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???