  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.
