Effects of gravity and friction constraints on bipedal balance control

The satisfaction of constraints between the foot and the ground during balancing of bipedal standing is important. In this work, the effects of two constraints, namely the gravity constraint and the friction constraint, on balancing of a simplified two-dimensional biped are considered. The bounds imposed on the control torque are first determined analytically. Such results not only show the specific constraint causing the control bounds, but also indicate the possible violation of the individual constraint. It is also found that the angular velocity plays a crucial role in satisfying the constraints. More importantly, it is found that in a region around the upright position within the critical angles, if the angular velocity is above the critical one, regardless of the control torque, the constraints cannot be satisfied. Another interesting finding is that between the gravity constraint and the friction constraint, the friction constraint is more dominant, thus should be considered carefully