Generation of an initial feasible point

Consider model of the system.

We assume, that initial state is given (in X_tilde form). A feasible ZMP profile can be build by selecting reference points, which satisfy inequality constraints. Then based on this profile we can find all states and control inputs:

1. since the coordinates of the current and the next ZMP positions are known, we can compute control inputs necessary to change position;
   1. given control inputs and current state we can find the next state;
   2. if there are more ZMP positions in ZMP profile go to step 1;
   3. perform variable substitution (rotation) to convert the feasible point to X_bar form.