We present a decentralized sliding mode control strategy for collective payload transport by a team of robots. The controllers only require robots' measurements of their own heading and velocity, and the only information provided to the robots is the target speed and direction of transport. The control strategy does not rely on inter-robot communication, prior information about the load dynamics and geometry, or knowledge of the transport team size and configuration. We initially develop the controllers for point-mass robots that are rigidly attached to a load and prove the stability of the system, showing that the speed and direction of the transported load will converge to the desired values in finite time. We also modify the controllers for implementation on differential-drive mobile robots. We demonstrate the effectiveness of the proposed controllers through simulations with point-mass robots, 3D physics simulations with realistic dynamics, and experiments with small mobile robots equipped with manipulators.