Abstract
Significant evolutions of aircraft, airspace and airport systems design and operations are driven by the continuous increase of air transport demand worldwide and by the concurrent push for a more economically viable and environmentally sustainable aviation. In the operational context, novel avionics and air traffic management (ATM) systems are being developed to take full advantage of the available communication, navigation and surveillance (CNS) performance. In order to attain higher operational, economic and environmental efficiencies, the generation of 4-dimensional trajectories (4DT) shall integrate optimisation algorithms addressing multiple objectives and constraints in real-time. Although extensive research has been performed in the past on the optimisation of aircraft flight trajectories and very efficient algorithms were widely adopted for the optimisation of vertical flight profiles, it is only in the last few years that higher levels of integration were proposed for automated 4DT planning and rerouting functionalities. This chapter presents the algorithms conceived for integration in next generation avionics and ATM Decision Support Systems (DSS), to perform the multi-objective optimisation of 4DT intents. In particular, the algorithms are developed for 4DT planning, negotiation, and validation (4-PNV) in online strategic and tactical operational scenarios, and are conceived to assist the human flight crews and ATM operators in planning and reviewing optimal 4DT intents in high air traffic density contexts. The presented implementation of the multi-objective 4DT optimisation problem includes a number of environmental objectives and operational constraints, also accounting for economic and operational performances as well as weather forecast information from external sources. The current algorithm verification activities address the Arrival Manager (AMAN) scenario within a Terminal Manoeuvring Areas (TMA), featuring automated point-merge sequencing and spacing of multiple arrival traffic in quasi real-time.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
ICAO. ICAO Aircraft Engine Emissions Databank [Online]. Available http://easa.europa.eu/node/15672.
References
Basset G, Xu Y, Yakimenko OA (2010) Computing short-time aircraft maneuvers using direct methods. J Comput Syst Sci Int 49:481–513. doi:10.1134/S1064230710030159
Ben-Asher JZ (2010) Optimal control theory with aerospace applications. American Institute of Aeronautics and Astronautics (AIAA), Reston
Benson DA, Huntington GT, Thorvaldsen TP, Rao AV (2006) Direct trajectory optimization and costate estimation via an orthogonal collocation method. J Guid Control Dyn 29:1435–1440. doi:10.2514/1.20478
Betts JT (1998) Survey of numerical methods for trajectory optimization. J Guid Control Dyn 21:193–207
Betts JT (2010) Practical methods for optimal control and estimation using nonlinear programming, 2nd edn, vol 19. SIAM
Betts JT, Cramer EJ (1995) Application of direct transcription to commercial aircraft trajectory optimization. J Guid Control Dyn 18:151–159
Betts JT, Huffman WP (1998) Mesh refinement in direct transcription methods for optimal control. Optimal Control Appl Methods 19:1–21
Betts JT, Huffman WP (1999) Exploiting sparsity in the direct transcription method for optimal control. Comput Optim Appl 14:179–201. doi:10.1023/A:1008739131724
Betts JT, Huffman WP (2004) Large scale parameter estimation using sparse nonlinear programming methods. SIAM J Optim 14:223–244. doi:10.1137/S1052623401399216
Betts JT, Biehn N, Campbell SL, Huffman WP (2000) Compensating for order variation in mesh refinement for direct transcription methods. J Comput Appl Math 125:147–158. doi:10.1016/S0377-0427(00)00465-9
Betts JT, Biehn N, Campbell SL, Huffman WP (2002) Compensating for order variation in mesh refinement for direct transcription methods II: computational experience. J Comput Appl Math 143:237–261. doi:10.1016/S0377-0427(01)00509-X
Betts JT, Campbell SL, Engelsone A (2007) Direct transcription solution of optimal control problems with higher order state constraints: theory vs practice. Optim Eng 8:1–19. doi:10.1007/s11081-007-9000-8
Bousson K, Machado P (2010) 4D flight trajectory optimization based on pseudospectral methods. World Acad Sci Eng Technol 70:551–557
Boyd JP (2000) Chebyshev and Fourier spectral methods, 2nd edn. Dover publications, Mineola
Brix K, Canuto C, Dahmen W (2013) Legendre-Gauss-Lobatto grids and associated nested dyadic grids. Aachen Inst Adv Study Comput Eng Sci (arXiv:1311.0028)
Darby CL, Hager WW, Rao AV (2011a) An hp-adaptive pseudospectral method for solving optimal control problems. Optimal Control Appl Methods 32:476–502. doi:10.1002/oca.957
Darby CL, Hager WW, Rao AV (2011b) Direct trajectory optimization using a variable low-order adaptive pseudospectral method. J Spacecraft Rockets 48:433–445. doi:10.2514/1.52136
Engelsone A, Campbell SL, Betts JT (2007) Direct transcription solution of higher-index optimal control problems and the virtual index. Appl Numer Math 57:281–296. doi:10.1016/j.apnum.2006.03.012
Funaro D (1992) Polynomial approximation of differential equations. Springer, Berlin
Gardi A, Sabatini R, Ramasamy S, Kistan T (2014) Real-time trajectory optimisation models for next generation air traffic management systems. Appl Mech Mater 629:327–332. doi:10.4028/www.scientific.net/AMM.629.327
Gardi A, Sabatini R, Ramasamy S (2016) Multi-objective optimisation of aircraft flight trajectories in the ATM and avionics context. Prog Aerosp Sci 83:1–36. doi:10.1016/j.paerosci.2015.11.006
