Restricted Discrete Invariance and Self-Synchronization For Stable Walking of Bipedal Robots
This addresses stability challenges in bipedal robot locomotion, but the approach appears incremental as it builds on known models like the 3D LIP.
The paper tackles the problem of achieving stable periodic walking in bipedal robots by identifying a low-dimensional invariant submanifold in the switching surface of hybrid locomotion models, and demonstrates through a numerical study that this leads to asymptotically stable walking.
Models of bipedal locomotion are hybrid, with a continuous component often generated by a Lagrangian plus actuators, and a discrete component where leg transfer takes place. The discrete component typically consists of a locally embedded co-dimension one submanifold in the continuous state space of the robot, called the switching surface, and a reset map that provides a new initial condition when a solution of the continuous component intersects the switching surface. The aim of this paper is to identify a low-dimensional submanifold of the switching surface, which, when it can be rendered invariant by the closed-loop dynamics, leads to asymptotically stable periodic gaits. The paper begins this process by studying the well-known 3D Linear Inverted Pendulum (LIP) model, where analytical results are much easier to obtain. A key contribution here is the notion of \textit{self-synchronization}, which refers to the periods of the pendular motions in the sagittal and frontal planes tending to a common period. The notion of invariance resulting from the study of the 3D LIP model is then extended to a 9-DOF 3D biped. A numerical study is performed to illustrate that asymptotically stable walking may be obtained.