This paper proposes an approach to formulation and integration of the governing equations for aircraft flight simulation that is based on a Lie group setting, and leads to a nonsingular coordinate-free numerical integration. Dynamical model of an aircraft is formulated in Lie group state space form and integrated by ordinary-differential-equation (ODE)-on-Lie groups Munthe-Kaas (MK) type of integrator. By following such an approach, it is assured that kinematic singularities, which are unavoidable if a three-angles-based rotation parameterization is applied for the whole 3D rotation domain, do not occur in the proposed noncoordinate formulation form. Moreover, in contrast to the quaternion rotation parameterization that imposes additional algebraic constraint and leads to integration of differential-algebraic equations (DAEs) (with necessary algebraic-equation-violation stabilization step), the proposed formulation leads to a nonredundant ODE integration in minimal form. To this end, this approach combines benefits of both traditional approaches to aircraft simulation (i.e., three angles parameterization and quaternions), while at the same time it avoids related drawbacks of the classical models. Besides solving kinematic singularity problem without introducing DAEs, the proposed formulation also exhibits numerical advantages in terms of better accuracy when longer integration steps are applied during simulation and when aircraft motion pattern comprises steady rotational component of its 3D motion. This is due to the fact that a Lie group setting and applied MK integrator determine vehicle orientation on the basis of integration of local (tangent, nonlinear) kinematical differential equations (KDEs) that model process of 3D rotations (i.e., vehicle attitude reconstruction on nonlinear manifold SO(3)) more accurately than “global” KDEs of the classical formulations (that are linear in differential equations part in the case of standard quaternion models).
Skip Nav Destination
Article navigation
March 2017
Research-Article
Lie Group Forward Dynamics of Fixed-Wing Aircraft With Singularity-Free Attitude Reconstruction on SO(3)
Zdravko Terze,
Zdravko Terze
Department of Aeronautical Engineering,
Faculty of Mechanical Engineering
and Naval Architecture,
University of Zagreb,
Ivana Lučića 5,
Zagreb 10002, Croatia
e-mail: zdravko.terze@fsb.hr
Faculty of Mechanical Engineering
and Naval Architecture,
University of Zagreb,
Ivana Lučića 5,
Zagreb 10002, Croatia
e-mail: zdravko.terze@fsb.hr
Search for other works by this author on:
Dario Zlatar,
Dario Zlatar
Department of Aeronautical Engineering,
Faculty of Mechanical Engineering
and Naval Architecture,
University of Zagreb,
Ivana Lučića 5,
Zagreb 10002, Croatia
e-mail: dario.zlatar@fsb.hr
Faculty of Mechanical Engineering
and Naval Architecture,
University of Zagreb,
Ivana Lučića 5,
Zagreb 10002, Croatia
e-mail: dario.zlatar@fsb.hr
Search for other works by this author on:
Milan Vrdoljak,
Milan Vrdoljak
Department of Aeronautical Engineering,
Faculty of Mechanical Engineering
and Naval Architecture,
University of Zagreb,
Ivana Lučića 5,
Zagreb 10002, Croatia
e-mail: milan.vrdoljak@fsb.hr
Faculty of Mechanical Engineering
and Naval Architecture,
University of Zagreb,
Ivana Lučića 5,
Zagreb 10002, Croatia
e-mail: milan.vrdoljak@fsb.hr
Search for other works by this author on:
Viktor Pandža
Viktor Pandža
Department of Aeronautical Engineering,
Faculty of Mechanical Engineering
and Naval Architecture,
University of Zagreb,
Ivana Lučića 5,
Zagreb 10002, Croatia
e-mail: viktor.pandza@fsb.hr
Faculty of Mechanical Engineering
