Self-Contained and Automatic Calibration of a Multi-Fingered Hand Using Only Pairwise Contact Measurements

TL;DR

This work presents a self-contained calibration framework for a multi-fingered hand that relies solely on pairwise fingertip contact measurements, eliminating external sensors. It formulates a MAP-based parameter identification problem using a task-oriented measurement function that captures relative fingertip positions, and proves that contact data suffice to identify all task-relevant DH parameters. The approach is augmented with an optimal experimental design to select informative contact poses, and a practical contact-generation and detection procedure is demonstrated on the DLR-Hand II. Real-world experiments reduce the maximal kinematic error from 17.7 mm to 3.7 mm and achieve substantial improvement in task-space accuracy, enabling robust dexterous in-hand manipulation without external tracking systems.

Abstract

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.

Figures (12)

• Figure 1: DLR-Hand II Butterfass2001DLRHand with thumb and index finger in contact for different poses. The kinematic tree of the whole hand is indicated in orange, and the three active joints plus the fourth passive joint are drawn together with the dimensions of the fingers. The other two fingers are far extended to allow for a large shared workspace of the current pair. For the whole calibration, all six finger pairs are measured and calibrated jointly.
• Figure 2: The scheme shows the actual contact measurement on the hardware (black) and the same joint configuration applied to the robot model (gray). The fingers are in penetration for the current set of calibration parameters. This error (red) should be minimized over the calibration process.
• Figure 3: The scheme shows the three measurement functions discussed in \ref{['sec:Hand-Calibration']}. Top (\ref{['sec:TaskMeasFun']}): The task measurement function $h_\mathrm{t}$ measures the relative positions of the end-effectors. Middle (\ref{['sec:ContactMeasFun']}): The contact measurement function $h_\mathrm{c}$ measures the scalar distance between two end-effectors. Bottom (\ref{['sec:VisMeasFun']}): The cartesian measurement function $h_\mathrm{v}$ uses an external tracking system to measure the absolute position of the end-effectors.
• Figure 4: The graphic shows the contact calibration approach for a four-fingered hand. For pairwise contact, two fingers always need to move out of the shared workspace of the current finger pair to ensure that self-collisions are avoided and the available configuration space for contact detection is well used.
• Figure 5: This figure shows the ordered eigenvalues for different measurement setups to analyze the sensitivity. The evaluation was done with the nominal kinematic of the DLR-Hand II; for a more generic hand, see the right plot. The task measurement function $h_\mathrm{t}$ is blue, and our contact measurement function $h_\mathrm{c}$ is red. Furthermore, we show three modes. For the one where all the pairs are calibrated simultaneously ($\mathop{\vcenter{\hbox{$\helphexagon$}}}$), the kernels of both measurement functions have the same size. The same is true for the calibration with three fingers ($\mathop{\vcenter{\hbox{$\blacktriangle$}}}$) However, the kernel sizes differ when just a single pair ($\mathop{\vcenter{\hbox{$\bullet$}}}$) is considered. The light gray vertical lines indicate the maximal number of parameters for each mode.