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Kinematically Exact Inverse-Simulation Techniques with Applications to Rotorcraft Aggressive-Maneuver Analyses

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Abstract

An inverse-simulation problem is reformulated to exactly satisfy the kinematic constraints imposed by the prescribed trajectory. Thereby, the problem can be transformed into an index 1 differential–algebraic equation that is much more easily solvable than the higher index system of the conventional formulation. Various numerical methods which have been successfully used in the pseudo-spectral inverse-simulation techniques are adopted with some modifications to efficiently solve the resultant system. The paper proposes a formal algorithm to describe the detailed solution process. The algorithm is applied to the analyses of the vertical, slalom, and helical-turn maneuvers of Bo-105. The simulation results with both the conventional and present formulations are compared to show the numerical features of the present methods. Effects of the solution-control parameters, the aggressiveness level of a maneuver, the quality of the prescribed trajectory, and the fidelity level of the math model are thoroughly investigated. The results of applications show that the proposed algorithm is extremely robust in that solution convergence is less sensitive to the maneuver aggressiveness, the quality of the generated trajectory, and the solution-control parameters. Therefore, it can be concluded that the kinematically exact inverse-simulation techniques deserve to be a one of the promising inverse-simulation methods like the pseudo-spectral inverse-simulation techniques.

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Abbreviations

DAE:

Differential-algebraic equation

KEIST:

Kinematically exact inverse-simulation technique

MTE:

Mission task element

NAE:

Nonlinear algebraic equation

PIST:

Pseudo-spectral inverse-simulation technique

\( {\mathbf{B}} \) :

Approximated Jacobian

\( {\mathbf{C}} \) :

Linear velocity transformation matrix

\( {\mathbf{f}} \) :

Net external force vector, function vector

\( {\mathbf{g}} \) :

Function vector in nonlinear algebraic equation

\( I_{j,k} \) :

Component of integration matrix

\( {\mathbf{J}} \) :

Moment of inertia matrix, Jacobian

\( K \) :

Number of waypoints along a trajectory

\( m \) :

Aircraft mass

\( {\mathbf{m}} \) :

Net external moment vector

\( N \) :

Number of quadrature points

\( N_{\text{h}} \) :

Number of time horizons

\( {\mathbf{p}} \) :

Prescribed trajectory parameter vector

\( {\mathbf{r}} \) :

Position vector, \( \left( {x,y,z} \right)^{T} \)

\( {\mathbf{r}}^{p} ,\psi^{p} \) :

Position and heading of prescribed trajectory

\( {\mathbf{x}} \) :

System state vector

\( {\mathbf{y}} \) :

Unknown states and controls

\( {\mathbf{T}} \) :

Angular rate transformation matrix

\( {\mathbf{u}} \) :

Control input vector

\( {\mathbf{v}} \) :

Linear velocity vector, \( \left( {u,v,w} \right)^{T} \)

\( \alpha \) :

Under-relaxation factor for NAE solver

\( \varepsilon \) :

Numerical tolerance

\( {\varvec{\upomega}} \) :

Angular velocity vector, \( \left( {p,q,r} \right)^{T} \)

\( {\boldsymbol{\varphi}} \) :

Angular position vector \( \left( {\phi ,\theta ,\psi } \right)^{T} \)

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Acknowledgements

This paper was supported by Konkuk University in 2017.

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Authors and Affiliations

  1. Department of Aerospace Information Systems Engineering, Konkuk University, Seoul, 05029, Republic of Korea

    Chang-Joo Kim,  Seong Han Lee &  Sung Wook Hur

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  1. Chang-Joo Kim
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Kim, CJ., Lee, S.H. & Hur, S.W. Kinematically Exact Inverse-Simulation Techniques with Applications to Rotorcraft Aggressive-Maneuver Analyses. Int. J. Aeronaut. Space Sci. 21, 790–805 (2020). https://doi.org/10.1007/s42405-020-00249-8

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