Optimizing rotary-wing UAV trajectory tracking: A comparative study of optimization methods

Abstract

The rising popularity of Unmanned Aerial Vehicles (UAVs) for surveillance, and delivery systems in different sectors have made it essential to implement control mechanisms that provide greater precision required during operations. Model Predictive Control (MPC) is known for its ability to handle large scale, multi-variable control problems with constraints in a systematic way. One of the most important parameters in MPC and which significantly affects confidence and its performance is $Q$ (gain) and $R$ (penalty). These matrices are important because they control the state errors and controlling effort that in turn is of immense use for exact stability to desired trajectories and optimum performance of the UAV. The thesis investigates the application of MPC in navigation and control of rotary-wing UAVs; also, particularly, it focuses on the critical tuning of the $Q$ (gain) and $R$ (penalty) matrices within the MPC framework. The work covers two main sections addressing fundamental aspects of optimization in the context of efficiency and effectiveness of MPC in complex flight maneuvers. The first part of the thesis assess variety of optimization strategies such as global, local, and hybrid; in order to find the most effective path for tuning the $Q$ and $R$ matrices. The evaluation is based on several criteria, including computational efficiency, precision in following a predefined trajectory, and overall system stability. The evaluation extensively considers the UAVs' operational dynamics modelled linearly, as well as their ability to follow a simple point-to-point trajectory in order to count in only computational cost of the optimization algorithms. Also, this portion of the thesis systematically compares the performance of each strategy through simulation tests and computational analyses, providing a quantitative foundation to support conclusions about the optimal approach, hybrid optimization strategy stands out with respect to these analyses. The objective is to identify a strategy that significantly enhances the operational capabilities of MPC-equipped UAVs, ensuring both high performance and stability in their control systems. The second part dives deeper into the practical applications of the selected hybrid optimization strategy by comparing five optimization algorithms to identify the most effective for adjusting the MPC parameters of UAVs. This part of the study is crucial for fine-tuning the earlier decision on the hybrid method in the first part of the study, ensuring that the chosen algorithm optimally supports the UAV's dynamic operations across various flight conditions. A detailed comparative analysis is carried out with five specific global optimization algorithms combined with the Nelder-Mead Simplex method within the structure of the hybrid optimization method. The assessed algorithms consist of Particle Swarm Optimization (PSO), Genetic Algorithm (GA), Simulated Annealing (SA), Ant Colony Optimization (ACO), and Big Bang-Big Crunch (BB-BC) versus a background of complex model dynamics and various trajectory requirements. This model of the UAV is tested in non-linear formats to include many different flight situations seen throughout real-world implementation; furthermore, this model is employed to simulate the flight paths of the UAVs that fly trajectories with different complexities, such as helical and "8" shape patterns, which tests the precision and adaptability of the algorithms. The research in this chapter is an effort to find the best algorithm used for dynamic UAV operations based on their performance through conversions rates, computational requirements and following a trajectory. In summary, the results of the study show a great potential that PSO and BB-BC have to reduce computational runtime while improving trajectory precision. While SA is offering the best convergence rate, it brings high computational costs. Also, ACO failed to perform satisfactorily on either criteria. The thesis findings are supported by the claim that: the hybrid optimization strategy integrating BB-BC and Nelder-Mead Simplex method proved to be the most efficient for tuning MPC parameters in quadrotor aircraft; thus, it introduces an interesting resource of improvements to UAV control. This thesis highlights the ability of hybrid optimization methods to greatly improve MPC application in UAVs, thus promoting research on a wider range of optimization algorithms and real-time implementation further enhance operational systems for unmanned aerial vehicles. This work not only offers an aid in theoretical advancements of control engineering but also root for practical implementations to improve the performances of drone-based applications.