The optimally stable ranges of 2n-legged wave gaits

The study of the optimally stable range of the wave gait is extended to the 2n-legged case (n⩾2). To accomplish this, an analytical method is applied to compare the longitudinal stability margin of the wave gait with all periodic and regular gaits. It is shown that the wave gait is optimally stable in the range of 3/4⩽β<1 for n=2, which confirms the analytical result of the R.B. McGhee and A.A. Frank (1968); and in the range of 1/2⩽β<1 for n=3, which confirms the numerical results of P. Bessonov and N.V. Umnov (1973). β is the time fraction of a cycle in which a leg is on the ground. For n>4, the wave gait is optimally stable in the range of 1/2⩽β<1 for most of these cases. However, there are 49 cases for which the lower bound of the optimally stable range is higher than 1/2. The optimally stable ranges of these cases are listed. Overall, the wave gait is optimally stable in the range of 2/3⩽β<1 for n⩾4. If the wave gait is compared with periodic and regular gaits, which are either symmetric or constant-phase-incremented, the wave gait is optimally stable in the range of 3/4⩽β<1 for n=2 and in the range of 1/2⩽β<1 for n⩾3