On the Dynamic Stability of Biped Locomotion

While biped locomotion involves very complicated dynamical processes, a good deal can be learned about stability and feedback control from an analysis of simplified mathematical models. This paper treats locomotion dynamics relative to planar motion under an assumption that leg mass can be ignored in comparison to body mass. Thus the hypothetical biped possesses one rotational degree of freedom and two translational degrees, leading to a sixth-order system of nonlinear differential equations. These equations are linearized and feedback control laws are then derived to produce the desired stable forward motion. The feedback laws proposed involve a combination of continuous and discrete concepts to produce both step length and step period control as well as control of body attitude and altitude. The applicability of the control laws to the nonlinear system in the presence of large disturbances is verified by computer simulation. Hopefully, the results presented are significant relative to control processes arising in lower extremity prostheses and orthoses as well as to the design of biped robots.