Cross-end-effector grasp generation seeks a unified model that generalizes across objects and across embodiments ranging from parallel grippers to dexterous end effectors. Existing grasp generators are typically designed for a fixed embodiment or encode embodiment identity with a static descriptor, which weakens transfer when topology, actuation coupling, and contact geometry differ substantially. We present EAGG, an embodiment-aligned grasp generator that represents each embodiment with a topology-aware end-effector graph and an embodiment-specific low-dimensional end-effector control space. A frozen end-effector-cognition backbone converts the current articulated state into geometry-aware tokens that act as a reusable morphology prior, and iterative geometry injection refreshes these tokens throughout sampling so that conditioning remains synchronized with the evolving end-effector geometry. On the MultiGripperGrasp benchmark, EAGG reaches 56.17% average success across six training end effectors, remaining within 1.10 percentage points of specialized training while preserving transfer to finetuning and zero-shot end effectors. Iterative geometry injection further reduces the pooled median contact distance from 0.239 cm to 0.189 cm. These results show that cross-end-effector grasp generation is strengthened by aligning embodiment structure inside a shared generator rather than suppressing embodiment differences. Code is available at https://github.com/wanhaoniu/EAGG.

翻译：摘要：跨末端执行器的抓取生成旨在构建一个统一模型，使其能够泛化到不同物体，并适用于从平行夹爪到灵巧末端执行器的多种体态。现有抓取生成器通常针对固定体态设计，或使用静态描述符编码体态身份，当拓扑结构、驱动耦合和接触几何存在显著差异时，这种设计会削弱迁移能力。我们提出EAGG，一种体态对齐的抓取生成器，它通过拓扑感知的末端执行器图和体态特定的低维末端执行器控制空间来表征每种体态。一个冻结的末端执行器认知骨架将当前关节状态转换为几何感知标记，作为可复用的形态学先验，而迭代几何注入在采样过程中刷新这些标记，使条件化与不断演变的末端执行器几何保持同步。在MultiGripperGrasp基准上，EAGG在六个训练末端执行器上的平均成功率达到56.17%，与专门训练的差距保持在1.10个百分点以内，同时保留了对微调与零样本末端执行器的迁移能力。迭代几何注入进一步将池化中位接触距离从0.239厘米降至0.189厘米。这些结果表明，通过在共享生成器内部对齐体态结构而非抑制体态差异，跨末端执行器抓取生成得以增强。代码已开源至 https://github.com/wanhaoniu/EAGG。