The disclosure relates to an end effector arrangement having an end effector for a manipulator and having a control for the end effector, wherein the end effector has a tool arrangement having a plurality of gripper devices for holding a planar workpiece, wherein at least one gripper device has a Bernoulli gripper unit, which has a discharge unit for channeling a flow SB from the Bernoulli gripper unit between gripper device and workpiece in a manner such that, in a delimited region between gripper device and the workpiece, the flow SB generates a low pressure for holding the workpiece, and wherein at least one gripper device has a different gripper unit, which carries the workpiece according to a physical principle which differs from that of the Bernoulli gripper unit.