Gait Controllability for Legged Robots

We present a general method for determining controllability of a class of kinematic legged robots. The method is general in that it is independent of the robot's morphology; in particular, it does not depend upon the number of legs. Our method is based on an extension of a nonlinear controllability test for smooth systems to the legged case, where the relevant mechanics are not smooth. Our extension is based on the realization that legged robot configuration spaces are stratified. The result is illustrated with a simple example. 1 Introduction This paper considers the issue of nonlinear gait controllability for legged robots. That is, we consider if a specified gait can allow the robot to move in any direction. This is important for two reasons. First, such controllability is a necessary condition for motion planning algorithms. (Clearly, if the robot cannot move in all directions, it is then impossible to specify an arbitrary path for the robot to follow). Secondly, controllability..