Relaxation On a Mesh a formalism for generalized Localization

1. Relaxation On a Mesha 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

2. 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

3. 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

4. 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

5. 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

6. The Mesh

7. 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

8. 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.

9. 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

10. Relaxation of Mesh Energy in spring between element a and b. Mesh with many rigid bodies

11. 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)

12. SLAM • Simultaneous localization and mapping • One robot with beacon detector and odometry • Environment with fix beacons

13. SLAM Data

14. SLAM Result

15. Multislam • Three Different robots each with beacon detector and odometry • Robots cannot detect each other and start at different points Environment with fix beacons

16. MSLAM Data

17. MSLAM Result

18. 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.

19. Uncalibrated Network

20. Calibrated network

21. 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

22. 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???