Multi-Robot Systems, Part II

1. Multi-Robot Systems, Part II April 3, 2007 “The mob has many heads but no brains”. -- English Proverb.

2. Today Last time Topics we’ll look at in Multi-Robot Systems • Introduction/Overview of Field • Issues in multi-robot communication • Swarm behaviors, including flocking, dispersion, aggregation, etc. • Formations • Task Allocation

3. Motion Coordination: Formation-Keeping • Objective: • Robots maintain specific formation while collectively moving along path • Examples: • Column formation: • Line formation: L. E. Parker, “Designing Control Laws for Cooperative-Agent Teams”, Proc. of ICRA, 1993.

4. Formations Key Issues: • What is desired formation? • How do robots determine their desired position in the formation? • How do robots determine their actual position in the formation? • How do robots move to ensure that formation is maintained? • What should robots do if there are obstacles? • How do we evaluate robot formation performance?

5. Example Movies of Column Formation-Keeping Parker, 1995 Parker et al., 2001

6. Issue in Formation Keeping: Local vs. Global Control • Local control laws: • No robot has all pertinent information • Appealing because of their simplicity and potential to generate globally emergent functionality • But, may be difficult to design to achieve desired group behavior • Global control laws: • Centralized controller (or all robots) possess all pertinent information • Generally allow more coherent cooperation • But, usually increases inter-agent communication

7. Descriptions: Global Goals, Global Knowledge, Local Control • Global Goals: • Specify overall mission the team must accomplish • Typically imposed by centralized controller • May be known at compile time, or only at run-time • Global Knowledge: • Additional information needed to achieve global goals • E.g., information on capabilities of other robots, on environment, etc. • Local Control: • Based upon proximate environment of robot • Derived from sensory feedback • Enables reactive response to dynamic environmental changes

8. Tradeoffs between Global and Local Control • Questions to be addressed: • How static is global knowledge? • How difficult is it to obtain reliable global knowledge? • How badly will performance degrade without use of global knowledge? • How difficult is it to use global knowledge? • How costly is it to violate global goals? • In general: • The more unknown the global information is, the more dependence on local control

9. Demonstration of Tradeoffs in Formation-Keeping • Measure of performance: Cumulative formation error: • Strategies to investigate: • Local control alone • Local control + global goal • Local control + global goal + partial global knowledge • Local control + global goal + more complete global knowledge Where di(t) = distance robot i is from ideal formation position at time t

10. Formation Keeping Objective Leader

11. Strategy I: Local Control • Group leader knows path waypoints • Each robot assigned local leader + position offset from local leader • As group leader moves, individual robots maintain relative position to local leaders

12. C B D A Results of Strategy I

13. Strategy II: Local Control + Global Goal • Group leader knows path waypoints • Each robot assigned global leader + position offset from global leader • As group leader moves, individual robots maintain relative position to global leader

14. C B D A Results of Strategy II

15. Strategy III: Local Control + Global Goal + Partial Global Knowledge • Group leader knows path waypoints • Each robot assigned global leader + position offset from global leader • Each robot knows next waypoint • As group leader moves, individual robots maintain relative position to global leader

16. C B D A Results of Strategy III

17. Strategy IV: Local Control + Global Goal+ More Complete Global Knowledge • Group leader knows path waypoints • Each robot assigned global leader + position offset from global leader • Each robot knows current and next waypoints • As group leader moves, individual robots maintain relative position to global leader

18. C B D A Results of Strategy IV

19. Time and Cumulative Formation Error Results Time Required to Complete Mission Strategy IV * Strategy III * Strategy II ******** **** Strategy I ********* * Time 0 10 20 30 40 50 Normalized Cumulative Formation Error Strategy IV *** Strategy III *** Strategy II ******** ** Strategy I ** **** ** *** ** Error 0 50 100 150 300 200 250

20. Summary of This Formation-Keeping Control Case Study • Important to achieve proper balance between local and global knowledge and goals • Static global knowledge ==> easy to use as global control law • Local knowledge ==> appropriate when can approximate global knowledge • Local control information should be used to ground global knowledge in the current situation.

