Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-23T01:08:11.906Z Has data issue: false hasContentIssue false
  • English
  • Français

Trajectory feasibility evaluation using path prescribed control of unmanned aerial vehicle in differential algebraic equations framework*

Published online by Cambridge University Press:  31 May 2017

T. Uppal ,
S. Raha  and
S. Srivastava
T. Uppal*
Affiliation:
Aeronautical Development Establishment, Bangalore, India
S. Raha
Affiliation:
Indian Institute of Science, Bangalore, India
S. Srivastava
Affiliation:
O/o Director General Aeronautical, Bangalore, India
*
[email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Mission simulation is a critical activity in the development and operation of Unmanned Aerial Vehicles (UAVs). It is important to ascertain the feasibility of a trajectory in a mission. In this work, an algorithm has been developed for feasibility study of a trajectory of a UAV using prescribed path optimal control through an inverse simulation method. This has been done under a Differential Algebraic Equations (DAE)/Inequalities (DAI) framework. The UAV model together with constraints is represented as a high index DAE system. The trajectory that UAV shall take is prescribed as one of the constraint equations. The solution for the DAE system is obtained using a variation of the alpha method that is capable of handling both equality and inequality constraints on system dynamics. The algorithm involves direct numerical integration of a DAI formulation in a time-stepping manner using a Sequential Quadratic Programming (SQP) solver that detects and satisfy active path constraints at each time step (mesh point). In this unique approach, the model and the constraints are always solved together. The method ensures stable solution at each time step, local minimum at each iteration of simulation and provides a regularised basis to the solver. A typical UAV trajectory has been simulated and demonstrated in this paper. This new approach can be used for path planning of UAVs before the actual control law is designed for flight control computer. Compared to other existing computationally intensive techniques, this approach is computationally simple, ensures continuous constraint satisfaction and provides a viable option for model predictive control of UAVs.

Keywords

Path planningregularisationDAEsinverse simulation
Type
Research Article
Information
The Aeronautical Journal , Volume 121 , Issue 1240 , June 2017 , pp. 770 - 789
Copyright
Copyright © Royal Aeronautical Society 2017 

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.)

Footnotes

*

Corresponding author Tarun Uppal. Tel. +91-80-25605681. Fax +91-80-25283188.

References

REFERENCES

1. Murray-Smith, D.J. Feedback methods for inverse simulation of dynamic models for engineering systems applications, Mathematical and Computer Modelling of Dynamical Systems, 2011, 17, (5), pp 515-541.Google Scholar
2. Goszczyński, J.A., Blajer, W. and Krawczyk, M. The inverse simulation study of aircraft flight path reconstruction, Transport, 2002, XVII, (3), pp 103-107.Google Scholar
3. Azam, M. and Singh, S.N. Invertibility and trajectory control for nonlinear maneuvers of aircraft, J. Guidance, Control, and Dynamics, 1994, 17, pp 192-200.Google Scholar
4. Kato, O. and Sugiura, I. An interpretation of aircraft general motion and control as inverse problem, J. Guidance, 1986, 9, pp 198-204.Google Scholar
5. Lane, S.H. and Stengel, R.F. Flight control design using non linear inverse dynamics, Automatica, 1988, 24, pp 471-483.Google Scholar
6. Snell, S.A. and Stout, P.W. Flight control law using nonlinear dynamic inversion combined with quantitative feedback theory, J. Dynamic Systems, Measurement, and Control, 1998, 120, pp 208-215.Google Scholar
7. Feron, E., Popovic, J., Dever, C., Mettler, B. and McConley, M. Nonlinear trajectory generation for autonomous vehicles via parameterized maneuver classes, J. Guidance, Control, and Dynamics, 2006, 29, (2), pp 289-302.Google Scholar
8. Campbell, S.L., Brenan, K.E. and Petzold, L.R. Numerical solution of initial-value problems in differential-algebraic equations, Classics Applied Mathematics, volume 4, 2nd revised ed, 1996, SIAM, Philadelphia, Pennsylvania, US.Google Scholar
9. Hairer, E. and Wanner, G. Solving ordinary differential equations 2. stiff and differential-algebraic problems, Springer Series in Computational Mathematics, volume 14, 2nd revised ed, 2004, Springer-Verlag, Berlin, Germany.Google Scholar
10. Ascher, U.M., Spiteri, R.J. and Pai, D.K. Programming and control of robots by means of dai, IEEE Transcations on Robotics and Automation, 2000, 16, (2), pp 135-145.Google Scholar
11. Barrlund, A, Numerical Solution of Higher Index Differential-Algebraic Systems, PhD Thesis, 1991, Department of Scientific Computing, Umea University, Umea, Sweden.Google Scholar
12. Campbell, S.L. High-index differential algebraic equations, J. Mechanics of Structures and Machines, 1995, 23, pp 199-222.Google Scholar
13. Campbell, S.L., Engelsone, A. and Betts, J.T. Direct transcription solution of higher-index optimal control problems and the virtual index, Applied Numerical Mathematics, 2007, 57, pp 281-296.Google Scholar
14. Pryce, J.D. and Nedialkov, N.S. Solving daes by taylor series: Daets code, J. Numerical Analysis, Industrial and Applied Maths, 2008, 3, pp 61-80.Google Scholar
15. Chung, J. and Hulbert, G.M. Time integration algorithm for structural dynamics with improved numerical dissipation: The generalized-alpha method, Transactions of ASME J. Applied Mechanics, 1993, 60, (2), pp 371-375.Google Scholar
16. Petzold, L., Yen, J. and Raha, S. A time integration algorithm for flexible mechanism dynamics: The dae-alpha method, Computer Methods in Applied Mechanics and Engineering, 1998, 158, pp 341-355.Google Scholar
17. Chandra Parida, N., Peter, J. and Raha, S. The alpha-method for solving differential algebraic inequality dai systems, International Journal of Numerical Analysis and Modeling, 2010, 7, (2), pp 240-260.Google Scholar
18. Parida, N.C. and Raha, S. The alpha-method direct transcription in path constrained dynamic optimization, SIAM J. Scientific Computing, 2009, 31, (3), pp 2386-2417.Google Scholar
19. Blajer, W. and Kolodziejczyk, K. A geometric approach to solving problems of control constraints: Theory and a dae framework, Multbody System Dynamics, 2004, 11, pp 343-364.CrossRefGoogle Scholar
20. Raha, S. and Petzold, L.R. Constraint partitioning for stability in path-constrained dynamic optimization problems, SIAM J. Scientific Computing, 2001, 22, pp 2051-2074.Google Scholar
21. Raha, S. and Petzold, L.R. Constraint partitioning for structure in path-constrained dynamic optimization problems, Applied Numerical Mathematics, 2001, 39, pp 105-126.CrossRefGoogle Scholar
22. Kolodziejczyk, K. and Blajer, W. A geometrical approach to solving problems of control constraints theory and a dae framework, Multibody System Dynamics, 2004, 11, (4), pp 343-364.Google Scholar
23. Murray, W., Gill, P.E. and Saunders, M.A. Snopt: An sqp algorithm for large-scale constrained optimization, SIAM J. on Optimization, 2002, 12, pp 979-1006.Google Scholar
24. Allgöwer, F., Findeisen, R., Imsland, L. and Foss, B. State and output feedback nonlinear model predictive control: An overview, European J. Control, 2003, 9, (2–3), 190-206.Google Scholar