  Model predictive control (MPC) has shown great success for controlling
complex systems such as legged robots. However, when closing the loop, the
performance and feasibility of the finite horizon optimal control problem (OCP)
solved at each control cycle is not guaranteed anymore. This is due to model
discrepancies, the effect of low-level controllers, uncertainties and sensor
noise. To address these issues, we propose a modified version of a standard MPC
approach used in legged locomotion with viability (weak forward invariance)
guarantees. In this approach, instead of adding a (conservative) terminal
constraint to the problem, we propose to use the measured state projected to
the viability kernel in the OCP solved at each control cycle. Moreover, we use
past experimental data to find the best cost weights, which measure a
combination of performance, constraint satisfaction robustness, or stability
(invariance). These interpretable costs measure the trade off between
robustness and performance. For this purpose, we use Bayesian optimization (BO)
to systematically design experiments that help efficiently collect data to
learn a cost function leading to robust performance. Our simulation results
with different realistic disturbances (i.e. external pushes, unmodeled actuator
dynamics and computational delay) show the effectiveness of our approach to
create robust controllers for humanoid robots.
