Adaptive control for estimating translations from image-based variations

We investigate the problem of learning the mapping between arbitrary image-based variations and variations in Euclidean space for the application of visual-servoing. We derive a linear formulation of the visuomotor function, which captures this relationship for three dimensional translations. The resulting expression defines how the origin of the world coordinate frame shifts in stereo images as the robot translates. The parameters of the visuomotor function are estimated online by using incremental least squares and are generalized to other coordinate frames origins by using a function approximation method. It follows that the system is able to estimate the three dimensional translations between pairs of stereo points without performing 3D reconstruction or requiring a specific coordinate system and is fully adaptive