Stable grasping under task-specific disturbances is important for robotic manipulation. However, most dexterous grasp synthesis methods are developed for highly actuated hands in free space, and low-DoF hands may not be able to realize the contact topologies required by these grasps. Meanwhile, support surfaces can provide useful contact forces, but are often treated only as geometric constraints. We present a support-aware grasp synthesis framework for object immobilization with low-DoF coupled hands. Given irregular object geometry, our method represents both hand and object local surface regions as graphs and searches for kinematically feasible matchings between them. We then refine the wrist pose and motor state for geometric contact feasibility and validates the refined grasps through physical rollouts. Starting from the validated grasp pose, an optional task-guided local search explores nearby grasp configurations by varying the wrist pose and motor state, and selects one according to the specified task condition. Experiments on diverse objects show that our method generates various grasp configurations that achieve high grasp success and strong disturbance resistance. Real-world experiments further demonstrate physically executable grasps which enable object immobilization in cooking scenario.

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