Many-Objective Optimal Control for Quadcopters

In this paper, a multi-input-multi-output (MIMO) optimal control for a six-degree-of-freedom UAV having four rotors powered by brushless DC motors is designed in many- objective settings. To this end, the mathematical model of the UAV is derived and then linearized around one of its operating points. Then, nested control algorithms with three loops are designed after dividing the UAV dynamics into small subsystems. The outermost loop includes two control algorithms that calculate the required roll and pitch to maneuver the vehicle to the desired X and Y position. At the same time, the innermost loop controls the angular velocities of each axis of the quadrotor. The control loop between the outer and inner loops is called the middle control loop, which regulates the attitude and altitude of the quadrotor. Finally, a many-objective optimization problem that involves 20 design parameters and ten objective functions is formulated and solved by SPEA2SDE (Strength Pareto Evolutionary Algorithm 2 with Shift-based Density Estimation (SDE)), which is one of the popular many-objective optimization approaches. Both stability and performance constraints are imposed on the optimization problem. Numerical simulations conducted on the nonlinear UAV model show that the proposed many-objective and optimal design method is quite effective.