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Self-alignment of an active head from observations of rotation matrices

In this paper we will show how rotation matrices obtained from image measurements, for instance via self-calibration of rotating cameras, may be used to self-align an active stereo head such that the optic axes of the cameras are parallel, horizontal and perpendicular to the elevation axis. Whereas general rotation matrices have three degrees of freedom, with robot heads we may generate motions with fewer degrees of freedom, and use prior knowledge of the kinematic chain to constrain the rotation matrices to have a particular form. We demonstrate how these constraints provide sufficient alignment information, and we provide fast, accurate and stable algorithms to achieve this task. Both a linear method, which minimizes an algebraic error, and two nonlinear methods which minimize meaningful errors, are presented, and we show in theory and experiments that they give virtually identical results. Results from both simulated data and from real images obtained from an active stereo head are presented.