Stabilizing Quadrotor Helicopter Based on Controlled Lagrangians

Energy shaping control for systems with underactuation degrees two by controlled Lagrangian method

“…As opposed to the controller, 31 the proposed controller could well accomplish the maneuver with more aggressive attitude deviation as shown in Figure 4 (the virtual angles) and Figure 5 (Euler angles), while the position responses are maintained almost the same as presented in Figure 6, and the proposed controller shows the robustness to the small body force perturbation as showed in Figure 7, which justifies the superiority of the nonlinear control design.…”

“…Therefore, (q, q) = (0, 0) is a asymptotically stable equilibrium of the system. Now that it is known that For comparison, a relate controller 31 considering the CL method for quadrotor helicopter based on linearization is taken for simulation, where the helicopter system presented in similar form of (45) was linearized and the CL method was applied to the horizontal subsystems, while the altitude and the heading were directly controlled by a PD controller. To show the superiority of the proposed control design, we apply the controller 31 to the nonlinear simplified system (45), while the proposed controller is applied to the nonlinear helicopter system (43) suffered with the small body force perturbation f s .…”

Stabilization control of quadrotor helicopter through matching solution by controlled Lagrangian method

“…The initial position is located at 𝜉( 0 To demonstrate the superiority of the proposed controller, we make comparisons with controllers presented in related works [30,31] which considered the underactuation problem of control for quadrotors (helicopters). The controller I [30] was designed based on hierarchical strategy, where the helicopter system was decomposed into inner-outer loop structure; the position loop controller was essentially a PD control bounded by hyperbolic tan- As shown in Figures 1 and 2, with a similar setting time, the proposed controller performs more steadily and neatly than controller I and controller II.…”

“…The controller I [30] was designed based on hierarchical strategy, where the helicopter system was decomposed into inner–outer loop structure; the position loop controller was essentially a PD control bounded by hyperbolic tangent function; and the attitude loop control was based on Lyapunov function and backstepping technique. Also, the controller II [31] from relate work considering CL‐based control for quadrotor is taken for comparison, where the quadrotor system was decoupled by linearization at the desired equilibrium, and the CL method was applied to horizontal subsystems with underactuation degree one, while the altitude channel and the heading channel were controlled by PD controllers.…”