Numerical method to estimate the initial state of the stable gaits for the underactuated biped robot with knees

When the initial state of the stable gaits does not match the structure parameter values, the robot may fall down. To estimate a initial state of the stable gaits for the biped robot with knees, a new numerical method is proposed in this paper. It is based on the theories of cell mapping and Poincareacute return map. This numerical method has general applicability. We can use this method to estimate the fixed point of the hybrid dynamic system. Experimental results verified the validity of this method. It shows that the gait from the initial state obtained with this numerical method will converge to a stable limit cycle. Therefore, this numerical method played a guiding role in the design of controllers in practice. We also have done research on the effect of the mass ratio of the shank and the thigh on the period. It is discovered that the period increases as the mass ratio increases, but the mechanical energy of a half of one step decreases as the mass ratio increases. Combining these results, the optimal mass ratio is almost from 1/4 to 1/10. This result has a positive meaning for bridging the gap between existing theoretical models and developing prototype machine.