Differentiable Contact Dynamics for Stable Object Placement Under Geometric Uncertainties

TL;DR

The paper addresses stable object placement under geometric uncertainty by introducing a differentiable contact dynamics framework that yields gradients of contact wrench with respect to uncertain geometry. It extends a differentiable simulator (Jade) to compute $\partial \mathbf{y}/\partial \boldsymbol{\theta}$ and uses gradient descent on $\boldsymbol{\theta}$ to align simulated and measured force-torque data, mitigating gradient initialization sensitivity by maintaining a belief over multiple geometric estimates. A belief-based, gradient-driven estimation-and-action loop is evaluated on a Franka robot across shape, pose, environment uncertainties, and even a full-cup coffee task, showing improved accuracy over particle-filter and heuristic baselines. These results demonstrate a general, model-based approach to robust contact-rich manipulation under geometry uncertainty with practical implications for robotic assembly and service tasks.

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, e.g., when the object pose or shape is not known accurately. This work leverages a differentiable simulation model 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 belief 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.

Figures (8)

• Figure 1: Place a full cup of coffee on a saucer (left) and then release it (right). (a) When the coffee cup is stably placed, i.e., the bottom surface of the cup is well aligned the saucer, there is no spill after release. (b) If the gripper releases right after a sensed contact without proper estimation of geometric uncertainty, the coffee is spilled.
• Figure 2: Our overall pipeline. At every timestep, we update the estimated geometry and plan a robot action from the estimation.
• Figure 3: Experimental setups. (a)-(c) Visualization of the task setups for (a) shape, (b) pose and (c) env: the left column shows the unknown geometric parameters, the middle columns show an ideal placement process, and the right column visualizes the distance to goal when releasing. (d) The ATI Gamma sensor and Franka Hand mounted on a Franka Research 3 arm. (e) The end-effector frame in which the motion and forces are represented.
• Figure 4: Our method has smaller distance to the goal errors when the robot releases. We plot the means and 95% confidence intervals over 10 test cases. For (a) shape, the errors are equivalent to angle errors. For (b) pose and (c) env, the errors are equivalent to distance errors.
• Figure 5: PF might suffer from "particle starvation". We plot estimation over time from 2 test cases of the shape task. In the same test case, ours (a) has good estimate, while PF (b) diverges on $d_{1}$ due to "particle starvation." (c) In a different test case, PF maintains good estimate.