Abstract
This paper addresses the question of what is the feasible range of movement for a body to remain balanced while standing. A feasible region in the center of mass position-velocity plane has been proposed previously. This paper shows that for a certain individual with given anatomical and mechanical characteristics, the feasible movements of the CoM, or more generally the range of states at which the control of balance would be possible, can be analytically found through a mechanical reasoning. This paper introduces a subspace of the motion state space, namely the integrated stable subspaces (ISS), and proves that the control of balance is possible all over the ISS. In order to illustrate how the method may be used in practice, the feasible region for a well-known one-DoF mechanical model as well as for a two-DoF one is found using this approach, and is compared to that found by the conventional method. The feasible region found by this method depends on the physical properties of a body including anatomical parameters of a body as well as the torque (control input) constraints. The method works with any arbitrary shape of the input constraint.
