**5. Markers**

Vision tracking techniques for robots are based on the numerous approaches: marker based, object features, or even on complete synthesis of the expected object. All of the them are interesting and the selection is application depended. The most valuable techniques for the controlled environment scenarios are marker based. The uncontrolled environments exist if the unexpected situations may occurs, related to the object occlusions, different lighting conditions, etc.

(a) Marker model (b) Mask model

the numerical tests. The dedicated renderer of the marker and mask at different positions, scale (distance), 3D rotations, and contrast is used. The contrast fitting is important due to variable light conditions. The white and black points are defined by the two coordinate pairs (Fig. 11). The black (*Xb*,*Yb*) and white point (*Xw*,*Yw*) define simplest contrast, brightness, and

The first optimization phase is quite simple and the exhaustive search is used for a priori defined spatial and angular resolutions. Positions are tested using subpixel resolutions, 10 times higher resolution in both direction, and rotations using 20 deg. angle resolutions. The scale is not tested, because different scales of markers have common central part. Contrast is also not tested and fixed. The advantages of this phase are the fixed computation cost and

The best position obtained from first phase due to obtained *l*<sup>2</sup> value is tested using optimization in second phase. The selection is driven by the threshold value for *l*<sup>2</sup> value. Second phase is started in parallel for obtained positions with enough low value of *l*2. Second phase is based on the gradient and non–gradient approaches. The constrained optimization

During second phase gradient search algorithm is used and after the optimization is stopped (due to achieving error small changes, or after selected number of iterations) the non–gradient

(d) Example of noised image of

263

marker at low resolution

(c) Filtered (blurred) marker before

Fig. 10. Model of marker and noised measurements

saturation parameters of image transformation.

downsampling

Estimation of Position and Orientation

for Non–Rigid Robots Control Using Motion Capture Techniques

possibilities in parallel processing.

is applied in all optimization phases.

The marker based techniques are very interesting, because different markers designs are possible. The light emitting markers are especially useful for poor lighting conditions. They need additional power connections (wires) for the bulbs or LEDs. The retroreflective markers reflect surrounding light and no additional power connection are necessary for them. The retroreflective markers are interesting for small size and small power robots, especially.

Controlled environment of the robot's work area gives an ability of the correct light setup for maximization performance of retroreflective markers. Markers may support angular estimation (3DoF) depending on own shape. The simplest matte ball markers are orientation less so only a 3D position (3DoF) is obtained by the triangulation using two or more cameras. The carefully selected set of such markers located at close distance gives ability of estimation of orientation. The larger markers with additional orientation features may support estimation of orientation.

In this paper, the four–sector circle with the boundary ring is used as marker (Fig. 10). Such marker gives an ability of orientation estimation with 180 degree accuracy, position and distance. Complete set of DoF (six of them) is possible to estimate. The estimation of all parameters is limited by the optical visibility of the markers. A low angle case between camera and marker plane are hard to process. This is the reason, why a ball shape markers are preferred, because they have superior visibility. Large markers support estimation of own parameters even for partial occlusions but it is not considered in following tests.

The marker uses boundary ring for improving separation between background and marker, what is important for the scale estimation, because estimation process should be related to the marker, not to the background.
