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Controller design for bipedal walking on dynamic rigid surfaces (DRSes), which are rigid surfaces moving in the inertial frame (e.g., ships and airplanes), remains largely underexplored. This paper introduces a hierarchical control approach that achieves stable underactuated bipedal walking on a horizontally oscillating DRS. The highest layer of our approach is a real-time motion planner that generates desired global behaviors (i.e., center of mass trajectories and footstep locations) by stabilizing a reduced-order robot model. One key novelty of this layer is the derivation of the reduced-order model by analytically extending the angular momentum based linear inverted pendulum (ALIP) model from stationary to horizontally moving surfaces. The other novelty is the development of a discrete-time foot-placement controller that exponentially stabilizes the hybrid, linear, time-varying ALIP. The middle layer translates the desired global behaviors into the robot’s full-body reference trajectories for all directly actuated degrees of freedom, while the lowest layer exponentially tracks those reference trajectories based on the full-order, hybrid, nonlinear robot model. Simulations confirm that the proposed framework ensures stable walking of a planar underactuated biped under different swaying DRS motions and gait types.
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This content will become publicly available on August 30, 2026
Time-Varying Foot Placement Control for Humanoid Walking on Swaying Rigid Surface
Locomotion on dynamic rigid surface (i.e., rigid surface accelerating in an inertial frame) presents complex challenges for controller design, which are essential to address for deploying humanoid robots in dynamic real-world environments such as moving trains, ships, and airplanes. This paper introduces a real-time, provably stabilizing control approach for humanoid walking on periodically swaying rigid surface. The first key contribution is an analytical extension of the classical angular momentum-based linear inverted pendulum model from static to swaying grounds whose motion period may be different than the robot’s gait period. This extension results in a time-varying, nonhomogeneous robot model, which is fundamentally different from the existing pendulum models. We synthesize a discrete footstep control law for the model and derive a new set of sufficient stability conditions that verify the controller’s stabilizing effect. Finally, experiments conducted on a Digit humanoid robot, both in simulations and on hardware, demonstrate the framework’s effectiveness in addressing bipedal locomotion on swaying ground, even under uncertain surface motions and unknown external pushes.
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- PAR ID:
- 10632265
- Publisher / Repository:
- IEEE
- Date Published:
- Journal Name:
- IEEE transactions on robotics
- ISSN:
- 1552-3098
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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