Collision-free trajectory tracking for Quadrotor UAVs: closed-form versus optimization-based controllers

This thesis addresses the critical problem of collision-free trajectory tracking for quadrotor un- manned aerial vehicles (UAVs) in dynamic and constrained environments. In this research, two of the most representative control strategies are compared: a closed-form tracking controller integrated with Control Barrier Functions (CBF) and optimization-based model predictive control (MPC). The proposed closed form tracking controller incorporates Control Barrier Functions (CBF) with an Elliptical Boundary (EB) that allows a quadrotor to pass through complex environments by dynamically filtering tracking commands resulting in unsafe regions to guarantee real-time safety clearance with high computational efficiency. On the other hand, two Model Predictive Control (MPC) approaches are implemented: one with explicit distance constraints, using Euclidean norms for obstacle avoidance Model Predictive Control-Distance Constraint (MPC-DC), and the other is Model Predictive Control-Control Barrier Function (MPC-CBF), which solves the problem by including CBF constraints into the optimization framework. The MPC-CBF framework provides smoother obstacle avoidance and better adaptability to dynamic environments at the expense of increased computational demand. A comparison between the elliptical volume and the spherical one (circular boundary) bounding the quadrotor body in tracking tasks, performed in the application of the CBF controller, demonstrates that the elliptical boundary framework offers improved obstacle avoidance with lower overshoot and better safety margins, while maintaining comparable tracking performance. MATLAB simulations with static and dynamic obstacles show that the tracking controller with Control Barrier Function-Elliptical Boundary (CBF-EB) is a robust and efficient solution for real-time quadrotor navigation under resource constraints. This approach follows practical applicability by assuming that the quadrotor’s center of mass remains within the elliptical boundary, leveraging the quasi-hovering flight condition for simplicity and efficiency.