Automating the manipulation of granular materials poses significant challenges due to complex contact dynamics, unpredictable material properties, and intricate system states. Existing approaches often fail to achieve efficiency and accuracy in such tasks. To fill the research gap, this article studies the small-scale and high-precision granular material digging task with unknown physical properties. A key scientific problem addressed is the feasibility of applying first-order gradient-based optimization to complex differentiable granular material simulation and overcoming associated numerical instability. A new framework, named differentiable digging robot (DDBot), is proposed to manipulate granular materials, including sand and soil. Specifically, we equip DDBot with a differentiable physics-based simulator, tailored for granular material manipulation, powered by GPU-accelerated parallel computing and automatic differentiation. DDBot can perform efficient differentiable system identification and high-precision digging skill optimization for unknown granular materials, which is enabled by a differentiable skill-to-action mapping, a task-oriented demonstration method, gradient clipping and line search-based gradient descent. Experimental results show that DDBot can efficiently (converge within 5 to 20 minutes) identify unknown granular material dynamics and optimize digging skills, with high-precision results in zero-shot real-world deployments, highlighting its practicality. Benchmark results against state-of-the-art baselines also confirm the robustness and efficiency of DDBot in such digging tasks.

翻译：自动化操控颗粒材料因其复杂的接触动力学、不可预测的材料特性以及错综的系统状态而面临重大挑战。现有方法在此类任务中往往难以兼顾效率与精度。为填补这一研究空白，本文研究了物理特性未知条件下的小尺度、高精度颗粒材料挖掘任务。所解决的一个关键科学问题是：将一阶梯度优化应用于复杂的可微分颗粒材料仿真的可行性，并克服相关的数值不稳定性。为此，我们提出了一种名为可微分挖掘机器人（DDBot）的新框架，用于操控包括沙土在内的颗粒材料。具体而言，我们为DDBot配备了一个专为颗粒材料操控设计的、基于可微分物理的仿真器，该仿真器由GPU加速并行计算与自动微分技术驱动。通过一个可微分技能到动作的映射、一种面向任务的演示方法、梯度裁剪以及基于线搜索的梯度下降，DDBot能够对未知颗粒材料进行高效的可微分系统辨识和高精度挖掘技能优化。实验结果表明，DDBot能够高效地（在5至20分钟内收敛）辨识未知颗粒材料动力学并优化挖掘技能，在零样本真实世界部署中取得高精度结果，凸显了其实用性。与最先进基线的基准测试结果也证实了DDBot在此类挖掘任务中的鲁棒性与高效性。