A Convex Methodology for Optimal Path Following with Electric Aircraft Taxi Systems Under Performance and Passing Time Constraints

Devices such as on-board electric drive systems are being proposed by airframers and suppliers with the purpose of reducing the fuel consumption and emissions during aircraft ground operations. In order to maximize the benefits for a given system architecture and to compare different configurations, fast and effective methods are necessary to ensure optimal pathfollowing. This paper presents a methodology for path-following optimization based on convex optimization theory, which allows to find a globally optimal solution in short time thanks to appropriate solvers. It will be shown how to describe the vehicle and the system dynamics in convex form and how to set up, discretize and solve the convex optimization problem under speed and performance constraints such as thermal limitations. A noteworthy result is that for this application, the optimal solutions for time minimization and fuel consumption minimization differ only marginally concerning travel times and fuel consumption. Also, time constraints for passing predefined waypoints are considered. In particular, constraints on the minimum time that must at least have elapsed before clearing a waypoint cannot be included exactly in the convex optimization problem. An approximate constraint and an iterative parameter-finding algorithm are proposed in this paper to reproduce this constraint in the convex optimization problem