A study of the stability of generalized wave gaits

The wave gait has been observed in animal and insect walking and has been widely implemented in the control of walking machines. It has been proved that the wave gait possesses the optimum stability among all periodic gaits under the geometrical condition that R/P < or = 1, where R and P are respectively the stroke and pitch of a walking machine. Recently, based on numerical results, a generalized hexapodal wave gait was reported to be more stable than the wave gait for R/P > 1. In this paper, in order to understand more about the generalized wave gait, an analytical method is applied to study its stability in three categories of multilegged systems: quadrupeds, hexapods, and 2n-legged systems (n > or = 4). Two optimal generalized wave gaits are found for quadrupeds, and three optimal gaits are found for each of the other two categories. For all three categories, one of the optimal generalized wave gaits is the wave gait. The stability and geometrical conditions of these optimal gaits are derived and verified numerically. Furthermore, it is shown that the quadrupedal generalized wave gaits have the optimum stability among all periodic gaits with the stepping sequence 1-4-2-3.