Model Independent Visual Servoing

1. Model Independent Visual Servoing CMPUT 610 Literature Reading Presentation Zhen Deng

2. Introduction • Summaries and Comparisons of Traditional Visual Servoing and Model independent Visual Servoing emphasizing on the latter. • Works are mostly from Jenelle A. Piepmeier’s thesis and Alexandra Hauck’s thesis

3. Visual Servo • Visual servo control has the potential to provide a low-cost, low-maintenance automation solution for unstructured industries and environments. • Robotics has thrived in ordered domains, it has found challenges in environments that are not well defined.

4. Traditional Visual Servoing • Precise knowledge of the robot kinematics, the camera model, or the geometric relationship between the camera and the robot systems is assumed. • Need to know the exact position of the end-effector and the target in the Cartesian Space. • Require lots of calculation.

5. Rigid Body Links

6. Forward Kinematics • The Denavit-Hartenberg Notation: i-1 T i = Rotz(q) . Transz(d) . Rotx(a) . Trans(a) • Transformation 0 T e=0 T 11 T 22 T 3 … n-1 T n n T e

7. Jacobian by Differential • Velocity variables can transformed between joint space and Euclidean space using Jacobian matrices • Dx = J * Dq • Dq = J \ Dx • Jij = ¶qi/ ¶xj

8. Calibrated Camera Model

9. Model Independent Visual Servoing • An image-based Visual Servoing method. • Could be further classified as dynamic look-and-move according to the classification scheme developed by Sanderson and Weiss. • Estimate the Jacobian on-line and does not require calibrated models of either of the camera configuration or the robot kinematics.

10. History • Martin Jagersand formulates the visual Servoing problem as a nonlinear least squares problem solved by a quasi-Newton method using Broyden Jacobian estimation. • Base on Martin’s work, Jenelle P adds a frame to solve the problem of grasping a moving target. • me ? …

11. Reaching a Stationary Target • Residual error f(q) = y(q) - y*. • Goal: minimize f(q) • Df = fk - fk-1 • Jk = Jk-1 + (Df-Jk-1Dq) DqT/ DqTDq • qk+1 = qk -J-1kfk

12. Reaching a Fixed Object

13. Tracking the moving object • Interaction with a moving object, e.g. catching or hitting it, is perhaps the most difficult task for a hand-eye system. • Most successful systems presented in paper uses precisely calibrated, stationary stereo camera systems and image-processing hardware together with a simplified visual environment.

14. Peter K. Allen’s Work • Allen et al. Developed a system that could grasp a toy train moving in a plain. The train’s position is estimated from(hardware-supported) measurements of optic flow with a stationary,calibrated stereo system. • Using a non-linear filtering and prediction, the robot tracks the train and finally grasps it.

15. “Ball player” • Andersson’s ping-pong player is one of the earliest “ball playing” robot. • Nakai et al developed a robotic volleyball player.

16. Jenelle’s modification to Broyden • Residual error f(q,t) = y(q) - y*(t). • Goal: minimize f(q,t) • Df = fk - fk-1 • Jk = Jk-1 + (Df - Jk-1Dq + (¶ y*(t)/ ¶t *Dt) ) DqT/ DqTDq • qk+1 = qk -(JkTJk)-1 JkT (fk - (¶ y*(t)/ ¶t *Dt) ).

17. Convergence • The residual error converges as the iterations increasing. • While the static method does not. • The mathematics proof of this result could be found in Jenelle’s paper.

18. Experiments with 1 DOF system

19. Results

20. 6 DOF experiments

21. Future work ? • Analysis between the two distinct ways of computing the Jacobian Matrix. • Solving the tracking problem without the knowledge of target motion. • More robust … ?

22. Literature Links • http://mime1.gtri.gatech.edu/imb/projects/mivs/vsweb2.html • A Dynamic Quasi-Newton Method for Uncalibrated Visual Servoing by Jenelle al • Automated Tracking and Grasping of a Moving Object with a Robotic Hand-Eye System. By Peter K. Allen

23. Summary • Model Independent approach is proved to be more robust and more efficient.