Programmable Magnetic Soft Robots via Assembled Magnetization and Joint-Mediated Symmetry Breaking

Magnetically actuated soft robots enable untethered operation in confined and complex environments; however, achieving controllable directional locomotion in structurally symmetric systems remains a fundamental challenge due to intrinsic force cancellation under uniform fields. Here, we present a modular strategy that integrates assembled programmable magnetization with energy-biased symmetry-breaking joints to overcome this limitation. By embedding hard-magnetic NdFeB microparticles into an Ecoflex matrix, discrete magnetic units with programmable magnetization are fabricated and assembled into higher-order architectures. We show that asymmetric film constraints prescribe joint polarity and bias strain-energy distribution during actuation, producing distinct deformation modes (folding versus bending) under identical magnetic inputs. This energy asymmetry breaks the balanced response of symmetric structures, enabling net directional motion under spatially uniform magnetic fields. Based on this principle, a segmented crawler achieves a maximum speed of 5.42 mm s^-1 under a half-wave magnetic field, while a quadruped robot realizes programmable multi-directional locomotion (±X, ±Y) via dual-field coupling, reaching a maximum speed of 3.125 mm s^-1. These results demonstrate that modular magnetization and joint-mediated energy bias can cooperatively generate controllable directional locomotion through mechanically encoded symmetry breaking. This work provides a scalable design framework for programmable magnetic soft robots under spatially uniform magnetic fields.