21. Another formation example:Let’s look at approach of Balch (1998) “Behavior-Based Formation Control for Multiagent Robot Teams”, by Tucker Balch, Ronald C. Arkin Published in: IEEE Transactions on Robotics and Automation December, 1998. Available online at: http://www.cs.cmu.edu/~trb/papers/formjour.ps.Z

22. Motor Schemas Used for Formation-Keeping • Move-to-goal • Avoid-static-obstacle • Avoid-robot • Maintain-formation: • Perceptual schema: detect-formation-position • Accomplished by: • Determining robot’s desired location for the formation type in use • Determining robot’s relative position in the overall formation • Determining other robots’ locations • Motor schema output vector: • Computed toward position whose magnitude is based on how far out of position the robot is

23. Output Vector Magnitude Calculation • Dead zone: • Robot is within acceptable positional tolerance. • Output vector magnitude is always 0. • Controlled zone: • Robot is somewhat out of position. • Output vector magnitude decreases linearly from a maximum at zone’s furthest edge to 0 at the inner edge. • Directional component: points toward dead zone’s center. • Ballistic zone: • Output vector magnitude is set to its maximum • Directional component points toward the center of the computed dead zone Magnitudes: Ballistic Zone Controlled Zone Dead Zone

24. Formation and Obstacle Avoidance • Barriers -- choices for handling include: • Move as a unit around barrier • Divide into subgroups • Choice depends upon relative strengths of behaviors

25. 4 1 2 4 3 3 2 4 3 1 2 4 2 3 1 2 1 1 4 2 1 3 3 4 1 3 4 2 Balch’s Formation Types and Position Determination Formations: Column Line Diamond Wedge Position Determination: Unit-center Leader Neighbor

26. Requirements of Formation Techniques • Unit-center approach: • Requires transmitter and receiver for all robots • Requires protocol for exchanging position information • Places heavy demand on passive sensor systems: each robot has to track 3 other robots that may be spread across a very large field of view • Leader-referenced approach: • Requires only one transmitter for leader and one receiver for each follower robot • Thus, has reduced communications bandwidth • Require tracking only one robot • However, leader may be too far away to sense • Local interactions among robots may make little sense, if they aren’t paying attention to each other • Neighbor-referenced approach: • Requires tracking only one other robot • However, less information on global formation requirements  could be more formation error

27. Balch’s Formation Results • For 90 degree turns: • Diamond formation best with unit-center-reference • Wedge, line formations best with leader-reference • For obstacle-rich environments: • Column formation best with either unit-center or leader-reference • Most cases: • Unit-center better than leader-center • Except: • If using human leader, not reasonable to expect to use unit-center • Unit-center requires transmitter and receiver for all robots, whereas leader-center only requires transmitter at leader plus receivers for all robots • Passive sensors are difficult to use for unit-center

28. 4 1 2 4 3 3 2 4 3 1 2 4 2 3 1 2 1 1 4 2 1 3 3 4 1 3 4 2 Balch’s Formation Types and Position Determination Formations: Column Line Diamond Wedge Position Determination: Unit-center Leader Neighbor

29. Summary of Balch Formation-Keeping Control Case Study • Formations can be maintained using a motor-schema, motion vector output approach • No single type of formation-control strategy is best for all types of formations • Different strategies have different sensing requirements • Different strategies have different levels of robustness • Keeping formations while moving around obstacles can be difficult

30. Task Allocation • Task allocation is the problem of determining which robot should perform which task(s) • Given:n robots, {r1, r2, …, rn} m tasks, {t1, t2, …, tm} • Objective: find mapping of tasks to robots, so that each task is accomplished in the best possible manner. • Challenge: This mapping has been shown to be NP-hard (I.e., possible solutions are exponential in the number of robots and tasks

31. Gerkey’s Taxonomy for Task Allocation • Tasks: single-robot (SR) or multi-robot (MR) • Robots: single-task (ST) or multi-task (MT) • Assignments: instantaneous (IA) or time-extended (TA) Combine these 3 axes into a single descriptive, such as: • SR-ST-TA: Single-robot tasks, single-task robots, with time-extended assignment • MR-ST-IA: Multi-robot tasks, single-task robots, instantaneous assignment

32. Most work: SR-ST-IA and SR-ST-TA • Today, we’ll give 2 examples: • ALLIANCE (Parker, 1994): Behavior-based task allocation • MURDOCH (Gerkey & Mataric, 2002): Market-based task allocation

33. Key Features of ALLIANCE • Fully distributed • Behavior-based • Works with heterogeneous robots • Enables dynamic task-reallocation • Reduced communication overhead; no negotiations • Uses mathematical motivation models, impatience and acquiescence, towards adaptive action selection • Implemented on a team of physical robots

34. Assumptions in ALLIANCE • Robots can detect the effects of their own actions. • Robot ri can detect the actions of other team members through explicit communication. • Robots on the team are not intentionally adversarial. • Tobots do not possess perfect sensors. • Any of the robot subsystems can fail. • The communication medium is not guaranteed to be available. • Robot failure cannot necessarily be communicated to other robots. • The robots do not have complete world knowledge. Note : The assumptions are made with respect to small to medium sized team of multi-robots.

