It is acknowledged that quadcopters, because of their low cost and flexibility, play a vital role in many areas of applications such as smart farming, natural disasters, package delivery, etc. It has been established that conventional quadcopters can perform various manipulations and control functions such as obstacle avoidance, terrain following, environmental navigation, and autonomous landing. Interestingly, flying insects can perform all those functions and far beyond, using ingenious strategies for perception and navigation. Additionally, flying insects can reconfigure their shapes to achieve desired goals such as accessing a tight space, landing and taking off in densely populated farmland for food foraging, and accessing indoor environments from outside. These bring up a new research topic, called self-arm management or morphing quadcopters. However, existing morphing quadcopters have been determined to have the following challenges: an increased weight budget and energy consumption, which translate to limited flight time, a loss of stability and controllability during morphing because of variation in the center of gravity, inertias, and the system dynamics. This research aimed at the mathematical modeling and design of backstepping control for morphing quadcopter application taking into consideration X, Y, T, H, and O morphing configurations. The choice of this control approach is due to its capability in ensuring Lyapunov stability robustness of the desired dynamics and handling all forms of nonlinearities. Simulation results obtained showed the effectiveness of the proposed control approach to adapt parameter variations in the model dynamics because of geometric reconfiguration. Furthermore, the control approach was investigated under instant changes in configurations every 15 s. Analyzing the control error performance, the controllers exhibit a maximum overshot of 0.015 (7.5%) and a settling time of 10s. Finally, a PID controller was designed for servo control of the arm, and a good tracking performance with minimum error was achieved.