# Self-synchronization and Self-stabilization of 3D Bipedal Walking Gaits

## TL;DR

This paper introduces a control strategy for 3D bipedal robots that achieves stable walking gaits by leveraging center of mass positioning and synchronization between sagittal and frontal plane motions, validated through simulations.

## Contribution

It extends stability principles from planar bipeds to 3D walking, proposing a virtual constraints-based control strategy using Hybrid Zero Dynamics for complex humanoid robots.

## Key findings

- Stable 3D walking gaits achieved in simulations
- Synchronization between sagittal and frontal motions demonstrated
- Robustness of the method confirmed through complex model testing

## Abstract

This paper seeks insight into stabilization mechanisms for periodic walking gaits in 3D bipedal robots. Based on this insight, a control strategy based on virtual constraints, which imposes coordination between joints rather than a temporal evolution, will be proposed for achieving asymptotic convergence toward a periodic motion. For planar bipeds with one degree of underactuation, it is known that a vertical displacement of the center of mass---with downward velocity at the step transition---induces stability of a walking gait. This paper concerns the qualitative extension of this type of property to 3D walking with two degrees of underactuation. It is shown that a condition on the position of the center of mass in the horizontal plane at the transition between steps induces synchronization between the motions in the sagittal and frontal planes. A combination of the conditions for self-synchronization and vertical oscillations leads to stable gaits. The algorithm for self-stabilization of 3D walking gaits is first developed for a simplified model of a walking robot (an inverted pendulum with variable length legs), and then it is extended to a complex model of the humanoid robot Romeo using the notion of Hybrid Zero Dynamics. Simulations of the model of the robot illustrate the efficacy of the method and its robustness.