# Global Position Control on Underactuated Bipedal Robots: Step-to-step Dynamics Approximation for Step Planning

arXiv: https://arxiv.org/abs/2011.06050 · HTML: https://mlsanity.com/paper/2011.06050/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Nov 2020.

## Built on by (most cited first, 4 of 4)

- [Autonomous Navigation of Underactuated Bipedal Robots in Height-Constrained Environments](https://mlsanity.com/paper/2109.05714/) (2021)
- [Interactive Dynamic Walking: Learning Gait Switching Policies with Generalization Guarantees](https://mlsanity.com/paper/2109.13417/) (2021)
- [Autotuning Bipedal Locomotion MPC with GRFM-Net for Efficient Sim-to-Real Transfer](https://mlsanity.com/paper/2409.15710/) (2024)
- [Terrain Consistent Reference-Guided RL for Humanoid Navigation Autonomy](https://mlsanity.com/paper/2605.15517/) (2026)

## Abstract (arXiv)

Global position control for underactuated bipedal walking is a challenging problem due to the lack of actuation on the feet of the robots. In this paper, we apply the Hybrid-Linear Inverted Pendulum (H-LIP) based stepping on 3D underactuated bipedal robots for global position control. The step-to-step (S2S) dynamics of the H-LIP walking approximates the actual S2S dynamics of the walking of the robot, where the step size is considered as the input. Thus the feedback controller based on the H-LIP approximately controls the robot to behave like the H-LIP, the differences between which stay in an error invariant set. Model Predictive Control (MPC) is applied to the H-LIP for global position control in 3D. The H-LIP stepping then generates desired step sizes for the robot to track. Moreover, turning behavior is integrated with the step planning. The proposed framework is verified on the 3D underactuated bipedal robot Cassie in simulation together with a proof-of-concept experiment.