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Trajectory optimization (TO) is one of the most powerful tools for generatingfeasible motions for humanoid robots. However, including uncertainties andstochasticity in the TO problem to generate robust motions can easily lead tointractable problems. Furthermore, since the models used in TO have always somelevel of abstraction, it can be hard to find a realistic set of uncertaintiesin the model space. In this paper we leverage a sample-efficient learningtechnique (Bayesian optimization) to robustify TO for humanoid locomotion. Themain idea is to use data from full-body simulations to make the TO stage robustby tuning the cost weights. To this end, we split the TO problem into twophases. The first phase solves a convex optimization problem for generatingcenter of mass (CoM) trajectories based on simplified linear dynamics. Thesecond stage employs iterative Linear-Quadratic Gaussian (iLQG) as a whole-bodycontroller to generate full body control inputs. Then we use Bayesianoptimization to find the cost weights to use in the first stage that yieldsrobust performance in the simulation/experiment, in the presence of differentdisturbance/uncertainties. The results show that the proposed approach is ableto generate robust motions for different sets of disturbances anduncertainties.

Robust Humanoid Locomotion Using Trajectory Optimization and Sample-Efficient Learning