# SLIP Walking over Rough Terrain via H-LIP Stepping and Backstepping-Barrier Function Inspired Quadratic Program

arXiv: https://arxiv.org/abs/2102.09691 · HTML: https://mlsanity.com/paper/2102.09691/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Feb 2021.

## Built on by (most cited first, 1 of 1)

- [Model-Informed Safe Reinforcement Learning for Bipedal Locomotion via Step-to-Step Prediction](https://mlsanity.com/paper/2609.34486/) (2026)

## Abstract (arXiv)

We present an advanced and novel control method to enable actuated Spring Loaded Inverted Pendulum model to walk over rough and challenging terrains. The high-level philosophy is the decoupling of the controls of the vertical and horizontal states. The vertical state is controlled via Backstepping-Barrier Function (BBF) based quadratic programs: a combination of control Lyapunov backstepping and control barrier function, both of which provide inequality constraints on the inputs. The horizontal state is stabilized via Hybrid-Linear Inverted Pendulum (H-LIP) based stepping, which has a closed-form formulation. Therefore, the implementation is computationally-efficient. We evaluate our method in simulation, which demonstrates the aSLIP walking over various terrains, including slopes, stairs, and general rough terrains with uncertainties.