Analytical dexterous grasping synthesis is often driven by grasp quality metrics. However, existing metrics possess many problems, such as being computationally expensive, physically inaccurate, and non-differentiable. Moreover, none of them can facilitate the synthesis of non-force-closure grasps, which account for a significant portion of task-oriented grasping such as lid screwing and button pushing. The main challenge behind all the above drawbacks is the difficulty in modeling the complex Grasp Wrench Space (GWS). In this work, we overcome this challenge by proposing a novel GWS estimator, thus enabling gradient-based task-oriented dexterous grasp synthesis for the first time. Our key contribution is a fast, accurate, and differentiable technique to estimate the GWS boundary with good physical interpretability by parallel sampling and mapping, which does not require iterative optimization. Second, based on our differentiable GWS estimator, we derive a task-oriented energy function to enable gradient-based grasp synthesis and a metric to evaluate non-force-closure grasps. Finally, we improve the previous dexterous grasp synthesis pipeline mainly by a novel technique to make nearest-point calculation differentiable, even on mesh edges and vertices. Extensive experiments are performed to verify the efficiency and effectiveness of our methods. Our GWS estimator can run in several milliseconds on GPUs with minimal memory cost, more than three orders of magnitude faster than the classic discretization-based method. Using this GWS estimator, we synthesize 0.1 million dexterous grasps to show that our pipeline can significantly outperform the SOTA method, even in task-unaware force-closure-grasp synthesis. For task-oriented grasp synthesis, we provide some qualitative results. Our project page is https://pku-epic.github.io/TaskDexGrasp/.

翻译：灵巧抓取的解析合成通常依赖于抓取质量指标。然而，现有指标存在诸多问题，例如计算成本高、物理精度不足以及不可微。此外，这些指标均无法支持非力闭合抓取的合成，而这类抓取在任务导向型操作（如瓶盖旋拧与按钮按压）中占据重要比例。上述缺陷背后的核心挑战在于难以对复杂的"抓取力旋量空间"进行建模。本研究通过提出一种新颖的GWS估计器克服了这一挑战，从而首次实现了基于梯度的任务导向灵巧抓取合成。我们的核心贡献包括：第一，提出一种快速、精确且可微的GWS边界估计技术，通过并行采样与映射实现良好的物理可解释性，无需迭代优化；第二，基于可微GWS估计器推导出任务导向能量函数以支持基于梯度的抓取合成，并提出可评估非力闭合抓取质量的指标；第三，通过一项创新技术改进现有灵巧抓取合成流程——即便在网格边与顶点处也能实现最近点计算的可微化。大量实验验证了我们方法的效率与有效性。在GPU上，我们的GWS估计器可在毫秒级内完成运算且内存占用极低，速度较经典离散化方法提升三个数量级以上。借助该估计器，我们合成了10万组灵巧抓取动作，结果表明即使在与任务无关的力闭合抓取合成任务中，本流程性能也显著超越现有最优方法。针对任务导向抓取合成，我们提供了部分定性结果。项目主页：https://pku-epic.github.io/TaskDexGrasp/。