Adaptive-Gains Enforcing Constraints in Closed-Loop QP Control
Résumé
We revisit an open problem of a class of constraints obtained through derivation in task-space control frameworks formulated as quadratic programs. It is common that weighted or strict-hierarchy task-space formulation result in a set of constraints to fulfill strictly and others to meet at best. In most implementation implying dynamics, the decision variables are: robot's joints acceleration, interaction forces (mostly physical contacts), and robot torques (that can be eliminated if torque bounds are known). However many constraints, e.g. joint constraints, do not write straightforwardly in terms of one of these decision variables. Previous work proposed solutions to write and enforce joint constraints. Yet, none of them worked properly in a closed-loop formulation of the QP when bounds are reached or when bounds change. In this letter, we show that joint constraints are part of a more general class of constraints such as collision avoidance, bounds of center of mass, constraints on field-of-view, Cartesian bounds on a given link, etc. We propose a general solution not only to enforce such a class of constraints at their bounds but also eliminating the chattering observed in all the existing methods; and more importantly, a systematic way to set the gains that allow stable behavior when bounds are reached in closed-loop.
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