Differentiable Contact Dynamics for Stable Object Placement Under Geometric Uncertainties

Abstract

From serving a cup of coffee to positioning mechanical parts during assembly, stable object placement is a crucial skill for future robots. It becomes particularly challenging under geometric uncertainties, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e.g.</i>, when the object pose or shape is not known accurately. This work leverages a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">differentiable simulation model</i> of contact dynamics to tackle this challenge. We derive a novel gradient that relates force-torque sensor readings to geometric uncertainties, thus enabling uncertainty estimation by minimizing discrepancies between sensor data and model predictions via gradient descent. Gradient-based methods are sensitive to initialization. To mitigate this effect, we maintain a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">belief</i> over multiple estimates and choose the robot action based on the current belief at each timestep. In experiments on a Franka robot arm, our method achieved promising results on multiple objects under various geometric uncertainties, including the in-hand pose uncertainty of a grasped object, the object shape uncertainty, and the environment uncertainty.