A proportional derivative sliding mode control for an overactuated quadcopter

Traditional quadcopters suffer from their intrinsic underactuation, which prevents them from tracking arbitrary trajectories. In this study, a step-by-step mathematical modeling of a tilt rotor quadcopter, i.e. a quadcopter with all its four rotors are allowed to be tilted independently around their arms’ extension, is derived. The tilting mechanism converts the classical quadcopter to an overactuated flying vehicle that has full control over its states. The nonlinear dynamical model is derived based on the Newton–Euler formalization. A novel trajectory tracking control scheme is then proposed and developed. The proposed controller combines the proportional derivative linear controller with the nonlinear sliding mode controller. In order to reduce the chattering effect of the sliding mode controller, the discontinuous Signum switching function is replaced by a continuous sigmoidal function. The controller parameters are then tuned with the aid of genetic algorithm as an optimization tool. The genetic algorithm objective function is set so as to get the best step response characteristics. A simulation based analysis is used to proof the system and controller capability in following complex trajectories. Finally, the proposed controller robustness and effectiveness are analyzed. The simulation test results reveal the validity and feasibility of the proportional derivative sliding mode controller. The proposed controller also performed well in the face of modeling imprecision, sensor noise, and external disturbances.