In this paper we propose a new flexible method for hand-eye calibration. The vast majority of existing hand-eye calibration techniques requires a calibration rig which is used in conjunction with camera pose estimation methods. Instead, we combine structure-from-motion with known robot motions and we show that the solution can be obtained in linear form. The latter solves for both the hand-eye parameters and for the unknown scale factor inherent with structure-from-motion methods. The algebraic analysis that is made possible with such a linear formulation allows to investigate not only the well known case of general screw motions but also such singular motions as pure translations, pure rotations, and planar motions. In essence, the robot-mounted camera looks to an unknown rigid layout, tracks points over an image sequence and estimates the camera-to-robot relationship. Such a self calibration process is relevant for unmanned vehicles, robots working in remote places, and so forth. We conduct a large number of experiments which validate the quality of the method by comparing it with existing ones.

This article formulates a generic representation of a path-following controller operating under contained motion, which was developed in the context of surgical robotics. It reports two types of constrained motion: i) Bilateral Constrained Motion, also called Remote Center Motion (RCM), and ii) Unilaterally Constrained Motion (UCM). In the first case, the incision hole has almost the same diameter as the robotic tool. In contrast, in the second state, the diameter of the incision orifice is larger than the tool diameter. The second case offers more space where the surgical instrument moves freely without constraints before touching the incision wall. The proposed method combines two tasks that must operate hierarchically: i) respect the RCM or UCM constraints formulated by equality or inequality, respectively, and ii) perform a surgical assignment, e.g., scanning or ablation expressed as a 3D path-following task. The proposed methods and materials were tested first on our simulator that mimics realistic conditions of middle ear surgery, and then on an experimental platform. Different validation scenarios were carried out experimentally to assess quantitatively and qualitatively each developed approach. Although ultimate precision was not the goal of this work, our concept is validated with enough accuracy (inferior to 100 micrometres) for ear surgery.