  Developing robust locomotion for humanoid robots is a complex task due to the
unstable nature of these robots and also to the unpredictability of the
terrain. A robust locomotion planner is one of the fundamental components for
generating stable biped locomotion. This paper presents an optimal closed-loop
biped locomotion planner which can plan reference trajectories even in
challenging conditions. The proposed planner is designed based on a
Time-Varying Model Predictive Control~(TVMPC) scheme to be able to consider
some constraints in the states, inputs and outputs of the system and also mixed
input-output. Moreover, the proposed planner takes into account the vertical
motion of the Center of Mass~(COM) to generate walking with mostly stretched
knees which is more human-like. Additionally, the planner uses the concept of
Divergent Component of Motion~(DCM) to modify the reference ZMP online to
improve the withstanding level of the robot in the presence of severe
disturbances. The performance and also the robustness of the proposed planner
are validated by performing several simulations using~\mbox{MATLAB}. The
simulation results show that the proposed planner is capable of generating the
biped locomotion robustly.
