Dexterous grasping is usually conducted for specific tasks, leading to heterogeneous constraints such as specific approach directions, desired contact regions, specified wrist trajectories, and functional hand poses. Our previous work, GraspXL, achieves scalable grasping motion synthesis for diverse objects and hand morphologies, while lacking controllability for synthesis under such various task-driven constraints. In this paper, we propose ConGraspXL, which extends GraspXL with controllable constraint-conditioned grasp motion synthesis that accommodates diverse task-driven constraints and their combinations. We introduce a hierarchical constraint formulation, enable flexible constraint composition with a masked residual interface, and improve control precision with dynamic hand centers and feed-forward wrist guidance. Without losing the strong generalization capabilities of GraspXL, ConGraspXL enables precise and flexible controllability for various individual constraints and their combinations, providing a plug-and-play low-level grasp controller for downstream applications such as whole-body grasp completion, functional grasping, and human-motion imitation.

翻译：暂无翻译