# Dynamics-Informed Reinforcement Learning for Agile and Energy-Efficient Locomotion of a Monopedal Hopping Quadcopter

arXiv: https://arxiv.org/abs/2609.15399 · HTML: https://mlsanity.com/paper/2609.15399/

## 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 5 of its 29 references that are in the map.
- First posted on arXiv 14 Sep 2026.

## 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, 5 of 5)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Comprehensive Overview of Reward Engineering and Shaping in Advancing Reinforcement Learning Applications](https://mlsanity.com/paper/2408.10215/) (2024)
- [Learning Optimal Advantage from Preferences and Mistaking it for Reward](https://mlsanity.com/paper/2310.02456/) (2023)
- [Nonlinear Model Predictive Control of a 3D Hopping Robot: Leveraging Lie Group Integrators for Dynamically Stable Behaviors](https://mlsanity.com/paper/2209.11808/) (2022)
- [PogoDrone: Design, Model, and Control of a Jumping Quadrotor](https://mlsanity.com/paper/2204.00207/) (2022)

## Abstract (arXiv)

Although aerial-legged robots offer combined agility and efficiency, controlling high-speed hopping under complex hybrid dynamics is challenging. Reinforcement Learning (RL) is promising but prone to energy-inefficient "reward hacking". We propose a Dynamics-Informed RL framework for a monopedal hopping quadcopter. By embedding a target Specific Energy into the reward, we constrain the optimization to a physically viable energy manifold, ensuring stable hopping behaviour. By rewarding the phase-consistent behavior, it can encourage bio-inspired stance-phase impulse. Furthermore, penalizing the electro-mechanical power waste induces the motors generate an efficient impulse. This enables the policy to inject energy strictly during spring restitution without heuristic state machines. MuJoCo simulations validate robust height regulation and forward velocity tracking up to 2.0 m/s despite severe attitude-contact coupling. Ultimately, our approach yields a highly agile hopping gait, reducing energy consumption by 82% and 73% compared to hovering baselines and inefficiency baseline, respectively.