FSW (feasible solution of wrench) for multi-legged robots

In this paper, we focus on a problem of how to confirm a feasible condition of applied force to a multi-legged robot on rough terrain. The problem often appeals as a subject of walking stability criterion for a legged robot. ZMP (zero moment point) is one of the well-known criteria. It shows the condition as footprints of a legged robot, but it cannot be defined on the rough terrain. Therefore, we suggest a new criterion FSW (feasible solution of wrench), which gives the feasible condition even on the rough terrain from the viewpoint of "wrench"-a special representation of force screw. And we present two short examples of FSW for a biped robot, how to analyse the validity of ZMP on stairs and how to design a force trajectory on rough terrain.