Fixture calibration with guaranteed bounds from a few correspondence-free surface points

TL;DR

Fixture pose calibration in robotic work cells is often slow and error-prone when using correspondence-based measurements. The paper proposes a correspondence-free method that measures a few surface points and uses a hierarchical grid on $SE(3)$ to produce a tight pose superset with guaranteed bounds on the true pose, plus a probabilistic pose distribution for confidence intervals. Key contributions include a tractable guaranteed-bounds framework, automatic ambiguity handling for symmetry, pose-likelihoods and confidence intervals, and a practical tool design with real-user validation. The approach enables easier, more reliable fixture calibration with explicit uncertainty quantification that can support downstream tasks that account for calibration uncertainty.

Abstract

Calibration of fixtures in robotic work cells is essential but also time consuming and error-prone, and poor calibration can easily lead to wasted debugging time in downstream tasks. Contact-based calibration methods let the user measure points on the fixture's surface with a tool tip attached to the robot's end effector. Most such methods require the user to manually annotate correspondences on the CAD model, however, this is error-prone and a cumbersome user experience. We propose a correspondence-free alternative: The user simply measures a few points from the fixture's surface, and our method provides a tight superset of the poses which could explain the measured points. This naturally detects ambiguities related to symmetry and uninformative points and conveys this uncertainty to the user. Perhaps more importantly, it provides guaranteed bounds on the pose. The computation of such bounds is made tractable by the use of a hierarchical grid on SE(3). Our method is evaluated both in simulation and on a real collaborative robot, showing great potential for easier and less error-prone fixture calibration. Project page at https://sites.google.com/view/ttpose

Figures (4)

• Figure 1: A user moves a robot to measure a few points on a fixture using a calibrated tool-tip attached to the end-effector of the robot. The tool consist of a 3D-printed mount with a 3 mm steel ball at the tip. The fixture is a 3D-printed MATLAB logo, fixated to the table using additional fixtures.
• Figure 2: Pose uncertainty for simulations on the MATLAB logo with varying sample error bounds. The true error for the expected pose (\ref{['eq:expected-pose']}) is shown in red and is within the confidence intervals and bounds. The pose uncertainties decrease proportionally with the sample error bound.
• Figure 3: Qualitative pose estimation results of three different objects from the SYMSOL murphy2021implicit dataset. From left to right: A cube, a cone and a cylinder. Top: The objects are rendered semi-transparently in blue together with ten simulated surface samples with noise, $b_\text{s} = 0.3\text{mm}$, in red. From the CAD model and noisy surface samples, our method provides a set of poses which are guaranteed to include the true pose. Bottom: We show the rotation part of the pose set with two rotational dimensions shown by the position on a sphere, shown in a Mollweide plot, and the last dimension visualized by color. The true rotation up to symmetry is shown by circles for discrete symmetries (cube) and "stroked" circles for continuous symmetries (cone and cylinder). Our method naturally captures all the modes without any prior knowledge about symmetries, and this ambiguity can be conveyed to a user.
• Figure 4: The tool-tip with the steel ball is shown in black. The fixture is shown in red, and the Minkowski sum of the steel ball and the fixture is illustrated by a dashed, red line. The center of the steel ball lies on the Minkowski sum surface independently of the angle of sampling.