Optimal Control for Enhanced Flight Performance of a Tilt-Rotor Drone

Master Student : Andrea Boldrini

Supervisor : Gregorio Marchesini

The use of unmanned aerial vehicles (UAVs) to perform physical interaction tasks is an effective and advanced solution which has been studied within the past years. However, a vast number of factors affect its performance and reliability, especially for high-pitch-angle maneuvers. This study investigates how it is possible to achieve highly precise setpoint tracking of a tilt-quadrotor equipped with a front-mounted gripper using optimal control techniques, specifically aiming to maximize the achievable pitch angle during hover. Furthermore, the study analyzes scenarios involving an external wrench generated on the vehicle and the use of the gripper to grasp a cylindrical target object. System dynamics were modeled, and control schemes were iteratively designed using Proportional-Integral-Derivative (PID), Linear-Quadratic Regulator (LQR), Linear Model Predictive Control (LMPC), and Nonlinear Model Predictive Control (NMPC), with PID serving as a baseline. An external wrench estimator was designed to estimate the current external disturbance to be accounted for in the control input assessment. Designs were initially simulated in MATLAB/Simulink to verify initial design success and then in ROS/Gazebo for higher-fidelity validation. PX4 Autopilot firmware, together with MAVLink communication protocol and MAVROS ROS package, and CasADi were utilized in this end. Quantitative analysis of advanced simulations revealed that model predictive control, particularly NMPC, yielded more precise setpoint tracking and near-vertical hovering compared to PID. The NMPC achieved an impressive pitch angle range of (-84°, 80°), and LMPC attained (-74°, 75°), significantly surpassing PID’s (-77°, 65°). LQR, however, did not improve baseline performance. Regarding disturbance handling, both NMPC and LMPC, unlike LQR and simple PID, were able to limit the position and attitude offset at steady state. Finally, a modified NMPC was evaluated for its ability to maintain stable contact while grasping a cylindrical target object, even during pitch angle changes. This was achieved by incorporating the adjoint of a penalty term into its cost function, optimizing its response to variations in the contact position (working point). This research demonstrates the suitability of model predictive control for high-pitch-angle maneuvers when the external wrench is correctly estimated. Furthermore, our findings imply that incorporating appropriate penalty terms into the cost function is crucial for enabling stable interaction with physical targets under variable pitch conditions.

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