Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-25T07:20:29.974Z Has data issue: false hasContentIssue false
  • English
  • Français

Trajectory optimisation of an aerobatic air race

Published online by Cambridge University Press:  03 February 2016

H. van der Plas  and
H. G. Visser
H. van der Plas
Affiliation:
Delft University of Technology, Delft, The Netherlands
H. G. Visser
Affiliation:
Delft University of Technology, Delft, The Netherlands
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper deals with the synthesis of optimal trajectories for aerobatic air races. A typical example of an air race event is the Red Bull Air Race World Series, where high-performance aerobatic aircraft fly a prescribed slalom course consisting of specially designed inflatable pylons, known as ‘air gates’, in the fastest possible time. The trajectory that we seek to optimise is based on such a course. The air race problem is formulated as a minimum-time optimal control problem and solved in open-loop form using a direct numerical multi-phase trajectory optimisation approach based on collocation and non-linear programming. The multiphase feature of the employed collocation algorithm is used to enable a Receding-Horizon optimisation approach, in which only a limited number of manoeuvres in sequence is considered. It is shown that the Receding-Horizon control approach provides a near-optimal solution at a significantly reduced computational cost relative to trajectory optimisation over the entire course. To avoid the path inclination singularity in the equations of motion based on Euler angles, a point-mass model formulation is used that is based on quaternions. Numerical results are presented for an Extra 300S, a purpose-designed aerobatic aircraft.

Type
Research Article
Information
The Aeronautical Journal , Volume 113 , Issue 1139 , January 2009 , pp. 1 - 8
Copyright
Copyright © Royal Aeronautical Society 2009 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Wuensche, H., Singularity-free Methods for Aircraft Flight Path Optimization Using Euler Angles and Quaternions, Master’s thesis, Aerospace Engineering Department, University of Texas, Austin, Texas, USA, 1982.Google Scholar
2. Well, K.H. and Wever, U.A., Aircraft trajectory optimization using quaternions — comparison of a nonlinear programming and a multiple shooting approach, Proceedings IFAC 9th Triennial World Congress, Budapest, Hungary, 1984, pp 1595–1602.Google Scholar
3. Stevens, B.L. and Lewis, F.L., Aircraft Control and Simulation, John Wiley & Sons, Toronto, Canada, 1992.Google Scholar
4. Ruijgrok, G., Elements of Airplane Performance, Delft University Press, Delft, The Netherlands, 1996.Google Scholar
5. Brinkman, K. and Visser, H.G., Optimal turn-back maneuver after engine failure in a single-engine aircraft during climb-out, Proceedings of the Institution of Mechanical Engineers — Part G, J Aero Eng, 2007, 221, (1), pp 17–27.Google Scholar
6. Visser, H.G. and Wijnen, R.A.A., Optimization of noise abatement departure trajectories, J Aircr, July-August 2001, 38, (4), pp 620–627.Google Scholar
7. Seywald, H. and Kumar, R., EZopt: An Optimal Control Toolkit, Analytical Mechanics Associates, Hampton, VA, USA, 1997.Google Scholar
8. Seywald, H., Trajectory optimization based on differential inclusion, J Guidance, Control and Dynamics, May — June 1994, 17, (3), pp 480–487.Google Scholar
9. Mayne, D.Q. and Michalska, H., Receding horizon control of nonlinear systems, IEEE Transactions on Automatic Control, July 1990, 35, (7), pp 814–824.Google Scholar
10. Crassidis, J.L., Markley, F.L., Anthony, T.C. and Andrews, S.F., Nonlinear predictive control of spacecraft, J Guidance, Control and Dynamics, November — December 1997, 20, (6), pp 1096–1103.Google Scholar