Integrated vision and touch sensing for CMMs

Original publisher: Gaithersburg, MD : U.S. Dept. of Commerce, Technology Administration, National Institute of Standards and Technology, [1997]. OCLC Number: (OCoLC)39150762 Subject: Computer vision. Excerpt: ... Uncalibrated vision results In this section, we describe our experiments and experiences in developing new image Jacobian-based techniques for CMM control. Our method assumes that a mechanism exists for picking out the tip of the probe in the image and for indicating the desired scan path. In this system, the probe tip and scan path are indicated by the user on the graphic user interface. We model the relationship between the camera system and image space using the following equa-tion: x U i - 1, where T = in end effector coordinates. ( 1 ) y w = P ( λ ) ⋅ T ⋅ T ⋅ T probe V cam 3 probe i z 1 Differentiating the above equation results in a relationship which relates image space with the 3D world. However, full knowledge of all the parameters is necessary to derive the complete Jacobian matrix. Since we assume that the calibration between image space and the world does not exist, we do not recover the image Jacobian directly. Instead, the system estimates the control movements for a 2D Z-X plane in. If y is kept con-W W stant, the differential relationship between image space and can be written as follows: δz a b δu =, for δy = 0. ( 2 ) δx c d δv where J, the estimate of the image Jacobian, is δz δz----------a b δu δv J = = ( 3 ) c d δx δx----------δu δv Eq. ( 2 ) links small linear moves in image space to small linear moves in W. The algorithm the system follows to derive the initial image Jacobian is: 1. Move the CMM to some position in where TIP is observable in image space. W 2. TIP projects to the point TIP ' in image space. ( Projections from 3D to 2D image space are denoted by the prime notation. ) 3. Move the probe to a new position TIP + ( 0, 0, δz ). The change in the pose of the probe tip in image space ( δu, δv ) is recorded. δz δz 4. Move ...