A Unified Approach to Integrate Unilateral Constraints in the Stack of Tasks

The control approaches based on the task function formalism, and particularly those structured as a prioritized hierarchy of tasks, enable complex behaviors with elegant properties of robustness and portability to be built. However, it is difficult to consider a straightforward integration of tasks described by unilateral constraints in such frameworks. Indeed, unilateral constraints exhibit irregularities that prevent the insertion of unilateral tasks at any priority level, other than the lowest, of a hierarchy. In this paper, we present an original method to generalize the hierarchy-based control schemes to account for unilateral constraints at any priority level. We develop our method first for task sequencing using only the kinematics description; then, we expand it to the task description, using the operational space formulation. The method applies in robotics and computer graphics animation. Its practical implementation is exemplified by realizing a real-manipulator visual servoing task and a humanoid avatar reaching task; both experiments are achieved under the unilateral constraints of joint limits.