Asymptotically Stable Walking of a Five-Link Underactuated 3D Bipedal Robot

TL;DR

This paper develops three feedback control strategies to achieve asymptotically stable, periodic, and fast walking gaits for a 3D underactuated bipedal robot with passive point feet, using an extension of virtual constraints and hybrid zero dynamics.

Contribution

It introduces a novel application of virtual constraints and hybrid zero dynamics to stabilize walking in a complex 3D underactuated robot with passive feet, including three distinct control strategies.

Findings

All three strategies successfully stabilize walking gait.

The event-based controller improves gait stability and speed.

Output selection significantly impacts stabilization effectiveness.

Abstract

This paper presents three feedback controllers that achieve an asymptotically stable, periodic, and fast walking gait for a 3D (spatial) bipedal robot consisting of a torso, two legs, and passive (unactuated) point feet. The contact between the robot and the walking surface is assumed to inhibit yaw rotation. The studied robot has 8 DOF in the single support phase and 6 actuators. The interest of studying robots with point feet is that the robot's natural dynamics must be explicitly taken into account to achieve balance while walking. We use an extension of the method of virtual constraints and hybrid zero dynamics, in order to simultaneously compute a periodic orbit and an autonomous feedback controller that realizes the orbit. This method allows the computations to be carried out on a 2-DOF subsystem of the 8-DOF robot model. The stability of the walking gait under closed-loop control is evaluated with the linearization of the restricted Poincar\'e map of the hybrid zero dynamics. Three strategies are explored. The first strategy consists of imposing a stability condition during the search of a periodic gait by optimization. The second strategy uses an event-based controller. In the third approach, the effect of output selection is discussed and a pertinent choice of outputs is proposed, leading to stabilization without the use of a supplemental event-based controller.