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.

翻译：解析式灵巧抓取合成通常由抓取质量指标驱动。然而，现有指标存在诸多问题，例如计算成本高、物理准确度低且不可微分。此外，这些指标均无法促进非力闭合抓取的合成——这类抓取在面向任务的抓取（如旋盖、按压按钮）中占据重要比例。上述所有缺陷背后的核心挑战在于难以对复杂的抓取力旋量空间（GWS）进行建模。本文通过提出一种新型GWS估计器克服了这一挑战，从而首次实现了基于梯度的面向任务灵巧抓取合成。我们的关键贡献在于：通过并行采样与映射提出一种快速、准确且可微分的GWS边界估计技术，该技术无需迭代优化且具备良好的物理可解释性。其次，基于可微分GWS估计器，我们推导出面向任务的能量函数以实现基于梯度的抓取合成，并提出评估非力闭合抓取的度量指标。最后，我们改进了先前的灵巧抓取合成流程，主要通过一项新技术使最近点计算（包括网格边与顶点）实现可微分。通过大量实验验证了方法的效率与有效性。我们的GWS估计器可在GPU上以毫秒级速度运行且内存消耗极低，速度比传统基于离散化的方法快三个数量级以上。利用该估计器，我们合成了10万个灵巧抓取，结果表明即使在无任务感知的力闭合抓取合成中，本方法也显著优于现有最优方法。针对面向任务的抓取合成，我们提供了部分定性实验结果。