Centralized Path Planning for Multi-aircraft in the Presence of Static and Moving Obstacles

Document Type : Original Article

Authors

1 Faculty of New Science and Technology, University of Tehran, Tehran, Iran

2 Faculty of Iranian Space Research Center, Tehran, Iran

Abstract

This article proposes a new approach for centralized path planning of multiple aircraft in presence of the obstacle-laden environment under low flying rules. The problem considers as a unified nonlinear constraint optimization problem. The minimum time and control investigate as the cost functions and the maximum velocity and power consider as the constraints. The pseudospectral method applies as a popular and fast direct method to solve the constrained path planning problem. The three-degree-of-freedom nonlinear point mass equations of motion with realistic operational aircraft constraints consider through the simplified mathematical model. The fixed obstacle considers as a combination of spheres with different radius. Also, the moving obstacles consider as a sphere with a known radius and fly at a constant speed. The effectiveness of the proposed concept will be demonstrated by presenting four case studies with a different number of aircraft along with the static and moving obstacles in various scenarios to ensure safe and effective flights.

Keywords


 
1. E. A. Munsif Vengattil, 9 May 2018. [Online]. Available:
https://www.reuters.com/article/us-uber-elevate/uber-opens-upinternational-contest-for-a-third-flying-taxi-city-idUSKBN1IA2TQ
2. M. Huber, Barrons, 10 May 2018. [Online]. Available:
https://www.barrons.com/articles/uber-targets-los-angeles-as-nextair-taxi-market-1525965120
3. Federal Aviation Administration, 30 April 2020. [Online].
Available: https://www.ecfr.gov/cgi-bin/text-idx?c=ecfr&sid=4d8
7705808eddb6d1f536f86f59ff284&tpl=/ecfrbrowse/Title14/14cfr1
19_main_02.tpl 
4. European Aviation Safety Agency,4 July 2018. [Online]. Available:
https://www.easa.europa.eu/regulations 
5. Part 135-Operating Requirements: Commuter and On-Demand
Operations and Rules Governing Persons On Board Such Aircraft,
Code of Federal Regulations, 2013. Available: https://
www.gleim.com/aviation/faraim/index.php?componentNum=135 
6. Civil Aviation (Rules of the Air) Regulations, (LN. 2014/256),
2014. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.
730.5430&rep=rep1&type=pdf 
7. Aeronautical Information Manual, U.S. Department of
Transportation, Federal Aviation Regulations, 2018.
https://www.sportys.com/media/pdf/eoc913.pdf 
8. Kosari, A. and Teshnizi, M. M., “Optimal Trajectory Design for
Conflict Resolution and Collision Avoidance of Flying Robots using
Radau-Pseudo Spectral Approach”, In 2018 6th RSI International
Conference on Robotics and Mechatronics (IcRoM), IEEE, (2018),
82–87.  
9. Fu, Y., Zhang, Y. and Yu, X., “An advanced sense and collision
avoidance strategy for unmanned aerial vehicles in landing phase”,
IEEE Aerospace and Electronic Systems Magazine, Vol. 31, No.
9, (2016), 40–52.  
10. Ghassemi, H., Sabetghadam, F. and Soltani, E., “A fast immersed
boundary fourier pseudo-spectral method for simulation of the
incompressible flows”, International Journal of Engineering -
Transaction C: Aspects, Vol. 27, No. 9, (2014), 1457–1466.  
11. Gong, Q., Kang, W. and Ross, I. M., “A pseudospectral method for
the optimal control of constrained feedback linearizable systems”,
IEEE Transactions on Automatic Control, Vol. 51, No. 7, (2006),
1115–1129.  
12. Hesthaven, J.S., Gottlieb, S. and Gottlieb, D., Spectral methods for
time-dependent problems, (Vol. 21), Cambridge University Press, 
(2007).
13. Kanjanawanishkul, K., “Path following and velocity optimizing for 
an omnidirectional mobile robot”, International Journal of
Engineering - Transaction A: Basics, Vol. 28, No. 4, (2015), 537–
545.  
14. Holden, J. and Goel, N., Fast-forwarding to a future of on-demand
urban air transportation, San Francisco, CA., (2016). 
15. Ma, Y.F. and Wu, X. Y., “Evaluation of air traffic management
system using a hybrid model”, In 2016 IEEE International
Conference on Industrial Engineering and Engineering Management
(IEEM), IEEE, (2016), 1294–1298.  
16. Krozel, J., Peters, M., Bilimoria, K.D., Lee, C. and Mitchell, J. S.,
“System performance characteristics of centralized and
decentralized air traffic separation strategies”, Air Traffic Control
Quarterly, Vol. 9, No. 4, (2001), 311–332.  
17. Jha, P., Suchkov, A., Crook, I., Tibitche, Z., Lizzi, J. and Subbu, R.,
“NextGen collaborative air traffic management solutions”, In AIAA
Guidance, Navigation and Control Conference and Exhibit, (2008),
1–12.  
18. Bicchi, A. and Pallottino, L., “On optimal cooperative conflict
resolution for air traffic management systems”, IEEE Transactions
on Intelligent Transportation Systems, Vol. 1, No. 4, (2000), 221–
231.  
19. Liu, W. and Hwang, I., “Probabilistic aircraft midair conflict
resolution using stochastic optimal control”, IEEE Transactions on
Intelligent Transportation Systems, Vol. 15, No. 1, (2013), 37–46.  
20. Zhu, L., Cheng, X. and Yuan, F. G., “A 3D collision avoidance
strategy for UAV with physical constraints”, Measurement, Vol.
77, (2016), 40–49.  
21. Holt, J., Biaz, S. and Aji, C. A., “Comparison of unmanned aerial
system collision avoidance algorithms in a simulated environment”,
Journal of Guidance, Control, and Dynamics, Vol. 36, No. 3,
(2013), 881–883.  
22. Omer, J., “A space-discretized mixed-integer linear model for airconflict
resolution
with
speed
and
heading
maneuvers”,
Computers
&
Operations
Research,
Vol.
58,
(2015),
75–86.

