Continuous physical interaction between robots and their environment is a requirement in many industrial and household tasks, such as sanding and cleaning. Due to the complex tactile information, these tasks are notoriously difficult to model and to sense. In this article, we introduce a closed-loop control method that is constrained to surfaces. The applications that we target have in common that they can be represented by probability distributions on the surface that correlate to the time the robot should spend in a region. These surfaces can easily be captured jointly with the target distributions using coloured point clouds. We present the extension of an ergodic control approach that can be used with point clouds, based on heat equation-driven area coverage (HEDAC). Our method enables closed-loop exploration by measuring the actual coverage using vision. Unlike existing approaches, we approximate the potential field from non-stationary diffusion using spectral acceleration, which does not require complex preprocessing steps and achieves real-time closed-loop control frequencies. We exploit geometric algebra to stay in contact with the target surface by tracking a line while simultaneously exerting a desired force along that line. Our approach is suitable for fully autonomous and human-robot interaction settings where the robot can either directly measure the coverage of the target with its sensors or by being guided online by markings or annotations of a human expert. We tested the performance of the approach in kinematic simulation using point clouds, ranging from the Stanford bunny to a variety of kitchen utensils. Our real-world experiments demonstrate that the proposed approach can successfully be used to wash kitchenware with curved surfaces, by cleaning the dirt detected by vision in an online manner. Website: https://geometric-algebra.tobiloew.ch/tactile_ergodic_control

翻译：机器人与环境之间的连续物理交互是许多工业和家务任务（例如打磨和清洁）中的必要需求。由于复杂的触觉信息，这些任务在建模和感知上通常极为困难。本文介绍了一种受限于曲面的闭环控制方法。我们针对的应用场景具有一个共同特点：它们可以用曲面上与机器人应在某区域停留时间相关的概率分布来表示。这些曲面可以很容易地与目标分布一起，通过彩色点云同步获取。我们提出了一种基于热方程驱动的区域覆盖（HEDAC）的遍历控制方法的扩展，该方法可用于点云。我们的方法通过使用视觉测量实际覆盖情况来实现闭环探索。与现有方法不同，我们利用谱加速从非平稳扩散中近似势场，这无需复杂的预处理步骤，并能实现实时的闭环控制频率。我们利用几何代数，通过跟踪一条线并同时沿该线施加期望的力，来保持与目标曲面的接触。我们的方法适用于全自主和人机交互场景。在这些场景中，机器人可以直接通过传感器测量目标的覆盖情况，或者通过人类专家的在线标记或注释来引导。我们通过斯坦福兔子到各种厨房用具的点云进行了运动学仿真测试，以评估该方法的性能。我们的真实世界实验表明，所提出的方法可以成功用于清洗具有曲面的厨房用具，通过在线方式清理视觉检测到的污垢。网站：https://geometric-algebra.tobiloew.ch/tactile_ergodic_control