Multi-Robot Formation Dr. Daisy Tang
Objectives Understand key issues in formationkeeping Understand various formation studied by Balch and Arkin and their pros/cons Understand local vs. global control Be able to determine best formation for given circumstances
Formation-Keeping Objective: Robots maintain specific formation while collectively moving along path Examples: Column formation Line formation
Key Issues in Formations What is the desired formation? How do robots determine their desired positionsin the formation? How do robots determine their actual positionsin the formation? How do robots move to ensure that a formation is maintained? What should robots do if there are obstacles? How do we evaluate robot formation performance?
What is Desired Formation? Dependent upon environment: Obstacle-free A few obstacles Cluttered Dependent upon sensing/communication capabilities and requirements: Ability to detect other robot positions Ability to communicate with each other Ability to sense effect of formation-keeping through the world
Possible Formations Formations can be hard-coded, in the sense that they specify Cartesian positions for all robots.
Possible Formations (con t.) Or, formations can be defined by constraints, which allow variation in Cartesian positions for robots Move object across room Maintain line-of-sight visibility
Some Formation Control Videos http://www.youtube.com/watch?v=yrn5b37mtl4 http://www.youtube.com/watch?v=t4elmvcmpbq http://www.youtube.com/watch?v=5izkl--bpyc
Behavior-Based Formation Control for Multi-Robot Teams Presented by Iain Lee
About This Paper Author: Tucker Balch, Member, IEEE Ronald C. Arkin, Senior Member, IEEE Published in: IEEE Transactions on Robotics and Automation December, 1998
Introduction Why formation-keeping? Formations allow individual team members to concentrate their sensors across a portionof the environment, while their partners cover the rest It is important when sensor assets are limited Widely used in military applications Potential applications in robotics: robot scout, search and rescue, agricultural coverage tasks, and security patrols Formation-keeping objective: Robots maintain specific formation while moving along path
Four Major Formation Type Line, column, diamond and wedge Used by U.S. Army mechanized scout platoons on the battlefield
Formation Maintenance Two steps: Detect-formation-position(perceptual) Maintain-formation(motor) Three techniques for formation position determination Unit-center-referenced Leader-referenced Neighbor-referenced
Motor Schema-Based Formation Control Basic motor schemas (behaviors): move-to-goal avoid-static obstacle avoid-robot maintain-formation noise Each schema generates a vector representing the desired behavioral response A gain valueis used to indicate the relative importance of the individual behaviors
Recall the Motor Schema Approach
Motor Schema Parameters High-level combined behavior is generated by multiplying the outputs of each primitive behavior by its gain, then summing and normalizing the results.
Maintain-Formation Vector Direction: Always in the direction of the desired formation position Magnitude: Depends on how far the robot is away from the desired position Length of arrow = m = magnitude Angle of arrow = d = direction
When There Are Obstacles To avoid obstacles like barriers, choices are: Move as a unit around the barrier Divide into subgroups Depends on the relative strengths of behaviors(gain)
So, What s the Result? Qualitative/Quantitative View
Experiment Setup Georgia Tech s MissionLabrobot simulation Sensors allow a robot to distinguish between robots, obstacles and goals Robots have several navigation waypoints to follow
A Qualitative Analysis (1) Four robots in formations
A Qualitative Analysis (2) Move around obstacles and through turns Leader-referenced (left) vs. unit-center-referenced (right)
A Quantitative Analysis (1) Three metrics: path ratio, position error and timeout of formation Two experiments: a 90 degrees turn and an obstacle field
A Quantitative Analysis (2) Results: For 90-degree turn: Diamond formation best with unit-center-ref. Wedge, line formations best with leader-ref. For obstacle field: Column formation best with either unit-centerref. or leader-ref. Most of the time: Unit-center-ref. formations perform better than leader-ref. formations
But Unit-center-ref. formations are not widely used: If using human leader, leader-ref. is better For communications restricted applications, the unit-center-ref. requires a transmitter and receiver for each robot and a protocol Passive sensors are difficult to use for unit-center-ref.
Conclusion This paper presents a behavior-based approach to implement formationkeeping, several different formation types are implemented and compared But there are some issues that are not discussed in this paper, like scalability and implementation of other possible formation types
Designing Control Laws for Cooperative Agent Teams Presented by Raymond Luc
Local vs. Global Control Local control laws: No robot has all pertinent information Appealing because of their simplicityand 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 increase inter-agent communication
Global Control Use global goals of the team and/or global knowledge about the team s current or upcoming actions to direct an individual s actions How do agents obtain such global knowledge? Centralized informant Interpretation through agent modeling Shortcomings: No adequate global info available Agent does not use all global info provided Processing requires time and resources, hard for real-world applications Changing global info
Local Control Guide actions based on information derived from agent s sensory data Allows agent to react to dynamics Global functionality can emergefrom interaction of local control laws However, certain global goals cannot be achieved through the use of local control laws alone
Tradeoffs between Global and Local Control Question #1: How static is the global knowledge? In general, the more static the global knowledge is, the more practical its use by a global control law Question #2: How difficult it is to approximate global knowledge? Question #3: How badly will performance degrade without the use of global knowledge? How difficult is it to use global knowledge? In general, the more unknown the global information is, the more dependence a team must have on local control, combined with approximations to global knowledge based on observation
Conflicting Global and Local Controls Global control laws use strictly global information Local control laws use strictly local information A better way: view global information as providing general guidance for longer-term actions, whereas local information indicates more short-term, reactive actions A composite control law
Formation Keeping Assumptions Each agent has ability to sense locations of its neighbors relative to itself (local knowledge) Agent is physically constrained by inability to move backwards Global goal: Agent reaches destination asap Agents maintain formation Global knowledge: Path the group to take (waypoints) Path the leader is taking
Demonstration of Tradeoffs in Formation-Keeping Performance is measured by 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
Formation-Keeping Objective
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 positionto local leaders
Strategy II: Local Control + Global Goal Group leaderknows path waypoints Each robot assigned global leader+ position offset from global leader As group leader moves, individual robots maintain relative positionto global leader
Strategy III: Local Control + Global Goal + Partial Global Knowledge Group leaderknows 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 positionto global leader
Strategy IV: Local Control + Global Goal + More Complete Global Knowledge Group leaderknows path waypoints Each robot assigned global leader+ position offset from global leader Each robot knows current and next waypoints As group leader moves, individual maintain relative positionto global leader
Time and Cumulative Formation Error
Summary of The Formation 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