weighted voting game based multi-robot team formation for distributed area coverage
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Weighted Voting Game Based Multi-robot Team Formation for Distributed Area Coverage. Ke Cheng and Prithviraj (Raj) Dasgupta Computer Science Department University of Nebraska, Omaha. Research Objective: Multi-robot Coverage. - PowerPoint PPT PresentationTRANSCRIPT
Weighted Voting Game Based Multi-robot Team Formation for Distributed Area Coverage
Ke Cheng and Prithviraj (Raj) DasguptaComputer Science Department University of Nebraska, Omaha
Research Objective: Multi-robot Coverage
• Use a set of robots to perform complete coverage of an initially unknown environment in an efficient manner
• Efficiency is measured in time and space– Time: reduce the time required to cover the
environment– Space: avoid repeated coverage of regions that have
already been covered
Tradeoff in achieving both simultaneously
Major Challenges
• Distributed – no shared memory or map of the environment that the robots can use to know which portion of the environment is covered
• Each robot has limited storage and computation capabilities– Can’t store map of the entire environment
• Other challenges: Sensor and encoder noise, communication overhead, localizing robots
How does a robot do area coverage?• Using an actuator (e.g., vacuum) or a sensor (e.g., camera or
sonar)
Source: Manuel Mazo Jr. and Karl Henrik Johansson, “Robust area coverage using hybrid control,”, TELEC'04, Santiago de Cuba, Cuba, 2004
Robot’s coverage tool
The region of the environment that passes under the swathe of the robot’s coverage tool is considered as covered
E-puck Mini Robot
IR sensors (8); range ~ 4 cm
Camera; 640 X 480 VGA
Bluetooth wirelesscommunication
LEDs
Mic + speaker
7 cm
4.1 cm
144 KB RAMdsPIC processor@14MIPS
Photo courtesy: Mobots group@EPFL http://mobots.epfl.ch
Multi-robot coverage: Individually coordinated robots using swarming
Global Objective: Complete coverage of
environment
Multi-robot coverage: Individually coordinated robots using swarming
Global Objective: Complete coverage of
environment
Local coverage rule of robot ......
...
Local coverage rule of robot
Local coverage rule of robot
Local coverage rule of robot
Local coverage rule of robot
Local coverage rule of robot
Multi-robot coverage: Individually coordinated robots using swarming
Global Objective: Complete coverage of
environment
Local coverage rule of robot ......
...
Local coverage rule of robot
Local coverage rule of robot
Local coverage rule of robot
Local coverage rule of robot
Local coverage rule of robot
Local interactions between robots
Multi-robot coverage: Individually coordinated robots using swarming
Global Objective: Complete coverage of
environment
Local coverage rule of robot ......
...
Local coverage rule of robot
Local coverage rule of robot
Local coverage rule of robot
Local coverage rule of robot
Local coverage rule of robot
Local interactions between robots
How well do the results of the local interactions translate to achieving the global objective?
Done empirically
References: 1. K. Cheng and P. Dasgupta, "Dynamic Area Coverage using Faulty Multi-agent Swarms" Proc. IEEE/WIC/ACM International Conference
on Intelligent Agent Technology (IAT 2007), Fremont, CA, 2007, pp. 17-24.2. P. Dasgupta, K. Cheng, "Distributed Coverage of Unknown Environments using Multi-robot Swarms with Memory and
Communication Constraints," UNO CS Technical Report (cst-2009-1).
Multi-robot coverage: Team-based robots using swarming
Global Objective: Complete coverage of
environment
Local coverage rule of robot-team ......
...
Local coverage rule of robot-team
Local coverage rule of robot-team
Local coverage rule of robot-team
Local coverage rule of robot-team
Local coverage rule of robot-team
Flocking technique to
maintain team formation
Multi-robot coverage: Team-based robots using swarming
Global Objective: Complete coverage of
environment
Local coverage rule of robot-team ......
...
Local coverage rule of robot-team
Local coverage rule of robot-team
Local coverage rule of robot-team
Local coverage rule of robot-team
Local coverage rule of robot-team
Flocking technique to
maintain team formation
Local interactions between robot teams
How well do the results of the local interactions translate to achieving the global objective?
Done empirically
Relevant publications: 1. K. Cheng, P. Dasgupta, Yi Wang ”Distributed Area Coverage Using Robot Flocks”, Nature and Biologically Inspired Computing (NaBIC’09), 2009.2. P. Dasgupta, K. Cheng, and L. Fan, ”Flocking-based Distributed Terrain Coverage with Mobile Mini-robots,” Swarm Intelligence Symposium 2009.
