# Adaptive Energy Regularization for Autonomous Gait Transition and Energy-Efficient Quadruped Locomotion

arXiv: https://arxiv.org/abs/2403.20001 · HTML: https://mlsanity.com/paper/2403.20001/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in RL for robot locomotion and manipulation, one of 15 directions in Deep reinforcement learning methods.
- Builds on 25 of its 41 references that are in the map.
- First posted on arXiv 29 Mar 2024.

## Placed in

- Deep reinforcement learning methods / [RL for robot locomotion and manipulation](https://mlsanity.com/deeprl/rl-for-robot-locomotion-and-manipulation/)

## Builds on (most cited first, 25 of 25)

- [Isaac Gym: High Performance GPU-Based Physics Simulation For Robot Learning](https://mlsanity.com/paper/2108.10470/) (2021)
- [Learning Quadrupedal Locomotion over Challenging Terrain](https://mlsanity.com/paper/2010.11251/) (2020)
- [Learning to Walk in Minutes Using Massively Parallel Deep Reinforcement Learning](https://mlsanity.com/paper/2109.11978/) (2021)
- [Learning agile and dynamic motor skills for legged robots](https://mlsanity.com/paper/1901.08652/) (2019)
- [Learning robust perceptive locomotion for quadrupedal robots in the wild](https://mlsanity.com/paper/2201.08117/) (2022)
- [Rapid Locomotion via Reinforcement Learning](https://mlsanity.com/paper/2205.02824/) (2022)
- [Robot Parkour Learning](https://mlsanity.com/paper/2309.05665/) (2023)
- [Walk These Ways: Tuning Robot Control for Generalization with Multiplicity of Behavior](https://mlsanity.com/paper/2212.03238/) (2022)
- [Reinforcement Learning for Robust Parameterized Locomotion Control of Bipedal Robots](https://mlsanity.com/paper/2103.14295/) (2021)
- [XIRL: Cross-embodiment Inverse Reinforcement Learning](https://mlsanity.com/paper/2106.03911/) (2021)
- [Sim-to-Real Learning of All Common Bipedal Gaits via Periodic Reward Composition](https://mlsanity.com/paper/2011.01387/) (2020)
- [GPU-Accelerated Robotic Simulation for Distributed Reinforcement Learning](https://mlsanity.com/paper/1810.05762/) (2018)
- [Concurrent Training of a Control Policy and a State Estimator for Dynamic and Robust Legged Locomotion](https://mlsanity.com/paper/2202.05481/) (2022)
- [Minimizing Energy Consumption Leads to the Emergence of Gaits in Legged Robots](https://mlsanity.com/paper/2111.01674/) (2021)
- [Fast and Efficient Locomotion via Learned Gait Transitions](https://mlsanity.com/paper/2104.04644/) (2021)
- [GenLoco: Generalized Locomotion Controllers for Quadrupedal Robots](https://mlsanity.com/paper/2209.05309/) (2022)
- [PaCo: Parameter-Compositional Multi-Task Reinforcement Learning](https://mlsanity.com/paper/2210.11653/) (2022)
- [Legs as Manipulator: Pushing Quadrupedal Agility Beyond Locomotion](https://mlsanity.com/paper/2303.11330/) (2023)
- [Advanced Skills through Multiple Adversarial Motion Priors in Reinforcement Learning](https://mlsanity.com/paper/2203.14912/) (2022)
- [Learning Torque Control for Quadrupedal Locomotion](https://mlsanity.com/paper/2203.05194/) (2022)
- [Learning a Contact-Adaptive Controller for Robust, Efficient Legged Locomotion](https://mlsanity.com/paper/2009.10019/) (2020)
- [Fast Contact-Implicit Model-Predictive Control](https://mlsanity.com/paper/2107.05616/) (2021)
- [Sim-to-Real Learning of Footstep-Constrained Bipedal Dynamic Walking](https://mlsanity.com/paper/2203.07589/) (2022)
- [Cross Domain Robot Imitation with Invariant Representation](https://mlsanity.com/paper/2109.05940/) (2021)
- [Efficient Multi-Task and Transfer Reinforcement Learning with Parameter-Compositional Framework](https://mlsanity.com/paper/2306.01839/) (2023)

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

- [QuietPaw: Learning Quadrupedal Locomotion with Versatile Noise Preference Alignment](https://mlsanity.com/paper/2503.05035/) (2025)
- [Residual Policy Gradient: A Reward View of KL-regularized Objective](https://mlsanity.com/paper/2503.11019/) (2025)
- [Energy-Efficient Omnidirectional Locomotion for Wheeled Quadrupeds via Predictive Energy-Aware Nominal Gait Selection](https://mlsanity.com/paper/2601.10723/) (2025)
- [Energy-Efficient Quadruped Locomotion with Compliant Feet](https://mlsanity.com/paper/2605.14411/) (2026)
- [LoComposition: Terrain-Adaptive Energy-Efficient Quadruped Locomotion without Gait Priors](https://mlsanity.com/paper/2606.15896/) (2026)

## Abstract (arXiv)

In reinforcement learning for legged robot locomotion, crafting effective reward strategies is crucial. Pre-defined gait patterns and complex reward systems are widely used to stabilize policy training. Drawing from the natural locomotion behaviors of humans and animals, which adapt their gaits to minimize energy consumption, we propose a simplified, energy-centric reward strategy to foster the development of energy-efficient locomotion across various speeds in quadruped robots. By implementing an adaptive energy reward function and adjusting the weights based on velocity, we demonstrate that our approach enables ANYmal-C and Unitree Go1 robots to autonomously select appropriate gaits, such as four-beat walking at lower speeds and trotting at higher speeds, resulting in improved energy efficiency and stable velocity tracking compared to previous methods using complex reward designs and prior gait knowledge. The effectiveness of our policy is validated through simulations in the IsaacGym simulation environment and on real robots, demonstrating its potential to facilitate stable and adaptive locomotion.