Adaptive-Gains Enforcing Constraints in Closed-Loop QP Control

In this letter, we revisit an open problem of constraints formulation in the context of task-space control frameworks formulated as quadratic programs. In most inverse dynamics implementations, the decision variables are: robot joints acceleration, interaction forces (mostly physical contacts), and robot torques. Nevertheless, many constraints, like distance and velocity bounds, are not written originally in terms of one of these decision variables. Previous work proposed solutions to formulate and enforce joint limits constraints. Yet, none of them worked properly in closed-loop, specifically when bounds are reached or when they are time-varying. First, we show that constraints like collision avoidance, bounds of center of mass, constraints on field-of-view, Cartesian and velocity bounds on a given link... are written in a generic class. Then, we formulate such a class of constraints with gain-parameterized ordinary differential inequality. An adaptive-gain method enforces systematically such class of constraints, and results on a stable behavior when their bounds (even when they vary with time) are reached in closed-loop. Experimental results performed on a humanoid robot validate our solution on a large panel of constraints.