Nonlinear analysis of an indirectly controlled limit cycle walker

Towards controlling the frequency of limit cycle locomotion as well as adapting to rough terrain and performing specific tasks, a novel and indirect method has been recently introduced using an active wobbling mass attached to limit cycle walkers. One of the strongest advantages of the method is the easiness of its implementation, prompting its applicability to a wide variety of locomotion systems. To deeply understand the nonlinear dynamics for further enhancement of the methodology, we use a combined rimless wheel with an active wobbling mass as an example to perform nonlinear analysis in this paper. First, we introduce the simplified equation of motion and the gait frequency control method. Second, we obtain Arnold tongue, which represents region of entrained locomotion. In regions where the locomotion is not entrained, we explore chaotic and quasi-periodic gaits. To characterize bistability of two different locomotions that underlie hysteresis phenomena, basins of attraction for the two locomotions were computed. The present nonlinear analysis may help understanding the detailed mechanism of indirectly controlled limit cycle walkers.