Revisiting the Determination of the Singularity Cases in the Visual Servoing of Image Points Through the Concept of Hidden Robot

The determination of the singularity cases in visual servoing is a tricky problem, which is unsolved for most of the image-based approaches. In order to avoid singularities, redundant measurements may be used. However, they lead to the presence of local minima. Moreover, they do not always ensure that singularities can be avoided. Here, we show that a concept named the “hidden robot,” which was formerly used for understanding the singularities of a vision-based controller dedicated to parallel robots, can be used for interpreting the singularities in the visual servoing of image points. These singularity cases were already found in the case in which three points are observed, but we show that the hidden robot concept considerably simplifies the analysis by using geometric interpretations of the mapping degeneracy and tools provided by the mechanical engineering community. Moreover, to the best of our knowledge, for the first time, we provide the singularity conditions when more than three points are observed. We also discuss how these tools could be extended in order to find the singularity cases of other visual servoing techniques (e.g., when lines are observed).