ECO: Energy-Constrained Optimization with Reinforcement Learning for Humanoid Walking

TL;DR

ECO introduces a constrained reinforcement learning framework that explicitly incorporates energy constraints, leading to more energy-efficient and stable humanoid walking compared to existing methods.

Contribution

The paper proposes ECO, a novel constrained RL approach that separates energy metrics from rewards, enabling more interpretable and efficient energy optimization in humanoid locomotion.

Findings

ECO significantly reduces energy consumption in humanoid walking.

ECO maintains robust walking performance in simulation and real-world transfers.

Outperforms MPC and standard RL methods in energy efficiency.

Abstract

Achieving stable and energy-efficient locomotion is essential for humanoid robots to operate continuously in real-world applications. Existing MPC and RL approaches often rely on energy-related metrics embedded within a multi-objective optimization framework, which require extensive hyperparameter tuning and often result in suboptimal policies. To address these challenges, we propose ECO (Energy-Constrained Optimization), a constrained RL framework that separates energy-related metrics from rewards, reformulating them as explicit inequality constraints. This method provides a clear and interpretable physical representation of energy costs, enabling more efficient and intuitive hyperparameter tuning for improved energy efficiency. ECO introduces dedicated constraints for energy consumption and reference motion, enforced by the Lagrangian method, to achieve stable, symmetric, and energy-efficient walking for humanoid robots. We evaluated ECO against MPC, standard RL with reward shaping, and four state-of-the-art constrained RL methods. Experiments, including sim-to-sim and sim-to-real transfers on the kid-sized humanoid robot BRUCE, demonstrate that ECO significantly reduces energy consumption compared to baselines while maintaining robust walking performance. These results highlight a substantial advancement in energy-efficient humanoid locomotion. All experimental demonstrations can be found on the project website: https://sites.google.com/view/eco-humanoid.