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Smooth Reference Command Generation and Control for Transition Flight of VTOL Aircraft Using Time-Varying Optimization

Jinrae Kim, John L. Bullock, Sheng Cheng, Naira Hovakimyan

TL;DR

This work tackles the challenge of generating smooth reference commands for VTOL Lift+Cruise transitions, where offline $\ell_{1}$-minimization can yield abrupt changes. It introduces CL-TVOpt, a closed-loop time-varying optimization method based on a prediction-correction interior-point framework that updates the reference via an ordinary differential equation (ODE), enabling online smoothing. Numerical results on a 2D Lift+Cruise model show that CL-TVOpt achieves smooth pitch and elevator commands while preserving thrust sparsity, outperforming the prior OL-Opt approach. The approach promises real-time applicability with avenues for extension to 3D dynamics and uncertainty handling.

Abstract

Vertical take-off and landing (VTOL) aircraft pose a challenge in generating reference commands during transition flight. While sparsity between hover and cruise flight modes can be promoted for effective transitions by formulating $\ell_{1}$-norm minimization problems, solving these problems offline pointwise in time can lead to non-smooth reference commands, resulting in abrupt transitions. This study addresses this limitation by proposing a time-varying optimization method that explicitly considers time dependence. By leveraging a prediction-correction interior-point time-varying optimization framework, the proposed method solves an ordinary differential equation to update reference commands continuously over time, enabling smooth reference command generation in real time. Numerical simulations with a two-dimensional Lift+Cruise vehicle validate the effectiveness of the proposed method, demonstrating its ability to generate smooth reference commands online.

Smooth Reference Command Generation and Control for Transition Flight of VTOL Aircraft Using Time-Varying Optimization

TL;DR

This work tackles the challenge of generating smooth reference commands for VTOL Lift+Cruise transitions, where offline -minimization can yield abrupt changes. It introduces CL-TVOpt, a closed-loop time-varying optimization method based on a prediction-correction interior-point framework that updates the reference via an ordinary differential equation (ODE), enabling online smoothing. Numerical results on a 2D Lift+Cruise model show that CL-TVOpt achieves smooth pitch and elevator commands while preserving thrust sparsity, outperforming the prior OL-Opt approach. The approach promises real-time applicability with avenues for extension to 3D dynamics and uncertainty handling.

Abstract

Vertical take-off and landing (VTOL) aircraft pose a challenge in generating reference commands during transition flight. While sparsity between hover and cruise flight modes can be promoted for effective transitions by formulating -norm minimization problems, solving these problems offline pointwise in time can lead to non-smooth reference commands, resulting in abrupt transitions. This study addresses this limitation by proposing a time-varying optimization method that explicitly considers time dependence. By leveraging a prediction-correction interior-point time-varying optimization framework, the proposed method solves an ordinary differential equation to update reference commands continuously over time, enabling smooth reference command generation in real time. Numerical simulations with a two-dimensional Lift+Cruise vehicle validate the effectiveness of the proposed method, demonstrating its ability to generate smooth reference commands online.
Paper Structure (12 sections, 15 equations, 7 figures, 1 table)

This paper contains 12 sections, 15 equations, 7 figures, 1 table.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Equations of Motion for 2D Lift+Cruise vehicle
  4. Time-varying optimization
  5. Optimization-based open-loop reference command generation with sparsity
  6. Closed-Loop Time-Varying Optimization for Smooth Reference Command Generation
  7. Algorithm
  8. Numerical Simulation
  9. Scenario 1: Hover-to-Cruise
  10. Scenario 2: Cruise-to-Hover
  11. Conclusion
  12. Simulation details

Figures (7)

  • Figure 1: Illustration of (a) Lift+Cruise (L+C) vehicle and (b) 2D model
  • Figure 2: Conceptual differences between OL-Opt (left) and the proposed CL-TVOpt (right).
  • Figure 3: Block diagrams of each method in simulation
  • Figure 4: Scenario 1 (Hover-to-Cruise): The result of OL-Opt.
  • Figure 5: Scenario 1 (Hover-to-Cruise): The result of CL-TVOpt (proposed).
  • ...and 2 more figures

Theorems & Definitions (1)

  • Remark 1: Online reference command generation