  In this paper, we present a novel two-level variable Horizon Model Predictive
Control (VH-MPC) framework for bipedal locomotion. In this framework, the
higher level computes the landing location and timing (horizon length) of the
swing foot to stabilize the unstable part of the center of mass (CoM) dynamics,
using feedback from the CoM states. The lower level takes into account the
swing foot dynamics and generates dynamically consistent trajectories for
landing at the desired time as close as possible to the desired location. To do
that, we use a simplified model of the robot dynamics projected in swing foot
space that takes into account joint torque constraints as well as the friction
cone constraints of the stance foot. We show the effectiveness of our proposed
control framework by implementing robust walking patterns on our
torque-controlled and open-source biped robot, Bolt. We report extensive
simulations and real robot experiments in the presence of various disturbances
and uncertainties.
