Micron-scale robots ($\mu$bots) have recently shown great promise for emerging medical applications. Accurate controlling $\mu$bots, while critical to their successful deployment, is challenging. In this work, we consider the problem of tracking a reference trajectory using a $\mu$bot in the presence of disturbances and uncertainty. The disturbances primarily come from Brownian motion and other environmental phenomena, while the uncertainty originates from errors in the model parameters. We model the $\mu$bot as an uncertain unicycle that is controlled by a global magnetic field. To compensate for disturbances and uncertainties, we develop a nonlinear mismatch controller. We define the model mismatch error as the difference between our model's predicted velocity and the actual velocity of the $\mu$bot. We employ a Gaussian Process to learn the model mismatch error as a function of the applied control input. Then we use a least-squares minimization to select a control action that minimizes the difference between the actual velocity of the $\mu$bot and a reference velocity. We demonstrate the online performance of our joint learning and control algorithm in simulation, where our approach accurately learns the model mismatch and improves tracking performance. We also validate our approach in an experiment and show that certain error metrics are reduced by up to $40\%$.

翻译：微型机器人（$\mu$bots）近年来在新型医疗应用中展现出巨大潜力。对其实现精确控制虽至关重要，却极具挑战性。本文研究了在存在扰动与不确定性的情况下，利用微型机器人跟踪参考轨迹的问题。扰动主要源于布朗运动及其他环境现象，而不确定性则来自模型参数的误差。我们将微型机器人建模为受全局磁场控制的不确定独轮车模型。为补偿扰动与不确定性，我们提出了一种非线性失配控制器，将模型失配误差定义为模型预测速度与微型机器人实际速度之间的差异。我们采用高斯过程学习模型失配误差关于施加控制输入的函数关系，随后通过最小二乘优化选择控制动作，使微型机器人实际速度与参考速度之差最小化。我们在仿真中验证了所提联合学习与控制算法的在线性能，结果表明该方法能准确学习模型失配并提升跟踪性能。实验验证进一步表明，特定误差指标可降低高达40%。