A self-contained calibration procedure that can be performed automatically without additional external sensors or tools is a significant advantage, especially for complex robotic systems. Here, we show that the kinematics of a multi-fingered robotic hand can be precisely calibrated only by moving the tips of the fingers pairwise into contact. The only prerequisite for this is sensitive contact detection, e.g., by torque-sensing in the joints (as in our DLR-Hand II) or tactile skin. The measurement function for a given joint configuration is the distance between the modeled fingertip geometries, but the actual measurement is always zero. In an in-depth analysis, we prove that this contact-based calibration determines all quantities needed for manipulating objects with the hand, i.e., the difference vectors of the fingertips, and that it is as sensitive as a calibration using an external visual tracking system and markers. We describe the complete calibration scheme, including the selection of optimal sample joint configurations and search motions for the contacts despite the initial kinematic uncertainties. In a real-world calibration experiment for the torque-controlled four-fingered DLR-Hand II, the maximal error of 17.7mm can be reduced to only 3.7mm.

翻译：自包含的标定程序无需额外外部传感器或工具即可自动执行，这对复杂机器人系统而言具有显著优势。本文证明，仅通过将多指机器人手的手指指尖成对移动至接触状态，即可精确标定其运动学参数。实现该方法的唯一前提是需要灵敏的接触检测能力（例如通过关节力矩传感（如我们的DLR-Hand II）或触觉皮肤）。对于给定的关节构型，测量函数为建模指尖几何形状间的距离，但实际测量值始终为零。通过深入分析，我们证明了这种基于接触的标定方法能够确定手部操作物体所需的所有参数（即指尖的差向量），其精度与使用外部视觉追踪系统和标记点的标定方法相当。我们描述了完整的标定方案，包括在初始运动学不确定条件下优化选择样本关节构型和接触搜索运动。在针对力矩控制四指DLR-Hand II的真实标定实验中，最大误差可从17.7mm降低至仅3.7mm。