35. Overview of ALLIANCE • Overall mission is decomposed into a set of high level tasks. • High level tasks are achieved by means of a number of behavior sets that an individual robot is capable of executing. • Behavior sets are classified as active, if robot is executing that behavior set, or hibernating, if otherwise. • Only one behavior set is active at any point in time. • The selection of the behavior set is done by means of motivational behaviors, each of which controls the activation of one behavior set.

36. ALLIANCE c r o s s - i n h i b i t i o n I n t e r - R o b o t M o t i v a t i o n a l M o t i v a t i o n a l M o t i v a t i o n a l C o m m u n i - B e h a v i o r B e h a v i o r B e h a v i o r c a t i o n B e h a v i o r B e h a v i o r B e h a v i o r S e t 1 S e t 0 S e t 2 L a y e r 2 A c t u a t o r s L a y e r 1 S e n s o r s L a y e r 0 ALLIANCE Architecture

37. Motivational Behaviors • ALLIANCE uses motivation for task monitoring and dynamic task reallocation. • Each motivational behavior receives input from a number of sources including: • Sensory feedback • Inter-robot communication • Inhibitory feedback • Internal motivations. These inputs are used to generate the output at any point of time. • The output defines the activation level of each behavior. • Once the activation level exceeds the preset threshold for each behavior, the behavior is activated. • ALLIANCE uses 2 types of internal motivation: impatience and acquiescence • Impatience: enables the robot to handle situations external to itself. • Acquiescence: enables the robot to handle internal situations.

38. Motivational Behaviors (con’t.) • A robot’s motivation value to activate a behavior is initialized to 0. • Over a period of time the robot’s motivation level increases at a rate that depends on the activities of its teammates: • If no robot is accomplishing a behavior, then the motivation level increases at a fast rate of impatience. • If another robot is working on the behavior then the motivational level increases at a slower rate of impatience. • At the same time the robot’s willingness to give up a task increases over time as long as the sensory task indicates the task is not being accomplished.

39. ALLIANCE Formal Model n robots m independent subtasks Behavior sets of robot ri Task in T that riis working on when aik is active Threshold of activation If sensory feedback of riat time t indicates that aij is applicable Otherwise If rihas received message from rk concerning task hi(aij) in (t1,t2) Otherwise If aijis active, , on robot riat time t activity_suppression Otherwise

40. ALLIANCE Formal Model (con’t.) otherwise otherwise

41. ALLIANCE Formal Model (con’t.) Whenever mij(t)> q, aijis activated.

42. Example Adaptive Box Pushing

43. Robot Control in Box Pushing

44. Robot Control in Box Pushing (con’t.)

45. Typical Behavior Traces in ALLIANCE

46. L-ALLIANCE • Dynamically updates the parameter settings based upon knowledge learned from previous experiences. • Each robot ‘observes’, evaluates and cataloges the performance of any team member whenever it performs a task of interest to that robot. • These ‘learned’ observations allow the robot to adapt their action selection over time. • The underlying algorithm is distributed across the behavior sets of ALLIANCE.

47. More Experiments • Experiments conducted on physical robots: teams of 3 R-2 robots were used in all experiments. • Hazardous waste cleanup mission • Mission requires two artificially ‘hazardous’ waste spills in an enclosed room to be cleaned up by a team of three robots. • The robot team must locate the two waste spills, move the spills to a goal location, while also periodically reporting the team progress to humans monitoring the system.

48. Summary of ALLIANCE Results • The cooperative team under ALLIANCE was robust • The team was able to respond autonomously to various types of unexpected events either in the environment or in the robot team without the need for external intervention. • The cooperative team need not have a priori knowledge of the abilities of the other team members to efficiently complete the task. • ALLAINCE allows the robot teams to accomplish their missions even when communication system breaks down.

49. Summary of ALLIANCE • ALLIANCE is a fully distributed, behavior based approach for fault tolerant mobile-robot cooperation. • ALLIANCE enhances team robustness through usage of motivational behavior mechanism. • Physical redundancy can be used to enhance fault tolerance of the system. • The L-ALLIANCE enhances ALLIANCE architecture by using learning algorithm to fine tune the impatience and acquiescence parameters. • The architecture has been implemented on a team of physical robots, thereby illustrating its feasibility.

50. Another Task Allocation Approach: MURDOCH (Gerkey ’02) • Anonymous communication via broadcast • saves bandwidth when sending messages to multiple recipients • allows robots to move in and out of range • Hierarchical task structure • each task is a tree containing other tasks • flexible enough to handle a wide variety of tasks • Auctions • scalable • cheap to broadcast and compute (only one round of bidding) • allow modularization • similar to CNP negotiation scheme, but without centralized broker