This paper proposes a new trajectory tracking method for a 6 degree-of-freedom (DOF) cable-suspended payload controlled by a team of quadrotors. Using the modeling convention of reconfigurable cable-driven parallel robots (RCDPRs) the coupled dynamics of the payload and the quadrotors are derived. Based on this dynamic model, a new dynamic control allocation approach is introduced to optimally distribute the virtual control input (i.e., the wrench to be exerted on the payload) among the cables and generate reference positions for the quadrotors on-line, while avoiding collisions between quadrotors and accounting for cable tension constraints. Furthermore, a new reinforcement-learning (RL) compensator is proposed to reduce tracking errors caused by the constraints in the quadrotors’ thrusts. Numerical simulations are conducted to validate the proposed approach.