3D Underactuated Bipedal Walking via H-LIP based Gait Synthesis and Stepping Stabilization

Abstract

In this paper, we present a Hybrid-Linear Inverted Pendulum (H-LIP) based approach for synthesizing and stabilizing 3D underactuated bipedal walking. The H-LIP model is proposed to capture the essential components of the underactuated part and actuated part of the robotic walking. The walking gait of the robot is then synthesized based on the H-LIP. We comprehensively characterize the periodic orbits of the H-LIP and provably derive their stepping stabilization. The step-to-step (S2S) dynamics of the H-LIP is then utilized to approximate the S2S dynamics of the horizontal state of the center of mass (COM) of the robotic walking, which results in a H-LIP based stepping controller to provide desired step sizes to stabilize the robotic walking. By realizing the desired step sizes, the robot achieves dynamic and stable walking. The approach is evaluated in both simulation and experiment on the 3D underactuated bipedal robot Cassie, which demonstrate dynamic walking behaviors with both versatility and robustness.

Robust Disturbance Rejection for Robotic Bipedal Walking: System-Level-Synthesis with Step-to-step Dynamics Approximation

“…We now introduce the stepping controller that is based on the approximation of the step-to-step (S2S) dynamics. We first define the S2S dynamics of bipedal walking and then introduce the Hybrid Linear Inverted Pendulum (H-LIP) based walking synthesis [10]: the S2S dynamics of the H-LIP is used to approximate the robot S2S dynamics. A statefeedback stepping controller, namely H-LIP stepping [12], [10], is then synthesized to discretely control the S2S state of the robot to achieve desired walking behaviors.…”

“…where x is the state of the robot, f n represents the nonlinear dynamics in the domain denoted by n, τ stands for the actuation, ∆ n→n+1 represents the discrete transition from The hybrid dynamics can be converted to a discrete stepto-step (S2S) dynamics [12], [10] which then facilitates step planning to stabilize walking. Let x − denote the pre-impact state before the swing foot strikes the ground.…”

“…In this paper, we focus on the in-depth study of robust bipedal stabilization that can reject push disturbances while respecting the kinematic feasibility of the physical robot. We first learn a step-to-step (S2S) dynamic model from the push-free robotic walking, which is generated using existing framework in [10]. The learned S2S (L-S2S) dynamics is a discrete dynamical system with the walking step size being the inputs.…”

“…The proposed approach can be viewed as an extension of stepping controllers [10], [12], [13], [14] that uses the S2S dynamics approximation to plan foot steps for bipedal walking stabilization. Here, the approximation of the S2S is directly learned from the walking data of the robot.…”

“…The application of the SLS also shows a great advantage over previous synthesis such as deadbeat control [10], [13], [15] and Linear Quadratic Regulators (LQR) [16] in [12] in bipedal stepping. The feedback controller obtained from the SLS includes the system constraints while optimizing a cost function of the states and inputs, which is very important in practice since the system constraints on the S2S dynamics are the kinematic constraints of the robot.…”