23. Alonso-Ayuso, A., Escudero, L.F. and Martín-Campo, F. J., “On
modeling the air traffic control coordination in the collision
avoidance problem by mixed integer linear optimization”, Annals
of Operations Research, Vol. 222, No. 1, (2014), 89–105.  
24. Cafieri, S. and Rey, D., “Maximizing the number of conflict-free
aircraft using mixed-integer nonlinear programming”, Computers &
Operations Research, Vol. 80, (2017), 147–158.  
25. Patel, R.B. and Goulart, P. J., “Trajectory generation for aircraft
avoidance maneuvers using online optimization”, Journal of
Guidance, Control, and Dynamics, Vol. 34, No. 1, (2011), 218–
230.  
26. Raghunathan, A.U., Gopal, V., Subramanian, D., Biegler, L.T. and
 
Samad, T., “Dynamic optimization strategies for three-dimensional
conflict resolution of multiple aircraft”, Journal of Guidance,
Control, and Dynamics, Vol. 27, No. 4, (2004), 586–594.  
27. Guo, T., Li, J., Baoyin, H. and Jiang, F., “Pseudospectral methods
for trajectory optimization with interior point constraints:
Verification and applications”, IEEE Transactions on Aerospace
and Electronic Systems, Vol. 49, No. 3, (2013), 2005–2017.  
28. Ross, I.M. and Karpenko, M., “A review of pseudospectral optimal
control: From theory to flight”, Annual Reviews in Control, Vol.
36, No. 2, (2012), 182–197.  
29. Dutykh, D., A brief introduction to pseudo-spectral methods:
application to diffusion problems, HAL Id: cel-01256472,
https://cel.archives-ouvertes.fr/cel-01256472v2, (2016). 
30. Garg, D., Patterson, M., Hager, W., Rao, A., Benson, D. and
Huntington, G., An overview of three pseudospectral methods for
the numerical solution of optimal control problems, HAL Id: hal01615132,
https://hal.archives-ouvertes.fr/hal-01615132,
(2017).
31. Mortazavi, H., Salahshoor, A. and Hamidi, H., “Designing and
modeling a control system for aircraft in the presence of wind
disturbance”, International Journal of Engineering - Transaction
C: Aspects, Vol. 30, No. 12, (2017), 1856–1862.  
32. Menon, P. K. A., “Short-range nonlinear feedback strategies for
aircraft pursuit-evasion”, Journal of Guidance, Control, and
Dynamics, Vol. 12, No. 1, (1989), 27–32.  
33. Wang, J. and Xin, M., “Integrated optimal formation control of
multiple unmanned aerial vehicles”, IEEE Transactions on Control
Systems Technology, Vol. 21, No. 5, (2012), 1731–1744.  
34. Redding, J., Amin, J., Boskovic, J., Kang, Y., Hedrick, K., Howlett,
J. and Poll, S., “A real-time obstacle detection and reactive path
planning system for autonomous small-scale helicopters”, In AIAA
Guidance, Navigation and Control Conferenc and Exhibit, (2007),
1–22.  
35. Yang, X., Alvarez, L.M. and Bruggemann, T., “A 3D collision
avoidance strategy for UAVs in a non-cooperative environment”,
Journal of Intelligent & Robotic Systems, Vol. 70, No. 1–4, (2013),
315–327.  
36. Pham, H., Smolka, S.A., Stoller, S.D., Phan, D. and Yang, J., “A
survey on unmanned aerial vehicle collision avoidance systems”,
arXiv:1508.07723, (2015), 1–10.  
37. Chen, W., Chen, J., Shao, Z. and Biegler, L. T., “Three-dimensional
aircraft conflict resolution based on smoothing methods”, Journal
of Guidance, Control, and Dynamics, Vol. 39, No. 7, (2016), 1481–
1490.  
38. Betts, J. T., “Survey of numerical methods for trajectory
optimization”, Journal of Guidance, Control, and Dynamics, Vol.
21, No. 2, (1998), 193–207.  
39. Lilium Jet, June 2016. [Online]. Available: https://www.aerospacetechnology.com/projects/lilium-jet