# Dynamics and Domain Randomized Gait Modulation with Bezier Curves for Sim-to-Real Legged Locomotion

arXiv: https://arxiv.org/abs/2010.12070 · HTML: https://mlsanity.com/paper/2010.12070/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Real-world robot offline RL, one of 13 directions in Offline RL and imitation learning from data.
- First posted on arXiv 22 Oct 2020.

## Placed in

- Offline RL and imitation learning from data / [Real-world robot offline RL](https://mlsanity.com/offlinerl/real-world-robot-offline-rl/)

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

- [Robust High-speed Running for Quadruped Robots via Deep Reinforcement Learning](https://mlsanity.com/paper/2103.06484/) (2021)
- [Quadruped Locomotion on Non-Rigid Terrain using Reinforcement Learning](https://mlsanity.com/paper/2107.02955/) (2021)
- [Unlock Reliable Skill Inference for Quadruped Adaptive Behavior by Skill Graph](https://mlsanity.com/paper/2311.06015/) (2023)

## Abstract (arXiv)

We present a sim-to-real framework that uses dynamics and domain randomized offline reinforcement learning to enhance open-loop gaits for legged robots, allowing them to traverse uneven terrain without sensing foot impacts. Our approach, D2-Randomized Gait Modulation with Bezier Curves (D2-GMBC), uses augmented random search with randomized dynamics and terrain to train, in simulation, a policy that modifies the parameters and output of an open-loop Bezier curve gait generator for quadrupedal robots. The policy, using only inertial measurements, enables the robot to traverse unknown rough terrain, even when the robot's physical parameters do not match the open-loop model. We compare the resulting policy to hand-tuned Bezier Curve gaits and to policies trained without randomization, both in simulation and on a real quadrupedal robot. With D2-GMBC, across a variety of experiments on unobserved and unknown uneven terrain, the robot walks significantly farther than with either hand-tuned gaits or gaits learned without domain randomization. Additionally, using D2-GMBC, the robot can walk laterally and rotate while on the rough terrain, even though it was trained only for forward walking.