# Guiding Energy-Efficient Locomotion through Impact Mitigation Rewards

arXiv: https://arxiv.org/abs/2510.09543 · HTML: https://mlsanity.com/paper/2510.09543/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RL for robot locomotion and manipulation, one of 15 directions in Deep reinforcement learning methods.
- Builds on 16 of its 26 references that are in the map.
- First posted on arXiv 10 Oct 2025.

## 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, 16 of 16)

- [Learning Agile Robotic Locomotion Skills by Imitating Animals](https://mlsanity.com/paper/2004.00784/) (2020)
- [Adversarial Motion Priors Make Good Substitutes for Complex Reward Functions](https://mlsanity.com/paper/2203.15103/) (2022)
- [Evaluation of Constrained Reinforcement Learning Algorithms for Legged Locomotion](https://mlsanity.com/paper/2309.15430/) (2023)
- [A Learning Framework for Diverse Legged Robot Locomotion Using Barrier-Based Style Rewards](https://mlsanity.com/paper/2409.15780/) (2024)
- [Learning to Walk and Fly with Adversarial Motion Priors](https://mlsanity.com/paper/2309.12784/) (2023)
- [Generative Design of NU's Husky Carbon, A Morpho-Functional, Legged Robot](https://mlsanity.com/paper/2104.05834/) (2021)
- [Optimization-free Ground Contact Force Constraint Satisfaction in Quadrupedal Locomotion](https://mlsanity.com/paper/2111.12557/) (2021)
- [Efficient Path Planning and Tracking for Multi-Modal Legged-Aerial Locomotion Using Integrated Probabilistic Road Maps (PRM) and Reference Governors (RG)](https://mlsanity.com/paper/2205.06392/) (2022)
- [A Letter on Progress Made on Husky Carbon: A Legged-Aerial, Multi-modal Platform](https://mlsanity.com/paper/2207.12254/) (2022)
- [Quadrupedal Locomotion Control On Inclined Surfaces Using Collocation Method](https://mlsanity.com/paper/2312.08621/) (2023)
- [Towards thruster-assisted bipedal locomotion for enhanced efficiency and robustness](https://mlsanity.com/paper/2005.00347/) (2020)
- [Thruster-assisted center manifold shaping in bipedal legged locomotion](https://mlsanity.com/paper/2006.03748/) (2020)
- [Unilateral Ground Contact Force Regulations in Thruster-Assisted Legged Locomotion](https://mlsanity.com/paper/2105.12082/) (2021)
- [Narrow-Path, Dynamic Walking Using Integrated Posture Manipulation and Thrust Vectoring](https://mlsanity.com/paper/2405.06070/) (2024)
- [Optimization free control and ground force estimation with momentum observer for a multimodal legged aerial robot](https://mlsanity.com/paper/2411.11216/) (2024)
- [Enabling steep slope walking on Husky using reduced order modeling and quadratic programming](https://mlsanity.com/paper/2411.11788/) (2024)

## Abstract (arXiv)

Animals achieve energy-efficient locomotion by their implicit passive dynamics, a marvel that has captivated roboticists for decades.Recently, methods incorporated Adversarial Motion Prior (AMP) and Reinforcement learning (RL) shows promising progress to replicate Animals' naturalistic motion. However, such imitation learning approaches predominantly capture explicit kinematic patterns, so-called gaits, while overlooking the implicit passive dynamics. This work bridges this gap by incorporating a reward term guided by Impact Mitigation Factor (IMF), a physics-informed metric that quantifies a robot's ability to passively mitigate impacts. By integrating IMF with AMP, our approach enables RL policies to learn both explicit motion trajectories from animal reference motion and the implicit passive dynamic. We demonstrate energy efficiency improvements of up to 32%, as measured by the Cost of Transport (CoT), across both AMP and handcrafted reward structure.