We present the design of a low-cost wheeled mobile robot, and an analytical model for predicting its motion under the influence of motor torques and friction forces. Using our proposed model, we show how to analytically compute the gradient of an appropriate loss function, that measures the deviation between predicted motion trajectories and real-world trajectories, which are estimated using Apriltags and an overhead camera. These analytical gradients allow us to automatically infer the unknown friction coefficients, by minimizing the loss function using gradient descent. Motion trajectories that are predicted by the optimized model are in excellent agreement with their real-world counterparts. Experiments show that our proposed approach is computationally superior to existing black-box system identification methods and other data-driven techniques, and also requires very few real-world samples for accurate trajectory prediction. The proposed approach combines the data efficiency of analytical models based on first principles, with the flexibility of data-driven methods, which makes it appropriate for low-cost robots. Using the learned model and our gradient-based optimization approach, we show how to automatically compute motor control signals for driving the robot along pre-specified curves.

中文翻译：

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基于微分物理的低成本轮式移动机器人模型识别与控制

我们介绍了低成本轮式移动机器人的设计，以及在电机扭矩和摩擦力影响下预测其运动的分析模型。使用我们提出的模型，我们展示了如何分析计算适当损失函数的梯度，该函数测量预测的运动轨迹和真实世界的轨迹之间的偏差，这些轨迹是使用 Apriltags 和头顶摄像机估计的。这些解析梯度允许我们通过使用梯度下降最小化损失函数来自动推断未知摩擦系数。优化模型预测的运动轨迹与现实世界中的运动轨迹非常吻合。实验表明，我们提出的方法在计算上优于现有的黑盒系统识别方法和其他数据驱动技术，并且还需要很少的真实样本来准确预测轨迹。所提出的方法将基于第一性原理的分析模型的数据效率与数据驱动方法的灵活性相结合，使其适用于低成本机器人。使用学习模型和我们基于梯度的优化方法，我们展示了如何自动计算电机控制信号以沿着预先指定的曲线驱动机器人。这使其适用于低成本机器人。使用学习模型和我们基于梯度的优化方法，我们展示了如何自动计算电机控制信号以沿着预先指定的曲线驱动机器人。这使其适用于低成本机器人。使用学习模型和我们基于梯度的优化方法，我们展示了如何自动计算电机控制信号以沿着预先指定的曲线驱动机器人。