用磁阵列实现20-120mm范围内的稳定二维磁力陷阱，可精准操控微型机器人。
Efficient Optimization of a Permanent Magnet Array for a Stable 2D Trap
- 通过GPU加速优化算法，自动计算磁阵列中每个磁体的最优朝向。
- 实验证明可在20-120mm距离内稳定捕获并控制毫米级机器人沿复杂轨迹运动。
- 算法3秒内可优化100个磁体，适用于任意数量磁体的磁力场定制。
无缆磁控生物医学微机器人在微创手术中具有高潜力，但远距离高驱动力仍具挑战。永磁体比电磁线圈提供更强磁力与转矩，但反馈控制更难。根据厄恩肖定理，静态永磁体无法在三维空间实现稳定磁阱。本文提出一种基于永磁体阵列的二维稳定磁力阱，其工作区域位于开放空间，与磁阵列距离可在20-120mm之间调节，契合人体解剖尺度。通过新型GPU加速优化算法，结合均方误差（MSE）与Adam优化器，高效求解任意数量磁体的最优取向。算法经数值模拟与双磁体物理实验验证，成功实现微机器人稳定捕获并沿复杂轨迹运动。优化流程可扩展至生成期望的力矢量场，且100磁体配置可在3秒内完成优化。
原文摘要 · Abstract (English)
Untethered magnetic manipulation of biomedical millirobots has a high potential for minimally invasive surgical applications. However, it is still challenging to exert high actuation forces on the small robots over a large distance. Permanent magnets offer stronger magnetic torques and forces than electromagnetic coils, however, feedback control is more difficult. As proven by Earnshaw's theorem, it is not possible to achieve a stable magnetic trap in 3D by static permanent magnets. Here, we report a stable 2D magnetic force trap by an array of permanent magnets to control a millirobot. The trap is located in an open space with a tunable distance to the magnet array in the range of 20 - 120mm, which is relevant to human anatomical scales. The design is achieved by a novel GPU-accelerated optimization algorithm that uses mean squared error (MSE) and Adam optimizer to efficiently compute the optimal angles for any number of magnets in the array. The algorithm is verified using numerical simulation and physical experiments with an array of two magnets. A millirobot is successfully trapped and controlled to follow a complex trajectory. The algorithm demonstrates high scalability by optimizing the angles for 100 magnets in under three seconds. Moreover, the optimization workflow can be adapted to optimize a permanent magnet array to achieve the desired force vector fields.
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