JPAS MOTO Paper FP&R

Full text

Multi-objective optimisation of aircraft flight trajectories in the ATM
and avionics context
Alessandro Gardi, Roberto Sabatini
n
, Subramanian Ramasamy
RMIT University, Melbourne, Victoria 3001, Australia
a r t i c l e i n f o
Article history:
Received 9 September 2015
Received in revised form
23 November 2015
Accepted 23 November 2015
Available online 12 April 2016
Keywords:
4-Dimensional flight trajectory
Air traffic management
Aircraft emissions
Avionics
Environmental impacts
Flight planning
Multi-objective optimisation
Optimal control
Sustainable aviation
Trajectory optimisation
a b s t r a c t
The continuous increase of air transport demand worldwide and the push for a more economically viable
and environmentally sustainable aviation are driving significant evolutions of aircraft, airspace and air-
port systems design and operations. Although extensive research has been performed on the optimi-
sation of aircraft 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 automation were proposed for
integrated flight planning and re-routing functionalities of innovative Communication Navigation and
Surveillance/Air Traffic Management (CNS/ATM) and Avionics (CNSþA) systems. In this context, the
implementation of additional environmental targets and of multiple operational constraints introduces
the need to efficiently deal with multiple objectives as part of the trajectory optimisation algorithm. This
article provides a comprehensive review of Multi-Objective Trajectory Optimisation (MOTO) techniques
for transport aircraft flight operations, with a special focus on the recent advances introduced in the
CNSþA research context. In the first section, a brief introduction is given, together with an overview of
the main international research initiatives where this topic has been studied, and the problem statement
is provided. The second section introduces the mathematical formulation and the third section reviews
the numerical solution techniques, including discretisation and optimisation methods for the specific
problem formulated. The fourth section summarises the strategies to articulate the preferences and to
select optimal trajectories when multiple conflicting objectives are introduced. The fifth section in-
troduces a number of models defining the optimality criteria and constraints typically adopted in MOTO
studies, including fuel consumption, air pollutant and noise emissions, operational costs, condensation
trails, airspace and airport operations. A brief overview of atmospheric and weather modelling is also
included. Key equations describing the optimality criteria are presented, with a focus on the latest ad-
vancements in the respective application areas. In the sixth section, a number of MOTO implementations
in the CNSþA systems context are mentioned with relevant simulation case studies addressing different
operational tasks. The final section draws some conclusions and outlines guidelines for future research
on MOTO and associated CNSþA system implementations.
&2016 Elsevier Ltd. All rights reserved.
Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1. ATM and avionics modernisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2. Environmental sustainability of aviation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3. Early trajectory optimisation research in aviation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.4. Trajectory optimisation research in the context of avionics and CNS/ATM evolutions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.5. Problem statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2. Theoretical framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1. Optimal control problem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2. Dynamic constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3. Path constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Contents lists available at ScienceDirect
journ al h om epage: ww w. el sevie r. co m/locat e/ pa erosc i
Progress in Aerospace Sciences
http://dx.doi.org/10.1016/j.paerosci.2015.11.006
0376-0421/&2016 Elsevier Ltd. All rights reserved.
n
Corresponding author.
E-mail address: roberto.sabatini@rmit.edu.au (R. Sabatini).
Progress in Aerospace Sciences 83 (2016) 1–36

2.4. Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.5. Cost functions and performance indexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.6. Resulting mathematical formulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3. Numerical solution methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.1. Lagrangian relaxation and first order optimality conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.2. Boundary-value problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.3. Iterative solution of unconstrained nonlinear programming problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.4. Indirect methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.4.1. Indirect shooting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.4.2. Indirect multiple shooting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.4.3. Indirect collocation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.4.4. Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.5. Direct methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.5.1. Direct shooting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.5.2. Multiple direct shooting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.5.3. Local collocation methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.5.4. Global collocation methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.5.5. Heuristic methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4. Multi-objective optimality. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
4.1. Pareto optimality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
4.2. A priori articulation of preferences. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
4.2.1. Weighted global criterion method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.2.2. Weighted min-max . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.2.3. Weighted product . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.2.4. Exponential weighted criterion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.2.5. Lexicographic and sequential goal programming methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.2.6. Physical programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.3. A posteriori articulation of preferences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.3.1. Physical programming. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
4.3.2. Normal boundary intersection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
4.3.3. Normal constraint method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
5. Optimality criteria and constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
5.1. Flight dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
5.1.1. Rigid body models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
5.1.2. Point-mass models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
5.2. Turbofan and turboprop engine models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
5.2.1. Pollutant emissions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
5.3. Operational costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
5.4. Atmosphere and weather . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
5.5. Trajectory optimisation in the presence of wind . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
5.6. Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
5.7. Condensation trails . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
5.8. Airspace and air traffic models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
6. CNSþA concepts and implementations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
6.1. Targeted operational timeframes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
6.2. System architectures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
6.3. Optimisation of arrival and departure trajectories. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
6.4. Trajectory optimisation in safety-critical applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
6.5. MOTO algorithm verification and validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
7. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
1. Introduction
The continuous growth of civil air transport and the increasing
adoption of manned and unmanned aerial vehicles for new and
more traditional roles is posing significant challenges to the
aviation community, as the current paradigms will not ensure the
desired levels of safety, efficiency and environmental sustainability
in the future unless substantial evolutions are introduced. As a
consequence, several large-scale aviation renovation initiatives
were launched in the last two decades. These research and de-
velopment activities are investigating, in particular, the most
promising technological and operational improvements that
would enhance the levels of safety, capacity, efficiency and
environmental sustainability associated with current and likely
future aviation business models in a holistic manner, hence by
specifically improving the design, manufacturing, operation and
lifecycle management of aircraft. In the operational domain, sig-
nificant progresses in terms of safety, capacity and efficiency of air
traffic are particularly expected from the implementation of novel
concepts and technologies in the Air Traffic Management (ATM)
and avionics domain, in line with the evolutions originally envi-
sioned by the Future Air Navigation Systems (FANS) special com-
mittee of the International Civil Aviation Organisation (ICAO) in
the 1980s [1]. The ATM relies on a large set of operational mea-
sures to fulfil its mission of preventing collisions and promoting an
ordered and expedite flow of air traffic[2,3]. In the current cen-
tralised command and control-oriented ATM configuration, these
measures are typically based on amending the lateral, vertical and
longitudinal navigation of aircraft as necessary, and can be per-
formed at various operational timeframes. As depicted in Fig. 1,
A. Gardi et al. / Progress in Aerospace Sciences 83 (2016) 1–362

