 below describes the real robot tests with the same test setup used in Simulation Test 2. The period of play was 11 minutes for each algorithm. Algorithm

Impede

Attack

Shots

OG

Goals

MAPS

9

97%

15

1

13

Greedy

85+

83%

20

5

13

Dumb Plan

4

79%

25

0

9

Table 3. Results of different algorithms against stationary opposition using real robots.

Many of these results are highly correlated with simulation results, demonstrating the effectiveness of the simulator. The most noticeable difference in real robot testing was the number of times the greedy algorithm caused robots to impede each other. They were generally quick to disengage, and if one robot was free, it would take a shot on goal, albeit straight at the goal keeper. Dumb Plan had a similar correlation of goal shooting to unsuccessful goals. MAPS would only take a shot at goal if there was a clear path to the goal, otherwise, the ball would be progressed towards an area or passed to a team-mate where a shot could be taken. It was also robust in controlling the ball. Rarely was the ball not near a robot due to the dynamic positions MAPS determines.

6 Figure 3. Opposition setup for simulation test 2 and for real robot tests.

Algorithm

Discussion

MAPS provides dynamic team formation in response to the changing environment. The formation is determined by the effect of the current environment state and the system goals. This has the effect of positioning robots so that the next change in environment state will concur with the plan MAPS is currently executing. Therefore, no gross movements of the robots are required to take advantage of the new environment state. MAPS is able to accomplish this by the emergent properties of combining the environment features as

potential fields. These features are available for each robot’s representation of the environment as considered by MAPS. This enables anticipation other robot actions when considering the sub-goals for a robot. As such, the robot actions are more predictable and plans are made to take advantage of this, resulting in better coordination.

7

Conclusion

The performance of MAPS demonstrates it is a capable system for multi-robot coordination in a highly dynamic environment. The paradigm uses potential fields as a medium to position robots around the environment in real time considering the system goal. The robots are coordinated by use of the same information being used for their actions. This information is determined from an external sensor, examining the past actions of the objects in the environment, and consideration of the system goal. The consequent analysis of these features enables coordinated actions to emerge such as passing the ball to a fellow robot, in the soccer robot case. The team has competed successfully in three international RoboCup competitions in the past year, coming second in RoboCup ’98, third in Pacific Rim RoboCup ’98, and making it to the quarter-finals in RoboCup ‘99. The level of competition has been improving leading to better technological development in many areas of small robot design. The coordination mechanisms are also becoming better as can be seen from watching the teams in the finals of these events. Future competitions will place more emphasis on the coordination strategies as a result of the rising standard of play.

8

Future Work

The results demonstrated in this paper show MAPS as a potential coordination mechanism for environments where the agents need to work together to more effectively and efficiently achieve their goals. In its current form, the values for the potential fields have been determined empirically. The next step is to allow an adaptation component to MAPS so it can derive some of these values itself. The method used must be able to work in real time, since it must contend with opposition strategies in the intended dynamic environments. Once this has been carried out and tested in the robot soccer domain, MAPS will also be trialed in the predator/prey environment [4]. This is intended to progress to having MAPS exist onboard the robots and the robots having localised sensing of the environment.

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