The Newton-Euler equations that govern multi-body systems are not integrable in general. However, they become so in the pendular mode, a specific way of moving where conservation of the angular momentum is enforced. This property was successfully showcased for locomotion over horizontal floors (2D locomotion) by walking pattern generators based on the LIPM and CART-table models. In this talk, we will see how to generalize these two models to 3D locomotion while taking into account both friction and tilted contacts, resulting into the FIP (3D version of LIPM) and COM-accel (3D version of CART-table) models. We will demonstrate both approaches in live simulations with the HRP-4 humanoid model.
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