next up previous contents
Next: 5.1 Trust Region Up: On-line Estimation of Visual-Motor Previous: 4.2 Model Estimation

5 Visual Servo Control

  In our framework the active robot agent specifies its actions in terms of desired visual perceptions tex2html_wrap_inline3540 . We need a control system capable of turning these goal perceptions into motor actions (in our system, joint movements). On the low level (excluding visual trajectory planning etc.) these movements are reactive. A simple control law, occuring in some form in most visual servoing research (e.g. [Conkie and Chongstitvatana, 1990, Hager et al., 1995, Hosoda and Asada, 1994]) is

(17) displaymath3935

where K is a gain matrix. In a discrete time system running at a fixed cycle frequency (at or below the 60Hz video frequency), the gain K turns into a step length tex2html_wrap_inline3918 : tex2html_wrap_inline3920 , where tex2html_wrap_inline3542 is the (least squares) solution to the (over determined) system

(18)  displaymath3937

This popular controller however has major deficiencies. Even for a convex problem ( tex2html_wrap_inline3878 in eq. 4.1 is convex) it is not guaranteed to be convergent [Dahlquist and Björck, 1995]. There is also the problem of selecting an tex2html_wrap_inline3918 so that the method converges, and does so reasonably quickly. Previous work has overcome these problems by only making a single, small distance move within a relatively smooth and well scaled region of f. A fixed tex2html_wrap_inline3918 , giving convergence within the small region can often be found by trial and error. For complete tasks this is not a viable solution, as moves may be over a large part of the robot workspace, and using a single, experimentally found tex2html_wrap_inline3918 is likely to be inefficient, as well as requiring a lot of trials to find that tex2html_wrap_inline3918 .





Martin Jägersand