A Convex Approach to High-fidelity Landing Trajectory Optimization for Advanced Air Mobility

Urban Air Mobility (UAM) presents an innovative solution for intra-urban and inter-urban transportation, promising enhanced flexibility, efficiency, and sustainability. However, the integration of UAM into densely populated city environments brings significant challenges, particularly in the precision landing of multi-rotor vehicles amid complex and dynamic urban landscapes. To address this challenge, our paper introduces a novel convex optimization approach to solve the high-fidelity landing problem of electric vertical take-off and landing (eVTOL) vehicles. In our method, we first conceptualize the eVTOL vehicle landing trajectory optimization as a high-dimensional, highly nonconvex optimal control problem. We then implement a series of convenient convexification techniques to transform this problem into a convex form. The core of our approach lies in the application of sequential convex programming (SCP), an advanced method known for its efficacy and real-time performance in handling complex optimization challenges. We conduct a comparative analysis of our SCP-based solution with results obtained from the GPOPS-II solver, a widely recognized general-purpose tool in optimal control. This comparison not only benchmarks the performance of our method but also highlights its potential advantages in solving complicated, dynamic trajectory optimization problems in the context of UAM.