Air-taxi trajectory optimization with aerodynamic and motor models

TL;DR

This work addresses the optimization of dynamic hover-to-cruise transitions for air-taxi missions by embedding five physics-based sub-models (flight dynamics, rotor aerodynamics, wing aerodynamics, motor performance, and aeroacoustics) into a large-scale multidisciplinary design optimization framework. Using direct transcription, the authors formulate and solve an optimal control problem for NASA's Lift-plus-Cruise concept to obtain minimum-energy and minimum-time transition trajectories, with additional pitch-angle and acoustic constraints. The study reveals that constraints can substantially alter trajectory shape and energy/time metrics, and shows that acoustic limits may render certain transitions infeasible without co-design of the aircraft. The results underscore the importance of joint trajectory- and aircraft-design optimization to meet performance and noise requirements in urban air mobility applications, and demonstrate a scalable approach for evaluating sub-models within complex AAM systems, with $\eta = \frac{0.5 m \Delta v^2 + mg \Delta h}{E}$ serving as a common efficiency metric across trajectories.

Abstract

To fulfill the vision for large-scale urban air mobility, air-taxi concepts must be carefully designed and optimized for their intended mission. Proposed air-taxi missions contain dynamic segments that are dominated by nonlinear dynamics. One such segment is the transition to and from hover and cruise that occurs at the start and end of the mission. Because this transition involves low-altitude and high-power flight, analyzing transition trajectories is critical for safe and economical urban air mobility. Optimization of the transition maneuver requires an optimal control approach that characterizes the trajectories of the system states through time. In this paper we solve this optimal control problem for air-taxi transition within a large-scale design-optimization framework. This framework allows us to include five physics-based models that describe flight dynamics, rotor aerodynamics, wing aerodynamics, motor performance, and acoustics with which we create a low-fidelity model of NASA's Lift-plus-Cruise air-taxi concept. We use this optimization problem formulation to compute transition trajectories that minimize time or minimize energy. Our results show that the Lift-plus-Cruise aircraft completes a minimum-energy transition in 80s with an energy expenditure of 13.3MJ and a minimum-time transition in 28s with an energy expenditure of 16.4MJ. We find that these trajectories contain large pitch angles and high sound pressure levels which are both undesirable for practical urban air mobility. Consequently, we explore trajectories that include pitch angle and acoustic constraints, and find that minimum time trajectories are significantly more affected by these constraints than minimum energy trajectories.

Figures (19)

• Figure 1: NASA's Lift-plus-Cruise air-taxi concept silva2018vtol.
• Figure 2: Coordinate system for the 3-DOF flight dynamics model.
• Figure 3: Cruise rotor surrogate models for thrust and power coefficients as a function of axial and edgewise free-stream velocity.
• Figure 4: Aerodynamic surrogate model for lift and drag coefficients (NACA-2412).
• Figure 5: Rotor broadband noise diagram for an arbitrary observer location (left). At each time step the sound pressure level from each rotor is evaluated over $\pm \text{500m}$ (right).