Robust humanoid control using a QP solver with integral gains

We propose a control framework for torque controlled humanoid robots that efficiently minimizes the tracking error in a Quadratic Programming (QP) formulated as multi-objective weighted tasks with constraints. It results in an optimal dynamically-feasible reference that can be tracked robustly, with exponential convergence, without joint torque feedback, in the presence of non modelled torque bias and low-frequency bounded disturbances. This is achieved by introducing integral gains in a Lyapunov-stable torque control, which exploit the passivity properties of the dynamical model of the robot and their effect on the dynamic constraints of the QP solver. The robustness of this framework is demonstrated in simulation by commanding our robot, the HRP-5P, to achieve simultaneously several objectives in the configuration and the Cartesian spaces, in the presence of non-modeled static and kinetic joint friction, as well as an uncertain torque scale.