The interactions of stance width and feedback control gain: A modeling study of bipedal postural control

By understanding and mimicking characteristics of postural control used by animals, scientist and engineers may develop standing autonomous robots that work safely within home environments, and treatment strategies that help people overcome postural impairments. To increase our understanding of postural control we developed physical and computational models of standing posture to explain the interrelation of stance width and feedback gain in controlling the stability and dynamics of the postural response. These models facilitated precise analysis of mechanical dynamics and their effects on compliant feedback control, and provided a real world physical implementation to verify predictions developed from simulation. Although previous studies have shown that a correlation exists between increased stance width and decreased postural responses, they have not quantified the relation between stance and the active control of standing posture. We show that a scaling of active feedback gain is required to maintain postural stability. This scaling of gains is dependent on the changing kinematic relations of the mechanical structure as it undergoes stance width adjustments. Specifically, we show that increasing stance width increases the leverage of the mechanical system. Feedback gains must be reduced by the reciprocal of the increase in mechanical leverage in order to maintain a consistent postural response; otherwise, the system may become unstable with increasing oscillations. We also evaluated the effects of increasing magnitudes of intrinsic stiffness on the postural response, and showed that intrinsic stiffness increases postural stability by facilitating stable responses over larger ranges of active feedback gain and increasing the stability of responses by decreasing settling time, oscillations, and displacement magnitude. The conclusions of this study were that the variation of mechanical leverage is responsible for changing the dynamics of the response during stance width variation, and that scaling of feedback gains with the changing mechanical leverage of stance width variations is required to maintain consistent response dynamics across stance widths.