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：自包含且可在无需额外外部传感器或工具的情况下自动执行的标定程序，对于复杂机器人系统尤为重要。本文证明，仅通过将多指机器人手的手指指尖两两接触运动，即可精确标定其运动学参数。该方法的唯一前提是具备灵敏的接触检测能力（例如，如我们DLR-Hand II手部采用的关节扭矩传感或触觉皮肤）。在给定关节构型下，测量函数定义为指尖几何模型之间的距离，而实际测量值始终为零。通过深入分析，我们证明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（即指尖差值向量），且其灵敏度与使用外部视觉跟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，包括最优采样关节构型的选择、以及即使存在初始运动学不确定性时仍能实现接触的搜索运动。针对扭矩控制四指DLR-Hand II手部的真实标定实验表明，最大误差可从17.7mm降至仅3.7mm。