Learning to Exploit Passive Dynamics for Energy-Efficient Target Hopping of a Spring-Legged Quadcopter

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.

Unmanned aerial vehicles (UAVs), particularly quadcopters, present unique challenges for autonomous control due to their underactuated dynamics: only four available control inputs must govern six degrees of freedom. This paper investigates a physics-aware, end-to-end deep reinforcement learning (DRL) approach that acts directly on low-level body inputs, total thrust and body torques $(T, τ_x, τ_y, τ_z)$, and closes the loop through a high-fidelity Simulink environment. Our simulator integrates a 12-state rigid-body model (MATLAB Level-2 S-Function) with (i) an Action2RPM allocation based on the Moore-Penrose pseudo-inverse of a coefficient matrix derived from thrust and drag terms, and (ii) first-order actuator dynamics for each motor (time constant $T_m = 0.076$ s), including rotor gyroscopic coupling. A shaped reward balances goal-reaching and stability using an exponential position well, attitude penalties, and quadratic velocity costs. Four DRL algorithms, DDPG, TD3, PPO, and SAC, are evaluated in two stages: (S1) thrust-only hover and (S2) hover with pitch torque and a translated goal. Results show that SAC and TD3 achieve superior stability and exploration efficiency, while PPO is less sample-efficient. The study highlights the significance of modeling actuator lags and aerodynamic moments for stable low-level control and provides a reproducible benchmark for quadcopter DRL.

Learning-based quadrupedal locomotion typically relies on complex reward formulations that entangle task specification, operational limits, gait preference, and terrain adaptation within a single optimization objective. We instead treat these functions through distinct mechanisms: rewards for task specification, constraints for operational limits, energy minimization for gait preference, and exteroceptive perception for adapting energy use to terrain difficulty. We show that these components jointly enable efficient, terrain-adaptive locomotion, and that removing each component exposes a distinct failure mode. Our formulation removes explicit gait priors (including air-time, contact-count, and foot-clearance targets) in favor of emergent behavior. Compared to a conventional complex-reward baseline, our formulation achieves comparable terrain traversal while reducing cost of transport by 56% and operational-limit violations by 96%. The resulting policies transfer zero-shot to a physical Unitree Go2 using LiDAR-based elevation mapping. Project website with videos: https://tinyurl.com/locomposition.