Method to Estimate the Basin of Attraction and Speed Switch Control for the Underactuated Biped Robot

The biped robots have higher mobility than conventional wheeled robots, especially when moving on rough terrains, up and down slopes and in environments with obstacles. The geometry of the biped robot is similar to the human beings, so it is easy to adapt to the human life environment and can help the human beings to finish the complex work. With the development of the society, the needs for robots to assist human beings with activities in daily environments are growing rapidly. Therefore, a large number of researches have been done on the bipedal walking. The dynamic system of the biped robot is a nonlinear hybrid dynamic system, which consists of continuous differential equations and discrete events dynamic maps. Therefore, this system is a complex nonlinear system. The most effective way of analyzing the global properties of the nonlinear system is probably the straightforward numerical evaluation to compute the motions and then to infer some global properties from the numerical results. It has been reported that the passive biped robot has weak tolerance for large disturbances. The basin of attraction is widely used as a measure for the disturbance rejection for the biped robots, and it is a total set of state variables from which the walker can walk successfully (Ning, L. et. al., 2007). The larger the size of the basin of attraction is, the stronger the stability is. Therefore, more and more researchers have studied the methods to compute the basin of attraction for the biped robot. The cell mapping method was proposed to compute the basin of attraction for the simplest walking model with point feet and the planar model with round feet (Schwab, A.L. & Wisse, M., 2001); (Ning, L. et. al., 2007). The results of experiments show that this method is effective; however, it is time-consuming for multidimensional state space (Zhang, P., et. al., 2008). Based on the bionics study, most humanoid robot control methods are in terms of the basic principles and characteristics of hominine gait. A robotic simulacrum potentially can be very useful. The passive biped robot can walk down along the slope only by inertial and gravitational force. But this passive walking has weak robust and stability. The basin of attraction of the simplest walker can only tolerate a deviation of 2% from the fixed point (Schwab, A.L. & Wisse, M., 2001). In 14