# Bayesian Optimization Meets Hybrid Zero Dynamics: Safe Parameter Learning for Bipedal Locomotion Control

arXiv: https://arxiv.org/abs/2203.02570 · HTML: https://mlsanity.com/paper/2203.02570/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 33 references that are in the map.
- First posted on arXiv 4 Mar 2022.

## Builds on (most cited first, 15 of 15)

- [A Tutorial on Bayesian Optimization](https://mlsanity.com/paper/1807.02811/) (2018)
- [Bayesian Optimization with Safety Constraints: Safe and Automatic Parameter Tuning in Robotics](https://mlsanity.com/paper/1602.04450/) (2016)
- [Reinforcement Learning for Robust Parameterized Locomotion Control of Bipedal Robots](https://mlsanity.com/paper/2103.14295/) (2021)
- [Bayesian Optimization with Unknown Constraints](https://mlsanity.com/paper/1403.5607/) (2014)
- [Sim-to-Real Learning of All Common Bipedal Gaits via Periodic Reward Composition](https://mlsanity.com/paper/2011.01387/) (2020)
- [Safe Controller Optimization for Quadrotors with Gaussian Processes](https://mlsanity.com/paper/1509.01066/) (2015)
- [Preference-Based Learning for Exoskeleton Gait Optimization](https://mlsanity.com/paper/1909.12316/) (2019)
- [Feedback Control of a Cassie Bipedal Robot: Walking, Standing, and Riding a Segway](https://mlsanity.com/paper/1809.07279/) (2018)
- [Robust Feedback Motion Policy Design Using Reinforcement Learning on a 3D Digit Bipedal Robot](https://mlsanity.com/paper/2103.15309/) (2021)
- [Robot Learning with Crash Constraints](https://mlsanity.com/paper/2010.08669/) (2020)
- [Animated Cassie: A Dynamic Relatable Robotic Character](https://mlsanity.com/paper/2009.02846/) (2020)
- [Rapid Trajectory Optimization Using C-FROST with Illustration on a Cassie-Series Dynamic Walking Biped](https://mlsanity.com/paper/1807.06614/) (2018)
- [Learning Controller Gains on Bipedal Walking Robots via User Preferences](https://mlsanity.com/paper/2102.13201/) (2021)
- [Multi-Fidelity Black-Box Optimization for Time-Optimal Quadrotor Maneuvers](https://mlsanity.com/paper/2006.02513/) (2020)
- [Control Lyapunov Functions for Compliant Hybrid Zero Dynamic Walking](https://mlsanity.com/paper/2107.04241/) (2021)

## Built on by (most cited first, 5 of 5)

- [Reinforcement Learning for Versatile, Dynamic, and Robust Bipedal Locomotion Control](https://mlsanity.com/paper/2401.16889/) (2024)
- [Adapting Rapid Motor Adaptation for Bipedal Robots](https://mlsanity.com/paper/2205.15299/) (2022)
- [Custom Sine Waves Are Enough for Imitation Learning of Bipedal Gaits with Different Styles](https://mlsanity.com/paper/2204.04157/) (2022)
- [Autotuning Bipedal Locomotion MPC with GRFM-Net for Efficient Sim-to-Real Transfer](https://mlsanity.com/paper/2409.15710/) (2024)
- [Cost-Aware Bayesian Optimization for Prototyping Interactive Devices](https://mlsanity.com/paper/2602.01774/) (2026)

## Abstract (arXiv)

In this paper, we propose a multi-domain control parameter learning framework that combines Bayesian Optimization (BO) and Hybrid Zero Dynamics (HZD) for locomotion control of bipedal robots. We leverage BO to learn the control parameters used in the HZD-based controller. The learning process is firstly deployed in simulation to optimize different control parameters for a large repertoire of gaits. Next, to tackle the discrepancy between the simulation and the real world, the learning process is applied on the physical robot to learn for corrections to the control parameters learned in simulation while also respecting a safety constraint for gait stability. This method empowers an efficient sim-to-real transition with a small number of samples in the real world, and does not require a valid controller to initialize the training in simulation. Our proposed learning framework is experimentally deployed and validated on a bipedal robot Cassie to perform versatile locomotion skills with improved performance on smoothness of walking gaits and reduction of steady-state tracking errors.