Magnetic soft robots embedded with hard magnetic particles enable untethered actuation via external magnetic fields, offering remote, rapid, and precise control, which is highly promising for biomedical applications. However, designing such systems is challenging due to the complex interplay of magneto-elastic dynamics, large deformation, solid contacts, time-varying stimuli, and posture-dependent loading. As a result, most existing research relies on heuristics and trial-and-error methods or focuses on the independent design of stimuli or structures under static conditions. We propose a topology optimization framework for magnetic soft robots that simultaneously designs structures, location-specific material magnetization and time-varying magnetic stimuli, accounting for large deformations, dynamic motion, and solid contacts. This is achieved by integrating generalized topology optimization with the magneto-elastic material point method, which supports GPU-accelerated parallel simulations and auto-differentiation for sensitivity analysis. We applied this framework to design magnetic robots for various tasks, including multi-task shape morphing and locomotion, in both 2D and 3D. The method autonomously generates optimized robotic systems to achieve target behaviors without requiring human intervention. Despite the nonlinear physics and large design space, it demonstrates exceptional efficiency, completing all cases within minutes. This proposed framework represents a significant step toward the automatic co-design of magnetic soft robots for applications such as metasurfaces, drug delivery, and minimally invasive procedures.

翻译：嵌入硬磁性颗粒的磁性软体机器人能够通过外部磁场实现无缆驱动，提供远程、快速且精确的控制，在生物医学应用中极具前景。然而，由于磁弹性动力学、大变形、固体接触、时变激励以及姿态相关载荷之间复杂的相互作用，此类系统的设计极具挑战性。因此，现有研究大多依赖于启发式试错方法，或仅关注静态条件下激励或结构的独立设计。本文提出一种面向磁性软体机器人的拓扑优化框架，该框架同步设计结构、位置特异性材料磁化分布与时变磁场激励，并综合考虑大变形、动态运动及固体接触效应。该框架通过将广义拓扑优化方法与磁弹性物质点法相结合而实现，后者支持GPU加速并行仿真及基于自动微分技术的灵敏度分析。我们应用该框架设计了适用于多种任务的磁性机器人，包括二维与三维环境下的多任务形变与运动。该方法能够自主生成优化的机器人系统以实现目标行为，无需人工干预。尽管涉及非线性物理过程与庞大的设计空间，该方法仍展现出卓越的计算效率，所有案例均在数分钟内完成。所提出的框架代表了向实现超构表面、药物递送及微创手术等应用领域磁性软体机器人自动协同设计迈出的重要一步。