A Convex Optimization Approach to Real-Time Merging Control of eVTOL Vehicles for Future Urban Air Mobility

To the best of our knowledge, this is the first paper focused on real-time, model-based optimization for merging control of air vehicles under the urban air mobility (UAM) concept of operations. The merging control of UAM vehicles flying along different airways or air corridors would become a bottleneck in the development and implementation of future UAM systems. In this preliminary work, we consider the merging control of two electric vertical take-off and landing (eVTOL) vehicles and formulate an optimal control problem that incorporates the flight dynamics of the vehicle and collision avoidance constraint. Two objective functions, i.e., minimum flight time and minimum control cost, are considered in the problem formulation. The problems are first solved using a general-purpose optimal control solver (GPOPS). Then, we introduce several new control variables to reduce the nonlinearity of the dynamic system, apply a lossless convexification technique to relax the resulting nonconvex control constraint, linearize the nonlinear terms in the dynamics, and develop a sequential convex programming method as an alternative approach to the UAM merging control problem considered in this paper. Simulation results are presented to demonstrate the performance of the developed methods.