# Learning Linear Policies for Robust Bipedal Locomotion on Terrains with Varying Slopes

arXiv: https://arxiv.org/abs/2104.01662 · HTML: https://mlsanity.com/paper/2104.01662/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 31 references that are in the map.
- First posted on arXiv 4 Apr 2021.

## Builds on (most cited first, 14 of 14)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [Learning Quadrupedal Locomotion over Challenging Terrain](https://mlsanity.com/paper/2010.11251/) (2020)
- [ALLSTEPS: Curriculum-driven Learning of Stepping Stone Skills](https://mlsanity.com/paper/2005.04323/) (2020)
- [Feedback Control For Cassie With Deep Reinforcement Learning](https://mlsanity.com/paper/1803.05580/) (2018)
- [Learning Memory-Based Control for Human-Scale Bipedal Locomotion](https://mlsanity.com/paper/2006.02402/) (2020)
- [Learning Task Space Actions for Bipedal Locomotion](https://mlsanity.com/paper/2011.04741/) (2020)
- [Contact-Aided Invariant Extended Kalman Filtering for Robot State Estimation](https://mlsanity.com/paper/1904.09251/) (2019)
- [Iterative Reinforcement Learning Based Design of Dynamic Locomotion Skills for Cassie](https://mlsanity.com/paper/1903.09537/) (2019)
- [Hybrid Zero Dynamics Inspired Feedback Control Policy Design for 3D Bipedal Locomotion using Reinforcement Learning](https://mlsanity.com/paper/1910.01748/) (2019)
- [Robust Quadrupedal Locomotion on Sloped Terrains: A Linear Policy Approach](https://mlsanity.com/paper/2010.16342/) (2020)
- [Combining Trajectory Optimization, Supervised Machine Learning, and Model Structure for Mitigating the Curse of Dimensionality in the Control of Bipedal Robots](https://mlsanity.com/paper/1711.02223/) (2017)
- [Angular Momentum about the Contact Point for Control of Bipedal Locomotion: Validation in a LIP-based Controller](https://mlsanity.com/paper/2008.10763/) (2020)
- [Reinforcement Learning Meets Hybrid Zero Dynamics: A Case Study for RABBIT](https://mlsanity.com/paper/1810.01977/) (2018)

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

- [Learning Bipedal Walking for Humanoids with Current Feedback](https://mlsanity.com/paper/2303.03724/) (2023)
- [Robust Humanoid Walking on Compliant and Uneven Terrain with Deep Reinforcement Learning](https://mlsanity.com/paper/2504.13619/) (2025)
- [Learning Smooth Time-Varying Linear Policies with an Action Jacobian Penalty](https://mlsanity.com/paper/2602.18312/) (2026)

## Abstract (arXiv)

In this paper, with a view toward deployment of light-weight control frameworks for bipedal walking robots, we realize end-foot trajectories that are shaped by a single linear feedback policy. We learn this policy via a model-free and a gradient-free learning algorithm, Augmented Random Search (ARS), in the two robot platforms Rabbit and Digit. Our contributions are two-fold: a) By using torso and support plane orientation as inputs, we achieve robust walking on slopes of up to 20 degrees in simulation. b) We demonstrate additional behaviors like walking backwards, stepping-in-place, and recovery from external pushes of up to 120 N. The end result is a robust and a fast feedback control law for bipedal walking on terrains with varying slopes. Towards the end, we also provide preliminary results of hardware transfer to Digit.