Legged robots have excellent terrestrial mobility for traversing diverse environments and, thus, have the potential to be deployed in a wide variety of scenarios. However, they are susceptible to falling and leg malfunction during locomotion. Although the use of a large number of legs can overcome these problems, it makes the body long and leads to many legs being constrained to contact with the ground to support the long body, which impedes maneuverability. To improve the locomotion maneuverability of such robots, this study focuses on dynamic instability, which induces rapid and large movement changes, and uses a 12-legged robot with a flexible body axis. Our previous work found that the straight walk of the robot becomes unstable through a Hopf bifurcation when the body-axis flexibility is changed, which induces body undulations. Furthermore, we developed a simple controller based on the Hopf bifurcation and showed that the instability facilitates the turning of the robot. In this study, we newly found that the straight walk becomes unstable through a pitchfork bifurcation when the body-axis flexibility is changed in a way different from that in our previous work. In addition, the pitchfork bifurcation induces a transition into a curved walk, whose curvature can be controlled by the body-axis flexibility. We developed a simple controller based on the pitchfork bifurcation characteristics and demonstrated that the robot can perform a turning maneuver superior to that with the previous controller. This study provides a novel design principle for maneuverable locomotion of many-legged robots using intrinsic dynamic properties.

Passive dynamic walking is a model that walks down a shallow slope without any control or input. This model has been widely used to investigate how stable walking is generated from a dynamic viewpoint, which is useful to provide design principles for developing energy-efficient biped robots. However, the basin of attraction is very small and thin, and it has a fractal-like complicated shape. This makes it difficult to produce stable walking. Furthermore, the passive dynamic walking shows chaotic attractor through a period-doubling cascade by increasing the slope angle, and the chaotic attractor suddenly disappears at a critical slope angle. These make it further difficult to produce stable walking. In our previous work, we used the simplest walking model and investigated the fractal-like basin of attraction based on dynamical systems theory by focusing on the hybrid dynamics of the model composed of the continuous dynamics with saddle hyperbolicity and the discontinuous dynamics by the impact at foot contact. We elucidated that the fractal-like basin of attraction is generated through iterative stretch and bending deformations of the domain of the Poincaré map by sequential inverse images of the Poincaré map. In this study, we investigated the mechanism for the disappearance of the chaotic attractor by improving our previous analysis. In particular, we focused on the range of the Poincaré map to specify the regions to be stretched and bent by the inverse image of the Poincaré map. We clarified the condition for the chaotic attractor to disappear and the mechanism why the chaotic attractor disappears based on the stretch-bending deformation in the basin of attraction.