The effects of parameter variation on the basins of attraction of passive walking models

Passive dynamic walking is a new concept for biped robots, supplying natural and high energy-efficient gaits. A completely uncontrolled and unactuated passive walker can walk stably down a gentle slope, only powered by gravity. However, these passive walkers are sensitive with mechanical parameter variation, and only carefully tuned models can walk stably. Furthermore, the stable gaits cannot endure large disturbance. Therefore, the effects of parameter variation on the basins of attraction of passive walking models are discussed. The models include the straight leg model and the model with knees. Both models have round feet and distributed mass. With the aid of cell mapping method, the basins of attraction of these models which have different parameter combinations have been obtained. A larger foot radius, a higher position of the center of mass, and a small moment of inertia, might be benefit for enhancing the basin of attraction of the straight leg model. A group of parameters has been chosen, and the straight leg model with this set of parameters has relatively large basin of attractions on different slopes. The parameters of the kneed model are derived from the straight leg model, and it also has large basin of attraction. The results show that both the models could endure larger disturbances than ever discovered.