Generation of robust trajectories for legged robots remains a challenging
task due to the underlying nonlinear, hybrid and intrinsically unstable
dynamics which needs to be stabilized through limited contact forces.
Furthermore, disturbances arising from unmodelled contact interactions with the
environment and model mismatches can hinder the quality of the planned
trajectories leading to unsafe motions. In this work, we propose to use
stochastic trajectory optimization for generating robust centroidal momentum
trajectories to account for additive uncertainties on the model dynamics and
parametric uncertainties on contact locations. Through an alternation between
the robust centroidal and whole-body trajectory optimizations, we generate
robust momentum trajectories while being consistent with the whole-body
dynamics. We perform an extensive set of simulations subject to different
uncertainties on a quadruped robot showing that our stochastic trajectory
optimization problem reduces the amount of foot slippage for different gaits
while achieving better performance over deterministic planning