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

arXiv · AI, language, vision and robotics · article · Sep 14, 2026 · UTC

Combining aerial thrust with spring-loaded hopping makes monopedal quadcopters promising for locomotion over complex terrain, but heuristic proportional-integral-derivative (PID) tuning limits coordination between active thrust and passive contact dynamics. We present a direct estimated-state-to-motor Proximal Policy Optimization (PPO) policy that commands four motors without an explicit hopping state machine or low-level attitude PID. Its reward combines Energy-Manifold Shaping for mass-normalized vertical-energy tracking and apex-state anchoring with Efficiency Shaping, which uses a history-

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