Characterization of frictional multi-legged equilibrium postures on uneven terrains

Quasistatic legged locomotion over uneven terrains requires characterization of the legged robot equilibrium postures as well as an understanding of the non-static motion modes that can develop at the contacts. This paper characterizes the frictional multi-legged equilibrium postures on a generic class called 'tame stances', which satisfy a generalized support polygon principle. To characterize the equilibrium postures, the paper lumps the legged mechanism's kinematic structure into a rigid body having a variable center of mass and maintaining the same contacts with the terrain. The equilibrium postures associated with a given set of contacts correspond to the locations of the center of mass at which the body is supported in static equilibrium by the same contacts under the influence of gravity. This paper thus characterizes the feasible equilibrium region of a rigid body having a variable center of mass and supported by multiple frictional contacts under the influence of gravity. The paper establishes that the feasible equilibrium region forms a convex set which has five types of boundary curves. These boundary curves are formulated analytically, illustrated with graphical examples, and associated with the onset of five non-static motion modes at the contacts. The paper also compares the analytical results against experimental measurements conducted on a legged mechanism prototype.