Continuous control law from unilateral constraints

The control approaches based on tasks, and particularly based on a hierarchy of tasks, enable to build complex behaviors with some nice properties of robustness and portability. However it is difficult to consider directly unilateral constraints in such a framework. Unilateral constraints presents some strong irregularities (in particular at the level of their derivative) that prevents the insertion of unilateral-based tasks at the high-priority level of a hierarchy. In this paper, we present an original method to generalize the hierarchy-based control schemes to take unilateral constraint into account at the top-priority level. We develop our method first at the kinematic level then directly at the dynamic level using the operational space. The method is then validated on a various set of robots by realizing a visual servoing under the constraint of joint limits.