and Naval Architecture,
University of Zagreb,
Ivana Lučića 5,
Zagreb 10002, Croatia
e-mail: viktor.pandza@fsb.hr
Search for other works by this author on:
Zdravko Terze
Department of Aeronautical Engineering,
Faculty of Mechanical Engineering
and Naval Architecture,
University of Zagreb,
Ivana Lučića 5,
Zagreb 10002, Croatia
e-mail: zdravko.terze@fsb.hr
Faculty of Mechanical Engineering
and Naval Architecture,
University of Zagreb,
Ivana Lučića 5,
Zagreb 10002, Croatia
e-mail: zdravko.terze@fsb.hr
Dario Zlatar
Department of Aeronautical Engineering,
Faculty of Mechanical Engineering
and Naval Architecture,
University of Zagreb,
Ivana Lučića 5,
Zagreb 10002, Croatia
e-mail: dario.zlatar@fsb.hr
Faculty of Mechanical Engineering
and Naval Architecture,
University of Zagreb,
Ivana Lučića 5,
Zagreb 10002, Croatia
e-mail: dario.zlatar@fsb.hr
Milan Vrdoljak
Department of Aeronautical Engineering,
Faculty of Mechanical Engineering
and Naval Architecture,
University of Zagreb,
Ivana Lučića 5,
Zagreb 10002, Croatia
e-mail: milan.vrdoljak@fsb.hr
Faculty of Mechanical Engineering
and Naval Architecture,
University of Zagreb,
Ivana Lučića 5,
Zagreb 10002, Croatia
e-mail: milan.vrdoljak@fsb.hr
Viktor Pandža
Department of Aeronautical Engineering,
Faculty of Mechanical Engineering
and Naval Architecture,
University of Zagreb,
Ivana Lučića 5,
Zagreb 10002, Croatia
e-mail: viktor.pandza@fsb.hr
Faculty of Mechanical Engineering
and Naval Architecture,
University of Zagreb,
Ivana Lučića 5,
Zagreb 10002, Croatia
e-mail: viktor.pandza@fsb.hr
1Corresponding author.
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received February 26, 2016; final manuscript received July 20, 2016; published online December 2, 2016. Assoc. Editor: Andreas Mueller.
J. Comput. Nonlinear Dynam. Mar 2017, 12(2): 021009 (11 pages)
Published Online: December 2, 2016
Article history
Received:
February 26, 2016
Revised:
July 20, 2016
Citation
Terze, Z., Zlatar, D., Vrdoljak, M., and Pandža, V. (December 2, 2016). "Lie Group Forward Dynamics of Fixed-Wing Aircraft With Singularity-Free Attitude Reconstruction on SO(3)." ASME. J. Comput. Nonlinear Dynam. March 2017; 12(2): 021009. https://doi.org/10.1115/1.4034398
Download citation file:
Get Email Alerts
Cited By
A robust numerical approach for the fractional Polio model by the Genocchi wavelet collocation method
J. Comput. Nonlinear Dynam
Generation of a Multi-wing Hyperchaotic System with a Line Equilibrium and its Control
J. Comput. Nonlinear Dynam
Bifurcation analysis and control of traffic flow model considering the impact of smart devices for drivers
J. Comput. Nonlinear Dynam
Related Articles
Coordinate Mappings for Rigid Body Motions
J. Comput. Nonlinear Dynam (March,2017)
Inverse Dynamics for Discrete Geometric Mechanics of Multibody Systems With Application to Direct Optimal Control
J. Comput. Nonlinear Dynam (October,2018)
Singularity-Free Lie Group Integration and Geometrically Consistent Evaluation of Multibody System Models Described in Terms of Standard Absolute Coordinates
J. Comput. Nonlinear Dynam (May,2022)
Pose Changes From a Different Point of View
J. Mechanisms Robotics (April,2018)
Related Proceedings Papers
Related Chapters
The Influence of Rate of Loading on the Strength of Wood and Wood-Base Materials
Symposium on Speed of Testing of Non-Metallic Materials
The Effect of Heat Treatment on Phosphorus Segregation in a Submerged-Arc Weld Metal
Effects of Radiation on Materials: 18th International Symposium
The Influence of Floodplains on Mercury Availability
Environmental Toxicology and Risk Assessment: Modeling and Risk Assessment Sixth Volume