Gardi A, Sabatini R, Kistan T, Lim Y, Ramasamy S (2015) 4-Dimensional trajectory functionalities for air traffic management systems. In: Proceedings: integrated communication, navigation and surveillance conference (ICNS 2015), Herndon, VA, USA
Garg D, Patterson M, Hager WW, Rao AV, Benson DA, Huntington GT (2010) A unified framework for the numerical solution of optimal control problems using pseudospectral methods. Automatica 46:1843–1851. doi:10.1016/j.automatica.2010.06.048
Garg D, Hager WW, Rao AV (2011) Pseudospectral methods for solving infinite-horizon optimal control problems. Automatica 47:829–837. doi:10.1016/j.automatica.2011.01.085
Gherman I, Schulz V, Betts JT (2006) Optimal flight trajectories for the validation of aerodynamic models. Optimization Methods and Software 21:889–900. doi:10.1080/10556780600872281
Hartjes S, Visser HG, Hebly SJ (2009) Optimization of RNAV noise and emission abatement departure procedures. In: Proceedings: AIAA aviation technology, integration, and operations conference 2009 (ATIO 2009), Hilton Head, SC, USA. doi:10.2514/6.2009-6953
Huntington GT, Rao AV (2008) Comparison of global and local collocation methods for optimal control. J Guid Control Dyn 31:432–436. doi:10.2514/1.30915
Jardin MR (2003) Real-time conflict-free trajectory optimization. In: Proceedings: 5th USA/Europe air traffic management research and development seminar (ATM 2003), Budapest, Hungary
Marler RT, Arora JS (2004) Survey of multi-objective optimization methods for engineering. Struct Multi Optim 26:369–395. doi:10.1007/s00158-003-0368
Patterson MA, Rao AV (2012) Exploiting sparsity in direct collocation pseudospectral methods for solving optimal control problems. J Spacecraft Rockets 49:364–377. doi:10.2514/1.A32071
Ramasamy S, Sabatini R, Gardi A (2015) Novel flight management systems for improved safety and sustainability in the CNS+A context. In: Proceedings: integrated communication, navigation and surveillance conference (ICNS 2015), Herndon, VA, USA. doi:10.1109/ICNSURV.2015.7121225
Rao AV (2010a) Trajectory optimization. In: Encyclopedia of aerospace engineering. Wiley
Rao AV (2010b) Survey of numerical methods for optimal control. Adv Astronaut Sci 135:497–528
Rao AV, Benson DA, Darby C, Patterson MA, Francolin C, Sanders I et al (2010) Algorithm 902: GPOPS, a MATLAB software for solving multiple-phase optimal control problems using the gauss pseudospectral method. ACM Transact Math Softw 37. doi:10.1145/1731022.1731032
Sabatini R, Gardi A, Ramasamy S, Kistan T, Marino M (2014) Novel ATM and avionic systems for environmentally sustainable aviation. In: Proceedings: practical responses to climate change. Engineers Australia convention 2014 (PRCC 2014), Melbourne, Australia. doi:10.13140/2.1.1938.0808
Sabatini R, Gardi A, Ramasamy S, Kistan T, Marino M (2015) Modern avionics and ATM systems for green operations. In: Blockley R, Shyy W (eds) Encyclopedia of aerospace engineering. Wiley
Soler M, Olivares A, Staffetti E (2010) Hybrid optimal control approach to commercial aircraft trajectory planning. J Guid Control Dyn 33:985–991. doi:10.2514/1.47458
Sorensen JA, Morello SA, Erzberger H (1979) Application of trajectory optimization principles to minimize aircraft operating costs. In: 18th IEEE conference on decision and control, vol 1, pp 415–421
Sridhar B, Ng H, Chen N (2011) Aircraft trajectory optimization and contrails avoidance in the presence of winds. J Guid Control Dyn 34:1577–1584. doi:10.2514/1.53378
The ATM target concept—D3. SESAR definition phase DLM-0612-001-02-00, 2007
Torres R, Chaptal J, Bes C, Hiriart-Urruty J-B (2009) Multi-objective clean take-off flight paths for civil aircraft. In: Proceedings: AIAA aviation technology, integration, and operations conference 2009 (ATIO 2009), Hilton Head, SC, USA. doi:10.2514/6.2009-6931
User Manual for the Base of Aircraft Data (BADA) Revision 3.11. Eurocontrol experimental centre (EEC) technical/scientific report no. 13/04/16-01, Brétigny-sur-Orge, France, 2013
Vaddi S, Sweriduk G, Tandale M (2012) 4D green trajectory design for terminal area operations using nonlinear optimization techniques. In: Proceedings: AIAA guidance, navigation, and control conference (GNC 2012), Minneapolis, MN, USA. doi:10.2514/6.2012-4755
Visser HG (1994) A 4D trajectory optimization and guidance technique for terminal area traffic management. Delft University of Technology
Visser H, Wijnen R (2001) Optimization of noise abatement arrival trajectories. In: Proceedings: AIAA guidance, navigation and control conference 2001 (GNC 2001), Montreal, Canada. doi:10.2514/6.2001-4222
von Stryk O, Bulirsch R (1992) Direct and indirect methods for trajectory optimization. Ann Oper Res 37:357–373. doi:10.1007/BF02071065
Wijnen RAA, Visser HG (2003) Optimal departure trajectories with respect to sleep disturbance. Aerosp Sci Technol 7:81–91. doi:10.1016/s1270-9638(02)01183-5
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Gardi, A., Sabatini, R., Marino, M., Kistan, T. (2016). Multi-objective 4D Trajectory Optimization for Online Strategic and Tactical Air Traffic Management. In: Karakoc, T., Ozerdem, M., Sogut, M., Colpan, C., Altuntas, O., Açıkkalp, E. (eds) Sustainable Aviation. Springer, Cham. https://doi.org/10.1007/978-3-319-34181-1_17
Download citation
DOI: https://doi.org/10.1007/978-3-319-34181-1_17
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-34179-8
Online ISBN: 978-3-319-34181-1
eBook Packages: EnergyEnergy (R0)