Modeling and Backstepping-based Nonlinear Control Strategy for a 6 DOF Quadrotor Helicopter

In this article, a nonlinear model of an underactuated six degrees of freedom （6 DOF） quadrotor helicopter is derived on the basis of the Newton-Euler formalism. The derivation comprises determining equations of the motion of the quadrotor in three dimensions and approximating the actuation forces through the modeling of aerodynamic coefficients and electric motor dynamics. The derived model composed of translational and rotational subsystems is dynamically unstable, so a sequential nonlinear control strategy is used. The control strategy includes feedback linearization coupled with a PD controller for the translational subsystem and a backstepping-based PID nonlinear controller for the rotational subsystem of the quadrotor. The performances of the nonlinear control method are evaluated by nonlinear simulation and the results demonstrate the effectiveness of the proposed control strategy for the quadrotor helicopter in quasi-stationary flights.

Controller design for 2-DOF underactuated mechanical systems based on controlled Lagrangians and application to Acrobot control

On the basis of controlled Lagrangians,a controller design is proposed for underactuated mechanical systems with two degrees of freedom.A new kinetic energy equation(K-equation)independent of the gyroscopic forces is found due to the use of their property.As a result,the necessary and sufficient matching condition comprises the new K-equation and the potential energy equation(P-equation)cascaded,the regular condition,and the explicit gyroscopic forces.Further,for two classes of input decoupled systems that cover the main benchmark examples,the new K-equation,respectively,degenerates from a quasilinear partial differential equation(PDE)into an ordinary differential equation(ODE)under some choice and into a homogeneous linear PDE with two kinds of explicit general solutions.Benefiting from one of the general solutions,the obtained smooth state feedback controller for the Acrobots is of a more general form.Specifically,a constant fixed in a related paper by the system parameters is converted into a controller parameter ranging over an open interval along with some new nonlinear terms involved.Unlike what is mentioned in the related paper,some categories of the Acrobots cannot be stabilized with the existing interconnection and damping assignment passivity based control(IDA-PBC)method.As a contribution,the system can be locally asymptotically stabilized by the selection of the new controller parameter except for only one special case.

Switched Three-Dimensional Decoupling Stabilization of Underactuated Autonomous Underwater Vehicles

A three-dimensional stabilization problem for underactuated autonomous underwater vehicles(AUVs)is addressed in this paper.A novel coordinate transformation form consisting of state modifications and input transformations is introduced such that the whole system is divided into two decoupled one-order subsystems.Some switching functions are presented to further decouple the underactuated dynamics and to produce persistently exciting(PE)signals for those underactuated states.Based on the aforementioned results,a quite simple control law is designed to achieve global three-dimensional asymptotic convergence of all states of underactuated AUVs.Comparative simulations are carried out to validate the effectiveness and performance of the proposed control scheme.