This paper proposes continuum deformation as a strategy for controlling the collective motion of a multiple quad-copter system (MQS) carrying a common payload. Continuum deformation allows expansion and contraction of inter-agent distances in a 2- D motion plane to follow desired motions of three team leaders. The remaining quadcopter followers establish the desired continuum deformation only by knowing leaders' positions at desired sample time waypoints without the need for inter-agent communication over the intermediate intervals. Each quadcopter applies a linear-quadratic Gaussian (LQG) controller to track the desired trajectory given by the continuum deformation in the presence of disturbance and measurement noise. Results of simulated cooperative aerial payload transport in the presence of uncertainty illustrate application of continuum deformation for coordinated transport through a narrow channel.