This thesis addresses Nonlinear Model Predictive Controller (NMPC) of multi-rotor Unmanned Aerial Vehicles (UAVs). It presents two primary contributions: i) a novel method of numerically analyzing flight controller performance, and ii) two novel NMPC components: an optimization algorithm and a UAV model. These contributions are assessed in a case study comparing a set of five NMPC systems on flight performance in nine tests including impulse response, periodic wind disturbances, and obstacle avoidance.
The Performance Analysis Methodology (PAM) proposed in this work calculates the probability of a controller maintaining a UAV's state output within a set of user defined benchmark values during flight tests. These tests can take many forms, but this thesis considers initial state errors, reference changes, disturbing winds, and obstacles. To estimate this probability, the PAM simulates multiple flights under each set of test conditions, analyzes each test flight individually to determine whether tracking error was within the desired benchmark values, and combines the analyzed data via statistical analysis. To generate accurate flight test data, a novel formulation of recursive Newton-Euler multibody dynamics is proposed, and models for commonly encountered vehicle subsystems are provided. To appropriately analyze the test flight data, a novel pseudo-Laplace transform is proposed capable of accounting for time-varying elements within the tracking error signals. Finally, to combine flight test data from multiple tests, two methods of statistical analysis, mean/variance analysis and binomial probability analysis, are provided. Combined into the PAM, these techniques form a novel means to determine how likely a control system is to safely maintain a UAV in a desired state despite disruption.
Two NMPC components are proposed in this thesis: i) an E-greedy kinodynamic tree algorithm for optimization, and ii) a derivative multi-rotor UAV model for cost prediction. The E-greedy tree algorithm expands the concept of random kinodynamic trees to incorporate game theory as a means of focusing tree growth. This produces an optimization algorithm that can identify low-cost control inputs faster than typical NMPC optimization techniques. The derivative multi-rotor model is designed to account for a wider range of dynamic effects in predicting the cost of control inputs. Where typical multi-rotor models in MPC literature assume that control signals directly specify the joint velocities of propellers and joint angles propeller blades, the derivative model models the propeller velocity and blade angle rates of change. As a result, the derivative multi-rotor model produces better prediction of future vehicle motion and, correspondingly, better predictions of cost. This thesis presents these two new components alongside three other NMPC optimization algorithms and two other NMPC multi-rotor vehicle models for comparison.
As a demonstration of both PAM and NMPC, the case study uses a large variable-pitch propeller quadrotor as the basis for analyzing the performance of six NMPCs (each a combination of an optimization algorithm and a multi-rotor model), and a PID reference tracking controller. Each controller is tested for performance on nine different tests covering a range of control challenges. The results from each test are used to create flight envelopes depicting the range of conditions within which each controller met selected performance benchmarks. The new NMPC optimization algorithm shows immediate advantages, achieving the goal of identifying low-cost control inputs faster. The new NMPC model shows promise, but was hindered by the computational capacity of the quadrotor's onboard processor. Finally, the PAM proves capable of performing a diverse set of tests, while producing data that can be quickly and easily interpreted.