Bipedal walking trajectory generation based on ZMP and Euler´s equations of motion

This article is aimed at presenting a technique to generate bipedal walking trajectories that can be applied to humanoid robots. The proposed method is based on maintatining the dynamic balance by using the ZMP criterion throughout single support phases. To be able to reach this goal, we employed ZMP equations in spherical coordinates, so that the rate change of intrinsic angular momentum terms in ZMP equations are included naturally by using Euler´s equations of motion. Thus, undesired torso angle fluctuations are successfully suppressed comparing to other methods in which intrinsic angular momentum rate changes are ignored or zero-referenced. Applying the aforementioned technique, we firstly performed simulations on a 3-D dynamic simulator. Upon simulations, we conducted walking experiments on the actual robot MARI-3. In conclusion, we obtained dynamically equilibrated and bipedal walking cycles in which torso angles are well suppressed in comparison with the conventional approach.