A Convex Approach to Advanced Air Mobility Trajectory Optimization

This dissertation addresses the challenge of real-time trajectory optimization for electric Vertical Take-Off and Landing (eVTOL) vehicles within the framework of Advanced Air Mobility (AAM). With urban airspaces becoming increasingly crowded, ensuring the safety, efficiency, and feasibility of eVTOL operations is crucial. This research primarily focuses on the development and application of convex optimization techniques to solve trajectory optimization problems that not only enhance operational capabilities but also ensure adherence to stringent safety and efficiency standards.

The study is structured into several critical analyses and methodological developments across multiple chapters. In the first chapter, I introduce a multi-phase trajectory optimization problem that transitions from cruise to landing phases, laying the groundwork for subsequent analyses. The approach taken demonstrates how various phases of flight can be seamlessly integrated and optimized using advanced mathematical models.

Following this, the second chapter delves into high-fidelity trajectory optimization that incorporates aerodynamic effects, significantly enhancing the realism and applicability of the optimization solutions proposed. Here, I employ the Sequential Convex Programming (SCP) method, renowned for its effectiveness in handling nonconvex problems by decomposing them into a series of convex subproblems that are computationally feasible to solve in real-time.

The results of these optimizations are validated through rigorous simulations, demonstrating that the convex optimization approaches adopted can successfully solve complex trajectory optimization problems efficiently. The simulations confirm that both the pseudospectral method and SCP can achieve the desired operational goals, highlighting the potential of these methods for on-board applications in a real-time environment.