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String stable platoons of all-electric aircraft with operating costs and airspace complexity trade-off

Lucas Souza e Silva, Luis Rodrigues

Abstract

This paper formulates an optimal control framework for computing cruise airspeeds in predecessor-follower platoons of all-electric aircraft that balance operational cost and airspace complexity. To quantify controller workload and coordination effort, a novel pairwise dynamic workload (PDW) function is developed. Within this framework, the optimal airspeed solution is derived for all-electric aircraft under longitudinal wind disturbances. Moreover, an analytical suboptimal solution for heterogeneous platoons with nonlinear aircraft dynamics is determined, for which a general sufficient condition for string stability is formally established. The methodology is validated through case studies of all-electric aircraft operating in air corridors that are suitable for low-altitude advanced/urban air mobility (AAM/UAM) applications. Results show that the suboptimal solution closely approximates the optimal, while ensuring safe separations, maintaining string stability, and reducing operational cost and airspace complexity. These findings support the development of sustainable and more autonomous air traffic procedures that will enable the implementation of emerging air transportation technologies, such as AAM/UAM, and their integration to the air traffic system environment.

String stable platoons of all-electric aircraft with operating costs and airspace complexity trade-off

Abstract

This paper formulates an optimal control framework for computing cruise airspeeds in predecessor-follower platoons of all-electric aircraft that balance operational cost and airspace complexity. To quantify controller workload and coordination effort, a novel pairwise dynamic workload (PDW) function is developed. Within this framework, the optimal airspeed solution is derived for all-electric aircraft under longitudinal wind disturbances. Moreover, an analytical suboptimal solution for heterogeneous platoons with nonlinear aircraft dynamics is determined, for which a general sufficient condition for string stability is formally established. The methodology is validated through case studies of all-electric aircraft operating in air corridors that are suitable for low-altitude advanced/urban air mobility (AAM/UAM) applications. Results show that the suboptimal solution closely approximates the optimal, while ensuring safe separations, maintaining string stability, and reducing operational cost and airspace complexity. These findings support the development of sustainable and more autonomous air traffic procedures that will enable the implementation of emerging air transportation technologies, such as AAM/UAM, and their integration to the air traffic system environment.
Paper Structure (20 sections, 3 theorems, 45 equations, 8 figures, 8 tables, 1 algorithm)

This paper contains 20 sections, 3 theorems, 45 equations, 8 figures, 8 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Background and Related Work
  3. Predecessor-follower operations and formation flights
  4. String stability in aircraft operations
  5. Airspace complexity metrics
  6. Problem statement and formulation
  7. Assumptions and aircraft dynamic model
  8. Pairwise dynamic workload (PDW)
  9. Problem formulation
  10. Problem solution
  11. OCP solution
  12. String stability of pairwise aircraft operations
  13. Results and validation
  14. Simulation parameters
  15. Pairwise dynamic workload metric
  16. ...and 5 more sections

Key Result

Theorem 1

Let $I_t$ be an interval of positive length such that $I_t=(t_1,t_2)\subset[0,t^*_f]$, with $t_2>t_1>0$ and $t_s \in [0,t^*_f]$ denotes a time instant. We define the time-dependent multiplier $\mu(t) = \mu_{b}(t) + \mu_s \delta(t-t_s)$, with $\mu_{b}(t) \geq 0$, $\mu_s \geq 0$ and $\delta(t-t_s)$ is

Figures (8)

  • Figure 1: Longitudinal heterogeneous and unidirectional predecessor-follower aircraft platoon
  • Figure 2: Comparison of airspace complexity metrics
  • Figure 3: Shooting Method Result, all-electric aircraft
  • Figure 4: All-electric aircraft platoon in an AAM corridor
  • Figure 5: Simulated flight scenario for different cost indices
  • ...and 3 more figures

Theorems & Definitions (3)

  • Theorem 1: Optimal cruise airspeed
  • Corollary 1: Suboptimal airspeed
  • Theorem 2: String stability