Due to the highly uncertain and dynamic nature of military conflict and planetary exploration missions, enabling aerial and terrestrial unmanned autonomous systems (UAS) to gracefully adapt to mission and environmental changes is a very challenging task. In particular, the United States Army, Air Force, Navy, and NASA have recently shown interest in the task of load transportation by means of UAS, which rely heavily on the knowledge of both the UAS model and the load dynamics to function. Most of the currently available autopilot systems for UAS were built without suspended load transportation capabilities and are thus not appropriate, for example, to assist soldiers or planetary explorers in the tasks of carrying and deploying supplies, transporting injured people, or warfare. This research provides knowledge to the problem of autonomous suspended load transportation, attending national agencies expectations that UAS will perform in a reliable manner even in the challenging situation when loads of uncertain characteristics are transported and deployed, which heavily modify the UAS dynamic during the execution of the task. This work presents a novel model-free adaptive wavenet PID (AWPID)-based controller for enabling aerial UAS to transport cable suspended loads of unknown characteristics. In order to accomplish this goal, a control design is presented which enables the UAS to perform a trajectory tracking task, based solely on the knowledge of the UAS position. The methodology proposes a novel structure, which identifies inverse error dynamics using a radial basis neural network with daughter Mexican hat wavelets activation function. A real-time load transportation mission consisting of a multi-rotorcraft UAS carrying a cable suspended load of unknown characteristics validates the effectiveness of the trajectory tracking control strategy, showing smooth control signals even when the mathematical model of the aerial UAS and load dynamics are not known.