A Hybrid Dynamical Extension of Averaging
  We extend a smooth dynamical systems averaging technique to a class of hybrid systems with a limit cycle that is particularly relevant to the synthesis of stable legged gaits. After introducing a definition of hybrid averageability sufficient to recover the classical result, we provide a simple illustration of its applicability to legged locomotion and conclude with some rather more speculative remarks concerning the prospects for further generalization of these ideas. 
Avik De, Samuel A. Burden, and Daniel E. Koditschek
cs.RO math.DS