Nonlinear Model Predictive Control for Unmanned Aerial Vehicles

Abstract

This paper discusses the derivation and implementation of a nonlinear model predictive control law for tracking reference trajectories and constrained control of a quadrotor platform. The approach uses the state-dependent coefficient form to capture the system nonlinearities into a pseudo-linear system matrix. The state-dependent coefficient form is derived following a rigorous analysis of aerial vehicle dynamics that systematically accounts for the peculiarities of such systems. The same state-dependent coefficient form is exploited for obtaining a nonlinear equivalent of the model predictive control. The nonlinear model predictive control law is derived by first transforming the continuous system into a sampled-data form and and then using a sequential quadratic programming solver while accounting for input, output and state constraints. The boundedness of the tracking errors using the sampled-data implementation is shown explicitly. The performance of the nonlinear controller is illustrated through representative simulations showing the tracking of several aggressive reference trajectories with and without disturbances.

Minimum control effort–based path planning and nonlinear guidance for autonomous mobile robots

“…The contribution of this component of the framework covered in this article is motivated by the developments of Ru and Subbarao. 34 However, the research presented distinguishes itself in that the NMPC guidance design is applied to a wheeled mobile robot which is verified in simulations. Overall, the contribution from this aspect of the work comes from the application of a combined planning and guidance scheme to a mobile robot vehicle and its comparison with another nonlinear guidance design based on backstepping.…”

“…The NMPC technique applied in this framework is given in "SDC-based NMPC" section of this article and is based on the developments found by Ru and Subbarao. 34 For this methodology, the SDC form is used to preserve the nonlinear nature of the vehicle's kinematic equations and the weight on the terminal state of the system is found by solving the discrete time SDRE. The guidance commands are then found by quadratic programming with input and state constraints enforced on the system.…”

Quadcopter Adaptive Trajectory Tracking Control: A New Approach via Backstepping Technique

“…Typically, the cascade principle is also applied to design a full control law based on the Lyapunov's direct method that guarantees the asymptotic stability of each loop [25][26][27][28][29][30][31][32] via the backstepping technique [33]. Model predictive control, which obtains some advantages of optimal control, was employed to carry out not only path-tracking problem, but also state constraints [34,35]. In order to tackle external disturbances, a robust nonlinear H ∞ controller [36] was proposed to track the reference trajectory.…”

Stability Driven Optimal Controller Design for High Quality Images

“…In wind generation systems, the stability problems were reduced to a linear matrix inequality (LMI) problem and the current controller was also designed by the LMI method [25]. For model predictive control (MPC) of a quad-rotor platform, control took the form of linear matrix inequalities [26]. LMI control was used for trajectory tracking instead of iterative learning control (ILC) [27].…”