Reasoning about distance is indispensable for establishing or avoiding contact in manipulation tasks. To this end, we present an online method for learning implicit representations of signed distance using piecewise polynomial basis functions. Starting from an arbitrary prior shape, our approach incrementally constructs a continuous representation from incoming point cloud data. It offers fast access to distance and analytical gradients without the need to store training data. We assess the accuracy of our model on a diverse set of household objects and compare it to neural network and Gaussian process counterparts. Distance reconstruction and real-time updates are further evaluated in a physical experiment by simultaneously collecting sparse point cloud data and using the evolving model to control a manipulator.

翻译：距离推理对于在操控任务中建立或避免接触至关重要。为此，我们提出了一种在线学习方法，利用片段多项式基函数隐式表示符号距离。该方法从任意初始形状出发，逐步根据输入的点云数据构建连续的符号距离表示。它能够快速访问距离值及其解析梯度，而无需存储训练数据。我们在多样化的家居物体数据集上评估了模型的精度，并将其与神经网络和高斯过程方法进行对比。通过物理实验进一步验证了距离重建与实时更新性能：实验过程中同步采集稀疏点云数据，并利用实时演变的模型控制机械臂。