Real-time running and jumping pattern generation for bipedal robots based on ZMP and Euler´s equations

This paper is presenting a method to generate real-time running and jumping trajectories that can be applied to bipedal humanoid robots. The proposed method is based on maintaining the overall dynamic balance by using the ZMP stability criterion throughout support phases. To be able to reach this goal, we utilize ZMP equations in spherical coordinates, so that the rate change of angular momentum terms in ZMP equations are included naturally by using Eulerian equations of motion for unsymmetrical bodies. Thus, undesired torso angle fluctuation is expected to be more restrainable comparing to other methods in which angular momentum information is ignored or zero-referenced. Applying the aforementioned technique, we primarily simulated running motion on a dynamic 3-D simulator. Secondarily, one-legged jumping experiments were conducted on the actual bipedal robot. In conclusion, we obtained repetitive and successful running and jumping cycles which satisfactorily verify the proposed method.