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

• URL: http://arxiv.org/abs/2609.15447v1
• Date: Mon, 14 Sep 2026 12:14:58 GMT
• Title: Learning to Exploit Passive Dynamics for Energy-Efficient Target Hopping of a Spring-Legged Quadcopter
• Abstract summary: We present a policy that commands four motors without an explicit hopping state machine or low-level attitude PID.<n>Its reward combines Energy-Manifold Shaping for mass-normalized vertical-energy tracking and apex-state anchoring with Efficiency Shaping.<n>In representative hardware runs, the PPO-based control stack reduced cycle-averaged measured electrical power by 30.7%.
• Score: 6.592942321170304
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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-aware power estimator to penalize general power use, impose an additional airborne-power cost, and penalize airborne near-stationarity. In representative hardware runs, the PPO-based control stack reduced cycle-averaged measured electrical power by 30.7% and mean total normalized thrust by 49.8% relative to the tuned PID-based control stack, while retaining repeatable commanded-height hopping and more concentrated landings. These observations are consistent with improved use of passive dynamics and reduced measured electrical demand.

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