In this paper we consider the problem of allowing a humanoid robot that is subject to a persistent disturbance, in the form of a payload-carrying task, to follow given planned footsteps. To solve this problem, we combine an online nonlinear centroidal Model Predictive Controller - MPC with a contact stable force parametrization. The cost function of the MPC is augmented with terms handling the disturbance and regularizing the parameter. The performance of the resulting controller is validated both in simulations and on the humanoid robot iCub. Finally, the effect of using the parametrization on the computational time of the controller is briefly studied.

Jet-powered vertical takeoff and landing (VTOL) drones require precise thrust estimation to ensure adequate stability margins and robust maneuvering. Small-scale turbojets have become good candidates for powering heavy aerial drones. However, due to limited instrumentation available in these turbojets, estimating the precise thrust using classical techniques is not straightforward. In this paper, we present a methodology to accurately estimate the online thrust for the small-scale turbojets used on the iRonCub - an aerial humanoid robot. We use a grey-box method to capture the turbojet system dynamics with a nonlinear state-space model based on the data acquired from a custom engine test bench. This model is then used to design an extended Kalman filter that estimates the turbojet thrust only from the angular speed measurements. We exploited the parameter estimation algorithm to ensure that the EKF gives smooth and accurate estimates even at engine failures. The designed EKF was validated on the test bench where the mean absolute error in estimated thrust was found to be within 2% of rated peak thrust.