# Time-Varying ALIP Model and Robust Foot-Placement Control for Underactuated Bipedal Robot Walking on a Swaying Rigid Surface

arXiv: https://arxiv.org/abs/2210.13371 · HTML: https://mlsanity.com/paper/2210.13371/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Oct 2022.

## Built on by (most cited first, 3 of 3)

- [Real-World Humanoid Locomotion with Reinforcement Learning](https://mlsanity.com/paper/2303.03381/) (2023)
- [HybridMimic: Hybrid RL-Centroidal Control for Humanoid Motion Mimicking](https://mlsanity.com/paper/2603.06775/) (2026)
- [Model-Informed Safe Reinforcement Learning for Bipedal Locomotion via Step-to-Step Prediction](https://mlsanity.com/paper/2609.34486/) (2026)

## Abstract (arXiv)

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 uninvestigated. This paper introduces a hierarchical control approach that achieves stable underactuated bipedal robot 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., the 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 model. The middle layer of the proposed approach is a walking pattern generator that translates the desired global behaviors into the robot's full-body reference trajectories for all directly actuated degrees of freedom. The lowest layer is an input-output linearizing controller that exponentially tracks those full-body reference trajectories based on the full-order, hybrid, nonlinear robot dynamics. Simulations of planar underactuated bipedal walking on a swaying DRS confirm that the proposed framework ensures the walking stability under different DRS motions and gait types.