This paper addresses the problem of driving a quadrotor vehicle along a predefined 3-D trimming path. The proposed solution relies on the definition of a path-dependent error space to express the dynamic model of the vehicle, which results in linear time-invariant dynamics for the error system. The controller synthesis problem is then formulated as a linear quadratic regulator problem for LTI systems. The control strategy adopts the D-methodology integrated with the anti-windup technique in order to achieve zero static error for the integral states and to avoid actuator saturation. Experimental results where a quadrotor follows a trimming trajectory are presented to illustrate the performance of the proposed controller.