From serving a cup of coffee to carefully rearranging delicate items, stable object placement is a crucial skill for future robots. This skill is challenging due to the required accuracy, which is difficult to achieve under geometric uncertainty. We leverage differentiable contact dynamics to develop a principled method for stable object placement under geometric uncertainty. We estimate the geometric uncertainty by minimizing the discrepancy between the force-torque sensor readings and the model predictions through gradient descent. We further keep track of a belief over multiple possible geometric parameters to mitigate the gradient-based method's sensitivity to the initialization. We verify our approach in the real world on various geometric uncertainties, including the in-hand pose uncertainty of the grasped object, the object's shape uncertainty, and the environment's shape uncertainty.

翻译：从端送一杯咖啡到精心重新排列易碎物品，稳定物体放置是未来机器人至关重要的技能。由于所需精度在几何不确定性条件下难以实现，这项技能具有挑战性。我们利用可微接触动力学，开发了一种在几何不确定性下实现稳定物体放置的原理性方法。通过梯度下降最小化力-力矩传感器读数与模型预测之间的差异，我们估计几何不确定性。为进一步缓解基于梯度的方法对初始化的敏感性，我们持续追踪多个可能几何参数的概率分布。我们在真实世界中验证了该方法对各种几何不确定性的适用性，包括抓取物体的手内位姿不确定性、物体形状不确定性以及环境形状不确定性。