Nonlinear Differential EquationBased Control for Trajectory Tracking and Obstacle Avoidance in UAVs

Due to the nonlinear nature of the physics regulating their flight, drones operating in real-world contexts have a basic challenge: they must safely navigate across areas full of moving impediments and unpredictable disturbances. In order to overcome this difficulty, control systems must embrace the complete complexity of drone dynamics rather than relying solely on linear approximations. In order to keep a drone locked onto a chosen flight route and simultaneously steer it away from obstacles in real time, this research presents a nonlinear control system. A dynamic model constructed from coupled nonlinear differential equations at the core of the method accurately depicts how a drone moves and reacts to control inputs. After that, a controller is made to continuously gauge the drone's deviation from its reference trajectory and produce corrective measures to get it back on course. A potential field technique, in which each obstacle projects an imperceptible repulsive barrier around itself, is used to manage obstacle avoidance. The control law automatically modifies its inputs to push the drone away as it gets closer to these boundaries, all without sacrificing the main objective of staying on the intended course. This stability guarantee's mathematical foundation is a Lyapunov-based argument that verifies the system's continued good behavior in the face of perturbation. The messy realities of actual flight, such as wind disturbances and the strict limitations set by onboard actuators, are also taken seriously by the framework. The drone consistently tracks its course, avoids collisions, and settles smoothly at the intended spot, according to simulation results across many test scenarios. When combined, the results provide compelling evidence for nonlinear modeling as a useful and effective basis for creating drone navigation systems that are safer and more autonomous.