Multi-robot teams for area coverage• Theoretical analysis: Forming teams gives a significant speed-up
in terms of coverage efficiency • Simulation Results: The speed-up decreases from the theoretical
case but still there is some speed-up as compared to not forming teams
• Based on Reynolds’ flocking model
• Leader referenced
• Follower robots designated specific positions within team
Coverage with Multi-robot TeamsSquare
Corridor
Office
Dynamic Reconfigurations of Robot Teams
• Having teams of robots is efficient for coverage• Having large teams of robots doing frequent
reformations is inefficient for coverage• Can we make the modules change their
configurations dynamically– Based on their recent performance: If a team of
robots is doing frequent reformations (and getting bad coverage efficiency), split the team into smaller teams and see if coverage improves
Coalition game-based team formation
• We used coalition games to solve the multi-robot team formation problem– Coalition games provide a theory to divide a set of
players into smaller subsets or teams– We used a form of coalition games called weighted
voting games (WVG)
Robot Team Formation for Coverage:Weighted Voting Game
Coalition Game Layer
Flocking-basedController
Mediator
A team needs to reconfigure
Calculate the best partition of a team
Maintain consistency
between coalition game result and team formations
17
Coalitional Games: Weighted Voting Game (WVG) Definitions
• N: set of players• v: characteristic function, assigns a real-valued utility to
each subset of players• Each player i is assigned a weight wi
– Wmax = S wi
• q: quota, fixed positive real number <= Wmax
• If there is a subset of players C whose weights taken together equal or exceed the quota, C is called a winning coalition and v(C) = 1– Players not part of winning coalition get v = 0
Weighted Voting Game: Definitions
• Minimal winning coalition: smallest subset of players whose weights reach the quota
• Veto player: player that appears in all winning coalitions, without him other players can’t reach quota– A game may not have a veto player
WVG Example
• N = {A, B, C, D}• wA = 45, wB = 25, wC = 15, wD = 15; quota = 51
– Winning coalitions are {A, B} {A, C} {A, D} {A, B, C} {A, B, D} {A, C, D} {B, C, D} {A, B, C, D}
• no veto player
• Same weights, quota = 56– Winning coalitions are {A, B} {A, C} {A, D} {A, B, C}
{A, B, D} {A, C, D} {A, B, C, D}• A is a veto player
Robot Coverage as WVG• Determining weights of players (robots)
– Modeled as coverage capability• Environment considered as a 2-D grid• Coverage map: Region covered by robot in last T timesteps• Coverage efficiency:
– Time: What fraction of the coverage map has been covered at least once?
– Space: What fraction of the coverage map has been covered more than once?
• Ci = a X qi – b X hi + C0
a=2, b=1, C0 = -0.04Ci = 1.96 Ci = 0.96
Breaking Ties Between Multiple Minimal Winning Coalitions
• Tie breaking using heuristic
Stability of Coalitions
• Is the partition of players imposed by the MWC going to be stable?– Yes, if it’s in the core of the game– Core: Sum of the payoffs of all the players in a team is at least
as great as the payoff of the whole team• Theorem 1: The core of a WVG is non-empty iff it has a
veto player• Theorem 2: The best minimal winning coalition (BMWC)
is in the core• Theorem 3: The best minimal winning coalition is unique
Outline of Algorithm for Team Reformation
• When a team needs to reconfigure– For all robots that are within communication range of
a leader robot• Find the veto players, set MWC = veto players
– If no veto players, don’t form team and move individually• If the veto players weights are enough to reach the quota
then stop*
• Else add players from non-veto set to MWC, one at a time, until sum of players’ weights reaches quota
*: If there are multiple MWCs apply heuristic to find BMWC
Experimental Results on Webots
Experimental Settings
Percentage of environment coveredafter 2 hours of clock-time simulations Repeated Coverage
after 2 hours of clock-time simulations
• E-puck robots• Wheel speed: 2.8 cm/sec• On-board GPS• Arena size: 4 m X 4m• Robot size = Grid cell size = 7 cm X 7 cm• Results averaged over 10 runs
Effect of Environment (Obstacles)20 robots, quota = 0.7 X Wmax
Effect of Communication Range20 robots, 10% of environment occupied by obstacles
Video Demo 1
Conclusions, Ongoing and Future Work
• Coalition games (WVGs) provide a suitable, structured mechanism to dynamically reconfigure multi-robot teams
• Ongoing work: Reduce the computation complexity of generating winning coalitions in a WVG
• Future work: Dynamically changing quota value based on performance, learning from long-term coverage histories
• Tests with physical robots
Acknowledgements• We are grateful to the sponsors of our
projects:– COMRADES project, Office of Naval Research– NASA Nebraska EPSCoR Mini-grant
Thank You!
For more informationC-MANTIC Lab: http://cmantic.unomaha.edu
Video Demo 2
Video Demo 3