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The paper presents a planner to generate walking trajectories by using the centroidal dynamics and the full kinematics of a humanoid robot. The interaction between the robot and the walking surface is modeled explicitly via new conditions, the Dynamical Complementarity Constraints. The approach does not require a predefined contact sequence and generates the footsteps automatically. We characterize the robot control objective via a set of tasks, and we address it by solving an optimal controlarXiv:2207.03198v1 fatcat:hfm2utmsxza27c7ge6k5ap3pf4