Bisection method for evaluation of attraction region of passive dynamic walking

A new numerical method for calculation of the attraction region of limit cycle in passive dynamic walking are proposed in the paper. The cell-mapping method is usually used in the evaluation of attraction region, but the calculation is complex and time-consuming. The existing studies show that the attraction region of passive dynamic walking gait is a continuous region and can be determined by its edge. The new calculation method called the bisection method is presented to determine the basin of attraction approximately simply by searching for its edge. Using the proposed bisection method, the basins of attraction are calculated for passive dynamic walker with and without knees, and the result is compared with the cell mapping method. Compared with the usually used cell mapping method, the bisection method can locate the attraction region with a much higher accuracy and yet need much less of calculation amount.