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The paper presents a planner to generate walking trajectories by using thecentroidal dynamics and the full kinematics of a humanoid robot. Theinteraction between the robot and the walking surface is modeled explicitly vianew conditions, the \emph{Dynamical Complementarity Constraints}. The approachdoes not require a predefined contact sequence and generates the footstepsautomatically. We characterize the robot control objective via a set of tasks,and we address it by solving an optimal control problem. We show that it ispossible to achieve walking motions automatically by specifying a minimal setof references, such as a constant desired center of mass velocity and areference point on the ground. Furthermore, we analyze how the contactmodelling choices affect the computational time. We validate the approach bygenerating and testing walking trajectories for the humanoid robot iCub.

Dynamic Complementarity Conditions and Whole-Body Trajectory Optimization for Humanoid Robot Locomotion