Advanced Turning Maneuver of a Many-Legged Robot Using Pitchfork Bifurcation

Abstract

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

Maneuverable and Efficient Locomotion of a Myriapod Robot with Variable Body-Axis Flexibility via Instability and Bifurcation

“…Our previous study 43 revealed that when all the spring constants for the body-segment yaw joints are reduced, the straight walk becomes unstable through Hopf bifurcation (this bifurcation changes the stability of an equilibrium point in a dynamical system by changing a parameter and creating a limit cycle 46 ), and body undulations appear, which was verified by a Floquet analysis with a simple robot model. In addition, another previous study 42 revealed that when only the spring constant k 1 for yaw joint 1 is reduced, the straight walk transitions into a left- or right-curved walk through pitchfork bifurcation (this bifurcation changes the stability of an equilibrium point and creates two equilibrium points 46 ), which was also verified by a Floquet analysis with a simple robot model.…”

“…The developed robot 43 was later improved. 42 , 44 In this study, the robot newly incorporated a variable stiffness mechanism. This robot is composed of six modules (modules 1–6).…”

“…We used the same controller for the legs as that in our previous study 42 , 44 to make the robot walk in a straight line. Specifically, we controlled the two pitch joints of each leg so that the leg tip follows the desired trajectory composed of trajectories for the swing and stance phases ( Fig.…”

“…Specifically, we made the body axis of a 12-legged robot flexible. Our previous study 42 showed that changing the body-axis flexibility produces pitchfork bifurcation. This bifurcation not only induces the dynamic instability of a straight walk but also the transition into a curved walk.…”

Another Mechanism for Gait Generation: Mechanical Stabilization Can Spontaneously Realize Walking in a Two-Legged Robot

“…In addition, bifurcation phenomena have been observed in areas other than walking motion. Aoi et al demonstrated the advanced turning maneuvers of a multilegged centipede robot using the bifurcation phenomenon as a parameter of the flexibility of its body segments [40]. In a study of bifurcated gait transitions, a semi-autonomous control system with two bifurcated attractors was proposed [41].…”