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<p>To address the efficiency and precision challenges in trajectory optimization for tilt-rotor electric vertical take-off and landing aircraft during the transition phase, this paper proposes a dimension reduction method based on constraint transformation. A 2D longitudinal nonlinear dynamic model is first established to formulate a multi-constrained optimal control problem with a minimum energy objective, incorporating constant-altitude, control boundary, flight envelope, and control rate constraints. To overcome high dimension and the inherent difficulty of handling state constraints within an indirect solution framework, an equivalent transformation strategy is developed to convert state equality constraints into control equality constraints. Specifically, a saturation control strategy is introduced to unify diverse control constraints, significantly enhancing the convergence and applicability of the indirect method. The necessary conditions for optimality are derived based on Pontryagin’s Maximum Principle, leading to a two-point boundary value problem solved via the single shooting method. Numerical simulations on a representative tilt-rotor eVTOL demonstrate that the proposed approach effectively generates high-precision optimal trajectories while strictly satisfying multiple constraints. The results validate the feasibility and superior performance of indirect methods in such complex trajectory optimization tasks.</p>

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An efficient transition trajectory optimization method for tilt-rotor eVTOL under multiple constraints

  • 期刊论文

  • 发表日期：

    2026年7月16日

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  • Songbai Xue,
  • Yunting Ran,
  • Yangyang Ma

摘要

To address the efficiency and precision challenges in trajectory optimization for tilt-rotor electric vertical take-off and landing aircraft during the transition phase, this paper proposes a dimension reduction method based on constraint transformation. A 2D longitudinal nonlinear dynamic model is first established to formulate a multi-constrained optimal control problem with a minimum energy objective, incorporating constant-altitude, control boundary, flight envelope, and control rate constraints. To overcome high dimension and the inherent difficulty of handling state constraints within an indirect solution framework, an equivalent transformation strategy is developed to convert state equality constraints into control equality constraints. Specifically, a saturation control strategy is introduced to unify diverse control constraints, significantly enhancing the convergence and applicability of the indirect method. The necessary conditions for optimality are derived based on Pontryagin’s Maximum Principle, leading to a two-point boundary value problem solved via the single shooting method. Numerical simulations on a representative tilt-rotor eVTOL demonstrate that the proposed approach effectively generates high-precision optimal trajectories while strictly satisfying multiple constraints. The results validate the feasibility and superior performance of indirect methods in such complex trajectory optimization tasks.