Robotic magnetic manipulation offers a minimally invasive approach to gastrointestinal examinations through capsule endoscopy. However, controlling such systems using external permanent magnets (EPM) is challenging due to nonlinear magnetic interactions, especially when there are complex navigation requirements such as avoidance of sensitive tissues. In this work, we present a novel trajectory planning and control method incorporating dynamics and navigation requirements, using a single EPM fixed to a robotic arm to manipulate an internal permanent magnet (IPM). Our approach employs a constrained iterative linear quadratic regulator that considers the dynamics of the IPM to generate optimal trajectories for both the EPM and IPM. Extensive simulations and real-world experiments, motivated by capsule endoscopy operations, demonstrate the robustness of the method, showcasing resilience to external disturbances and precise control under varying conditions. The experimental results show that the IPM reaches the goal position with a maximum mean error of 0.18 cm and a standard deviation of 0.21 cm. This work introduces a unified framework for constrained trajectory optimization in magnetic manipulation, directly incorporating both the IPM's dynamics and the EPM's manipulability.

翻译：机器人磁力操控通过胶囊内窥镜为胃肠道检查提供了一种微创方法。然而，由于非线性磁相互作用，使用外部永磁体（EPM）控制此类系统具有挑战性，尤其是在存在复杂导航要求（如避开敏感组织）时。在本工作中，我们提出了一种结合动力学和导航要求的新型轨迹规划与控制方法，该方法使用固定在机械臂上的单个EPM来操控内部永磁体（IPM）。我们的方法采用了一种约束迭代线性二次调节器，该调节器考虑了IPM的动力学特性，以生成EPM和IPM两者的最优轨迹。受胶囊内窥镜操作启发而进行的广泛仿真和真实世界实验证明了该方法的鲁棒性，展示了其对外部干扰的适应能力以及在变化条件下的精确控制能力。实验结果表明，IPM到达目标位置的最大平均误差为0.18厘米，标准差为0.21厘米。这项工作为磁力操控中的约束轨迹优化引入了一个统一框架，直接整合了IPM的动力学特性和EPM的可操控性。