Slack variable method for state variable constraint

The slack variable method is introduced into receding horizon control with inequality constraint, and formulation about swing leg was described. Generally, the conditions that swing leg does not fall under the floor altitude can be described as inequality state variable constraint. It is difficult to treat this as a states variable constraint, because there is no control input variable explicitly. In this paper, it proposes dealing this with a problem using slack variable. This simple formulation can be applied to varied legged robot with any number of legs.