Actuators are an essential part of a robot, creating movement between the robot and its environment. Actuators with flexible shapes allow them to operate in a wider variety of environments, and actuators with multiple degrees of freedom allow them to generate more complex motions. Here we propose a soft pneumatic actuator in the form of a thin, flexible sheet that can generate different motion vector fields on a surface. The proposed actuator is made by a novel multilayer additive process, which allows dozens of thin pneumatic chambers and multi-channel pneumatic circuits connecting them to be precisely formed in a thin soft body. A soft body containing such a complex pneumatic network can have a high degree of freedom and act like a transducer, with its surface dynamically responding to the input pressures. Depending on the input sequence, the proposed actuator can generate surface movements in six different directions, at different speeds, and over different distances, which we demonstrate through analytical models and experiments. We show that our proposed actuator can be used in a variety of environments where conventional rigid and thick actuators are difficult to use, including inspection and obstacle removal in narrow pipes, in-hand manipulation between conventional robotic grippers, and object transportation.