# Energy-Efficient Quadruped Locomotion with Compliant Feet

arXiv: https://arxiv.org/abs/2605.14411 · HTML: https://mlsanity.com/paper/2605.14411/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 54 references that are in the map.
- First posted on arXiv 14 May 2026.

## Builds on (most cited first, 9 of 9)

- [Learning to Walk in Minutes Using Massively Parallel Deep Reinforcement Learning](https://mlsanity.com/paper/2109.11978/) (2021)
- [Learning robust perceptive locomotion for quadrupedal robots in the wild](https://mlsanity.com/paper/2201.08117/) (2022)
- [Walk These Ways: Tuning Robot Control for Generalization with Multiplicity of Behavior](https://mlsanity.com/paper/2212.03238/) (2022)
- [Whole-Body Nonlinear Model Predictive Control Through Contacts for Quadrupeds](https://mlsanity.com/paper/1712.02889/) (2017)
- [An Efficient Optimal Planning and Control Framework For Quadrupedal Locomotion](https://mlsanity.com/paper/1609.09861/) (2016)
- [Adaptive Energy Regularization for Autonomous Gait Transition and Energy-Efficient Quadruped Locomotion](https://mlsanity.com/paper/2403.20001/) (2024)
- [Online Dynamic Trajectory Optimization and Control for a Quadruped Robot](https://mlsanity.com/paper/2008.12687/) (2020)
- [Kinodynamic Model Predictive Control for Energy Efficient Locomotion of Legged Robots with Parallel Elasticity](https://mlsanity.com/paper/2503.05666/) (2025)
- [HAC-LOCO: Learning Hierarchical Active Compliance Control for Quadruped Locomotion under Continuous External Disturbances](https://mlsanity.com/paper/2507.02447/) (2025)

## Abstract (arXiv)

Quadruped robots are often designed with rigid feet to simplify control and maintain stable contact during locomotion. While this approach is straightforward, it limits the ability of the legs to absorb impact forces and reuse stored elastic energy, leading to higher energy expenditure during locomotion. To explore whether compliant feet can provide an advantage, we integrate foot compliance into a reinforcement learning (RL) locomotion controller and study its effect on walking efficiency. In simulation, we train eight policies corresponding to eight different spring stiffness values and then cross-evaluate their performance by measuring mechanical energy consumed per meter traveled. In experiments done on a developed quadruped, the energy consumption for the intermediate stiffness spring is lower by ~ 17% when compared to a very stiff or a very flexible spring incorporated in the feet, with similar trends appearing in the simulation results. These results indicate that selecting an appropriate foot compliance can improve locomotion efficiency without destabilizing the robot during motion.