Dynamic Walking on Highly Underactuated Point Foot Humanoids: Closing the Loop between HZD and HLIP

TL;DR

This work addresses dynamic locomotion for highly underactuated point-foot humanoids by closing the loop between full-order Hybrid Zero Dynamics gait generation and HLIP-based online stabilization. It presents a unified framework where HLIP constraints are embedded in offline HZD trajectory optimization and an HLIP regulator stabilizes online by adjusting step-lengths and swing-foot references, mapped to the full-order robot via inverse kinematics. The contributions include HLIP-integrated gait generation, an online HLIP-based regulation mechanism, and extensive validation on the ADAM robot, including nominal walking, push recovery, and rough-terrain locomotion. The results demonstrate robust, fast-paced locomotion for point-foot humanoids and offer a practical path toward more capable dynamic walking in underactuated systems.

Abstract

Realizing bipedal locomotion on humanoid robots with point feet is especially challenging due to their highly underactuated nature, high degrees of freedom, and hybrid dynamics resulting from impacts. With the goal of addressing this challenging problem, this paper develops a control framework for realizing dynamic locomotion and implements it on a novel point foot humanoid: ADAM. To this end, we close the loop between Hybrid Zero Dynamics (HZD) and Hybrid linear inverted pendulum (HLIP) based step length regulation. To leverage the full-order hybrid dynamics of the robot, walking gaits are first generated offline by utilizing HZD. These trajectories are stabilized online through the use of a HLIP based regulator. Finally, the planned trajectories are mapped into the full-order system using a task space controller incorporating inverse kinematics. The proposed method is verified through numerical simulations and hardware experiments on the humanoid robot ADAM marking the first humanoid point foot walking. Moreover, we experimentally demonstrate the robustness of the realized walking via the ability to track a desired reference speed, robustness to pushes, and locomotion on uneven terrain.

Figures (10)

• Figure 1: Snapshots of ADAM tracking the nominal HZD gaits with a stabilizing HLIP controller.
• Figure 2: An overview over the control framework showing the closed loop interaction between the HZD gait generation and the HLIP regulator.
• Figure 3: The HLIP states $p$ and $v$ are defined as the linear horizontal COM movement relative to the stance foot.
• Figure 4: The swing foot $x$ and $y$ position trajectories are functions of the current swing foot position, the desired step lengths, and the nominal HZD gait swing foot trajectories.
• Figure 5: The joint coordinates of the humanoid robot ADAM.