It is difficult to guarantee an empty living environment to prevent unexpected contact between the object being manipulated by the robot and unplanned obstacles. In this paper, we propose a planar compliant contact control method for planar manipulation to cope with unexpected contact. We first use sheet gel as a multi-dimensional passive elastic element and combine it with a two-finger gripper to design a multi-dimensional elastic gripper. Subsequently, we explore the lumped parameter model for the force-displacement relationship of gel deformation and combine the model with the high impedance motion of robots to design an elastic interaction controller. The controller not only actively adjusts the deformation of the gel to provide the desired contact force and torque depending on contact, but also performs avoidance by following the surface of obstacles. Finally, we design and deploy several planar compliant contact experiments to validate the proposed method and demonstrate the unexpected contact response in human-robot co-packing. The results show that our method enables the robot to remain compliant in the face of unexpected contact caused by unplanned obstacles, which provides a guarantee for safe manipulation. Physics experiments can be viewed in the attached video.