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					  Relaxation On a Mesh
a formalism for generalized
      Localization
                            By
 Andrew Howard, Maja J Matari´c and Gaurav Sukhatme
  Robotics Research Labs, Computer Science Department,
             University of Southern California
                       Presented by
        Prasanna Joshi and Sameer Menon
       Collaborative computing

• Emergence of reliable wireless
  communications
• Compact, low power microprocessor
  devices and sensors e.g. PDA, Cell Phone
• Development of sensor/actuator networks
  – Sensor Fusion
  – Joint planning and execution
  – Needs knowledge of spatial configuration
                         Problems
• Localization
  – Localizing the robot in unknown environment

• Calibration
  – To check, adjust and determine the position of   sensors in the sensor
    network

• Special case of generalized location
  problem
  – Determine the pose of elements of network
             Mesh Analogy
• Physical Mesh
  – Rigid Bodies connected by springs.
• Rigid Body
  – Network elements e.g. Sensors, robots.
• springs
  – Constraints among the elements
  – Energy in spring is zero when constraints are
    satisfied
          Static localization
• Each element has Beacon or Beacon
  sensor
• Identity and Pose of each beacon can be
  determined
• Each beacon sensor measurement is a
  constraint
• When the springs are relaxed all the
  constraints are satisfied
The Mesh
         Dynamic localization
• Each element also has motion sensor
• Changes in position can be measured
• Each element is represented by series of
  bodies
• Two types of constraints
  – among the elements
  – among the states of elements at different times.
• By relaxation the global pose of all elements at
  all times can be found
              Localization

• Every entity defines a Local Coordinate
  System (LCS)
• Every measurement is a relationship
  between LCS.
• Find coordinate transformations that are
  consistent with these relations.
            Formalization
• Two diff sensors measure the pose of the
  same object at the same time Za and Zb
• Each will be with respect to its own LCS.
• But Za and Zb are the same point



Ta and Tb map Za and Zb to Global C.S
         Relaxation of Mesh
Energy in spring between element a and b.




Mesh with many rigid bodies
Contd…
• Total force acting on the body is




• Updated the pose for each body




• The System is iterated till it converges (total force on
  body falls below a threshold)
                SLAM
• Simultaneous localization and mapping
• One robot with beacon detector and
  odometry
• Environment with fix beacons
SLAM Data
SLAM Result
               Multislam

• Three Different robots each with beacon
  detector and odometry
• Robots cannot detect each other and start
  at different points
Environment with fix beacons
MSLAM Data
MSLAM Result
              Calibration
• Single mobile robot with beacon and
  odometry
• Environment with the beacon detectors
• Calibration of network formulated as
  localization problem
• The successive positions of the robot,
  maps the environment.
Uncalibrated Network
Calibrated network
                   Pros
• Algorithm scales linearly with n
• The actual implementation of the code is
  simple and small
• Applicable to both static and dynamic
  elements.
• No need for dealing with inverting matrices
  or dealing with 3n dimensions
                    Cons
• Does not scale to maps involving natural
  landmarks
• The mesh size increases linearly with time
  – Can be mitigated by deleting or merging older
    parts of mesh.
• Does the system always converge???

				
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posted:10/11/2012
language:English
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