# Learning Symmetric and Low-energy Locomotion

arXiv: https://arxiv.org/abs/1801.08093 · HTML: https://mlsanity.com/paper/1801.08093/

## Key facts

- Cited by 61 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jan 2018.

## Built on by (most cited first, 30 of 61)

- [How to Train Your Robot with Deep Reinforcement Learning; Lessons We've Learned](https://mlsanity.com/paper/2102.02915/) (2021)
- [Character Controllers Using Motion VAEs](https://mlsanity.com/paper/2103.14274/) (2021)
- [Embodied Intelligence via Learning and Evolution](https://mlsanity.com/paper/2102.02202/) (2021)
- [Trace and Pace: Controllable Pedestrian Animation via Guided Trajectory Diffusion](https://mlsanity.com/paper/2304.01893/) (2023)
- [Adversarial Motion Priors Make Good Substitutes for Complex Reward Functions](https://mlsanity.com/paper/2203.15103/) (2022)
- [Learning Vision-Guided Quadrupedal Locomotion End-to-End with Cross-Modal Transformers](https://mlsanity.com/paper/2107.03996/) (2021)
- [Minimizing Energy Consumption Leads to the Emergence of Gaits in Legged Robots](https://mlsanity.com/paper/2111.01674/) (2021)
- [Real-Time Style Modelling of Human Locomotion via Feature-Wise Transformations and Local Motion Phases](https://mlsanity.com/paper/2201.04439/) (2022)
- [InterMimic: Towards Universal Whole-Body Control for Physics-Based Human-Object Interactions](https://mlsanity.com/paper/2502.20390/) (2025)
- [Fast and Efficient Locomotion via Learned Gait Transitions](https://mlsanity.com/paper/2104.04644/) (2021)
- [Not Only Rewards But Also Constraints: Applications on Legged Robot Locomotion](https://mlsanity.com/paper/2308.12517/) (2023)
- [Neural Categorical Priors for Physics-Based Character Control](https://mlsanity.com/paper/2308.07200/) (2023)
- [Composite Motion Learning with Task Control](https://mlsanity.com/paper/2305.03286/) (2023)
- [Symmetry Considerations for Learning Task Symmetric Robot Policies](https://mlsanity.com/paper/2403.04359/) (2024)
- [Leveraging Symmetry in RL-based Legged Locomotion Control](https://mlsanity.com/paper/2403.17320/) (2024)
- [UniPhys: Unified Planner and Controller with Diffusion for Flexible Physics-Based Character Control](https://mlsanity.com/paper/2504.12540/) (2025)
- [ControlVAE: Model-Based Learning of Generative Controllers for Physics-Based Characters](https://mlsanity.com/paper/2210.06063/) (2022)
- [AMP: Adversarial Motion Priors for Stylized Physics-Based Character Control](https://mlsanity.com/paper/2104.02180/) (2021)
- [Discovering Diverse Athletic Jumping Strategies](https://mlsanity.com/paper/2105.00371/) (2021)
- [AdaptNet: Policy Adaptation for Physics-Based Character Control](https://mlsanity.com/paper/2310.00239/) (2023)
- [A GAN-Like Approach for Physics-Based Imitation Learning and Interactive Character Control](https://mlsanity.com/paper/2105.10066/) (2021)
- [A Survey on Reinforcement Learning Methods in Character Animation](https://mlsanity.com/paper/2203.04735/) (2022)
- [Learning Bipedal Walking On Planned Footsteps For Humanoid Robots](https://mlsanity.com/paper/2207.12644/) (2022)
- [Generative GaitNet](https://mlsanity.com/paper/2201.12044/) (2022)
- [Learning to Get Up](https://mlsanity.com/paper/2205.00307/) (2022)
- [A Unified and General Humanoid Whole-Body Controller for Versatile Locomotion](https://mlsanity.com/paper/2502.03206/) (2025)
- [ZEST: Zero-shot Embodied Skill Transfer for Athletic Robot Control](https://mlsanity.com/paper/2602.00401/) (2026)
- [Cascaded Compositional Residual Learning for Complex Interactive Behaviors](https://mlsanity.com/paper/2212.08954/) (2022)
- [GROVE: A Generalized Reward for Learning Open-Vocabulary Physical Skill](https://mlsanity.com/paper/2504.04191/) (2025)
- [AMOR: Adaptive Character Control through Multi-Objective Reinforcement Learning](https://mlsanity.com/paper/2505.23708/) (2025)

## Abstract (arXiv)

Learning locomotion skills is a challenging problem. To generate realistic and smooth locomotion, existing methods use motion capture, finite state machines or morphology-specific knowledge to guide the motion generation algorithms. Deep reinforcement learning (DRL) is a promising approach for the automatic creation of locomotion control. Indeed, a standard benchmark for DRL is to automatically create a running controller for a biped character from a simple reward function. Although several different DRL algorithms can successfully create a running controller, the resulting motions usually look nothing like a real runner. This paper takes a minimalist learning approach to the locomotion problem, without the use of motion examples, finite state machines, or morphology-specific knowledge. We introduce two modifications to the DRL approach that, when used together, produce locomotion behaviors that are symmetric, low-energy, and much closer to that of a real person. First, we introduce a new term to the loss function (not the reward function) that encourages symmetric actions. Second, we introduce a new curriculum learning method that provides modulated physical assistance to help the character with left/right balance and forward movement. The algorithm automatically computes appropriate assistance to the character and gradually relaxes this assistance, so that eventually the character learns to move entirely without help. Because our method does not make use of motion capture data, it can be applied to a variety of character morphologies. We demonstrate locomotion controllers for the lower half of a biped, a full humanoid, a quadruped, and a hexapod. Our results show that learned policies are able to produce symmetric, low-energy gaits. In addition, speed-appropriate gait patterns emerge without any guidance from motion examples or contact planning.