Traditional legged runners and climbers have relied heavily on gait generators in the form of internal clocks or reference trajectories. In contrast, here we present physical experiments with a fast, dynamical, vertical wall climbing robot accompanying a stability proof for the controller that generates it without any need for an additional internal clock or reference signal. Specifically, we show that this “self-exciting” controller does indeed generate an “almost” globally asymptotically stable limit cycle: the attractor basin is as large as topologically possible and includes all the state space excluding a set with empty interior. We offer an empirical comparison of the resulting climbing behavior to that achieved by a more conventional clock-generated gait trajectory tracker. The new, self-exciting gait generator exhibits a marked improvement in vertical climbing speed, in fact setting a new benchmark in dynamic climbing by achieving a vertical speed of 1.5 body lengths per second. For more information: Kod*Lab