Exploiting the Equations of Motion For Biped Robot Control with Enhanced Stability

The scope of the present contribution is the derivation of the equations of motion and its field of application for humanoid robots, in particular legged robots. The derivation is performed in a modular and structured manner and it is shown how these equations can be exploited for the control of biped robots. The used methods allow to easily adopt the kinematic structure of single limbs and to reuse results obtained for limbs with similar kinematic structure but different inertial parameters such as in case the left leg is a mirrored version of the right one. After finding a recursive formulation to calculate the equations of motion we perform various state transformations and apply some model simplifications to obtain expressions that can be used to efficiently solve control problems. Two applications, compensating for the overall angular momentum and calculation of feed-forward torques, are shown. In both applications we can exploit the recursive calculation of the equations of motion used during the subsystem synthesis giving rise to real-time algorithms that can be used on a physical humanoid robot system.

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