Eulerian ZMP resolution: Real-time jogging and jumping trajectory planning for bipedal robots

This paper is aimed at presenting a method to generate real-time jogging and jumping trajectories that can be applied to bipedal humanoid robots. The proposed method is based on ensuring the dynamic balance in a feasible way. For this purpose, we utilized the ZMP stability criterion and projectile motion throughout support and flight phases, respectively. In order to achieve dynamically equilibrated jogging and jumping, we discretized ZMP equations in spherical coordinates, so that angular momentum information is included in a natural way. Hence, undesired torso angle fluctuation is greatly decreased comparing to other methods, in which angular momentum is ignored. Applying the aforementioned technique, Eulerian ZMP Resolution, we firstly simulated bipedal jogging motion on a 3-D dynamic simulator. Secondarily, one-legged jumping experiments are conducted on the actual bipedal robot. As the result, we obtained repetitive and stable jogging and jumping cycles, which satisfactorily verify the proposed method.