  Trajectory optimization (TO) is one of the most powerful tools for generating
feasible motions for humanoid robots. However, including uncertainties and
stochasticity in the TO problem to generate robust motions can easily lead to
intractable problems. Furthermore, since the models used in TO have always some
level of abstraction, it can be hard to find a realistic set of uncertainties
in the model space. In this paper we leverage a sample-efficient learning
technique (Bayesian optimization) to robustify TO for humanoid locomotion. The
main idea is to use data from full-body simulations to make the TO stage robust
by tuning the cost weights. To this end, we split the TO problem into two
phases. The first phase solves a convex optimization problem for generating
center of mass (CoM) trajectories based on simplified linear dynamics. The
second stage employs iterative Linear-Quadratic Gaussian (iLQG) as a whole-body
controller to generate full body control inputs. Then we use Bayesian
optimization to find the cost weights to use in the first stage that yields
robust performance in the simulation/experiment, in the presence of different
disturbance/uncertainties. The results show that the proposed approach is able
to generate robust motions for different sets of disturbances and
uncertainties.
