We present a decentralized adaptive control strategy for collective payload transport by differential-drive robots with manipulator arms. The controllers only require robots' measurements of their own heading and velocity and their manipulator angle and angular 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 number of robots and their distribution around the payload. We first design the desired manifolds of motion for the entire system such that they are compatible with the holonomic constraints between the robots and the payload. Then, we design adaptive controllers for a team of differential-drive robots that initially grasp a payload in an arbitrary configuration. We also analytically establish the stability and convergence of the system trajectories to the desired payload motion. We demonstrate the effectiveness of the proposed controllers through 3D physics simulations with realistic dynamics.