In teleoperation, research has mainly focused on target approaching, where we deal with the more challenging object manipulation task by advancing the shared control technique. Appropriately manipulating an object is challenging due to the fine motion constraint requirements for a specific manipulation task. Although these motion constraints are critical for task success, they often are subtle when observing ambiguous human motion. The disembodiment problem and physical discrepancy between the human and robot hands bring additional uncertainty, further exaggerating the complications of the object manipulation task. Moreover, there is a lack of planning and modeling techniques that can effectively combine the human and robot agents motion input while considering the ambiguity of the human intent. To overcome this challenge, we built a multi-task robot grasping model and developed an intent-uncertainty-aware grasp planner to generate robust grasp poses given the ambiguous human intent inference inputs. With these validated modeling and planning techniques, it is expected to extend teleoperated robots functionality and adoption in practical telemanipulation scenarios.