Numerical optimization techniques for nonlinear quadrotor control

Currently, quadrotors have become very popular and have different applications in entertainment, transportation, rescue and military areas, among others. A key activity in the design of quadrotors is the flight control. A well-known flight controller is the PD, which is sufficient to make the quadcopter to hover in the air. One crucial problem with this type of controllers is the coefficient tuning. Typically, linear models are supposed for the latter, however, in this work we study the use of two optimization techniques for coefficient tuning when the dynamic model is nonlinear. These techniques refer to parametric control tuning based on numerical strategies using Conjugate Gradient (CG) optimization. We also analyze the optimal control law for the same nonlinear model by applying the Pontryagin's Maximum Principle, which yields the conditions to numerically find the optimal flight control to transfer the quadrotor between hovering states. We carried out a comparison of the behavior of the quadcopter dynamics regarding the tuned parametric controls obtained with the two CG strategies and with the achieved optimal control. In addition, we analyzed, from the point of view of the user, which one of these strategies is the easiest to implement.