addressing, in particular, the fusion of cooperative and non-co-
operative surveillance data for accurate detection, tracking and
safe steering. The reader is referred to the literature in the domain
for further detail.
6.5. MOTO algorithm verification and validation
All MOTO algorithms conceived for CNSþA integration require
extensive validation by simulation in realistic test scenarios.
Simulation cases shall cover all phases of flight and airspace con-
figurations. Particular emphasis is given to the TMA, as trajectories
of climbing and descending aircraft usually intersect, requiring
frequent tactical ATM interventions, and more generally the con-
strained airport capacity can lead the arrival traffic to stack, even
when disruptions are not present. While concepts such as 4DT
point-merge and Continuous Curved Descent Approaches (CCDA)
are currently experimented to reduce TMA congestion [216–219],
practical implementation aspects are being investigated, especially
in the 4DT-TBO context. The Arrival Manager (AMAN) is re-
sponsible of the optimised sequencing and spacing of arrival traffic
towards a single final approach segment. The AMAN scenario is
the most representative case study of online tactical TMA opera-
tions for ATM DSS implementations of MOTO-4D [205]. The
ground-based ATM system implementing MOTO-4D algorithms
identifies the best arrival sequence among the available options in
terms of multiple and conflicting objectives. Longitudinal separa-
tion is enforced at the merge-point in the form of path constraints
and boundary conditions to ensure sufficient separation upon
landing, and to prevent separation infringements in the approach
phase itself. Notwithstanding, the ATM DSS implementing MOTO-
4D shall be capable to perform point-merge at any metering point.
After the initial set of optimal intents has been stored in the ATM
DSS, the point-merge sequencing algorithm allocates the available
time slots according to suitable optimal scheduling decision-logics.
As a reference, assuming a minimum longitudinal separation of
4 nautical miles on the approach path for medium category air-
craft approaching at 140 knots, the allocated time slots are char-
acterized by a 90 160 seconds separation depending on the
wake-turbulence categories of two consecutive traffics. Example
4D-AMAN simulation results of an ATM DSS implementing MOTO-
4D algorithms are depicted in Fig. 32.
Waypoints and lines depicted in magenta represent the flyable
and concisely-described 4DT consisting of a limited number of fly-
by and overfly 4D waypoints, obtained through an operational 4DT
smoothing algorithm [146].Fig. 33 depicts the computed 4DT in
the AMAN schedule display format.
AMAN implementations of MOTO-4D such as the one pre-
sented above are actively researched and evolving to address in-
accurate trajectory predictions, air-ground trajectory synchroni-
sation issues, unforeseen perturbations and the dynamic handling
of multiple altitude/airspeed/path constraints in real-time.
7. Conclusion
Considerable research efforts have addressed the theoretical
developments and practical implementations of trajectory opti-
misation algorithms to improve the economic, operational and
environmental performances of air traffic. The progresses in op-
timal control and nonlinear programming have recently resulted
in very efficient numerical solution methods, enabling real-time
applications even when complex nonlinear models and multiple
constraints are introduced. A number of studies evidenced the
significant gains that could be attained by optimising individual
manoeuvres, procedures, flight phases or entire flight routes. In
several works, the practical implementation of these promising
solutions in the civil aviation domain was associated with con-
siderable challenges, as the conventional and largely procedural
Air Traffic Management (ATM) operational paradigm would have
posed significant restrictions. The adoption of continuously up-
dated 4-Dimensional Trajectory (4DT) descriptors with high na-
vigational accuracy and predictability, in conjunction with data-
link based 4DT negotiation and validation functionalities are pro-
viding an opportunity for the full exploitation of 4DT optimisation
methods into the next generation avionics and ATM systems.
Novel avionics and ATM Decision Support Systems (DSS) are cur-
rently being researched and developed to introduce the 4DT based
operations paradigms. These systems are designed to deploy ad-
vanced air-to-ground trajectory planning, negotiation and valida-
tion functionalities to enhance the safety, efficiency and environ-
mental sustainability of air traffic operations. In view of the re-
cognised potential, this article reviewed the current theoretical
knowledge on the optimisation of aircraft flight trajectories with
emphasis on multiple and often conflicting objectives. Guidelines
for the development of efficient Multi-Objective Trajectory Opti-
misation (MOTO) algorithms specifically tailored for novel Com-
munication Navigation and Surveillance/ATM (CNS/ATM) and
Avionics (CNSþA) systems were presented and possible im-
plementations were discussed. MOTO algorithms have a clear
potential to enable real-time planning and re-planning of more
environmentally efficient and economically viable flight routes by
simultaneously addressing the dynamic nature of both weather
and air traffic conditions. It is therefore anticipated that a combi-
nation of MOTO and Dynamic Airspace Management (DAM)
techniques will effectively enable the next step in the CNS þA
driven evolutions of the global ATM network.
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