“…When μ N /μ T 1, the undulatory system moves in the direction opposite to that of the wave propagation, so that forward propulsion is by retrograde (head-to-tail) body waves (see, e.g., [4], [9]- [12], [21]- [23]). By contrast, when μ N /μ T < 1, or when μ N /μ T 1 (as is the case in our system), the overall locomotion is along the body wave direction, so that forward motion is by direct (tail-to-head) waves (for analysis and relevant robotic implementations, see [1]- [3], [6], [8]). …”