Four arm-mounted piezoelectric harvesters on a quadrotor: a verified energy account and its consequences for energy-aware deep reinforcement learning navigation

Abstract Piezoelectric patches bonded to the four arms of a multirotor, combined with deep reinforcement learning (DRL) policies that favour high-harvest flight, have been proposed as a route to longer endurance. This paper tests that proposal with a single energy account in which structure, transducer, propulsion and policy share physical units. A finite-element (FE) model of a DJI F450 arm carrying its motor tip mass and a PZT-5A patch, verified against closed-form solutions and reproduced by an independent implementation, shows that the tip mass lowers the first bending frequency from 57.68 Hz to 18.43 Hz; neglecting it overestimates the mission-average harvest about 28-fold. With the tip mass, four root-mounted patches deliver 0.70 µW averaged over a representative mission (0.42 mJ in 10 min, 3.3×10 − 9 of propulsion energy). Even an arm resonance-tuned to the hover blade-passing frequency raises the four-arm hover output only to 21 µW (1.4×10 − 7 of hover power), and a ± 5% change in take-off mass removes more than half of it. The FE harvest model and a rotor-speed-dependent propulsion model are then embedded in a mapless 3-D obstacle-avoidance task. Over five seeds and 200 held-out scenarios, SAC reaches the highest success (83.6 ± 3.6%, against 72.4% for PPO and 59.5% for DQN), whereas PPO uses 15.5% less energy per metre, so no algorithm dominates. An energy term in the reward lowers SAC energy per metre by 13.2% without loss of success; a harvest bonus does not increase harvesting and erodes most of that saving (+ 12.6%, Holm-adjusted p = 0.039). Endurance is gained by energy-aware flight, not by harvest-seeking policies.