Air Navigation and control

General introduction to trajectory optimization for commercial aircraft

In the future European Air Traffic Management (ATM) system, the trajectory becomes the fundamental element of a new set of operating procedures collectively referred to as Trajectory-Based Operations (TBO). The underlying idea in TBO is the concept of business trajectory. The business trajectory is the trajectory that best meets airline business interests. This business interests may be, for instance, minimum duration, minimum consumption, or minimum operational cost. The TBO concept of operations and the notion of business trajectory will result in more efficient 4D trajectories that will be necessarily flown under the presence of constraints due to, for instance, airport operations or Air Traffic Control (ATC) intervention. Any modification in that trajectory will result in a change in the cost effectiveness of the operation. Thus, the future ATM system should modify the business trajectory as little as possible. Overall, the necessary tactical intervention will be limited to exceptions, so the development of techniques for strategic planning of business 4D trajectories will be key, resulting in significant fuel savings for airlines.

Flight Plan otpimization

Introduction, Motivation and Goal
The goal of this research activity is to determine the flight plan of commercial airplanes that minimizes the direct operative cost of airliners in a flight between two assigned airports considering, the existing non-flight zones, the weather information such as forecasted storms and wind and other constraints like passage over waypoints. Effective flight planning can not only reduce fuel costs, but also time-based costs and lost revenue from payload that can not be carried, simply by choosing efficient routes and altitudes, speed, and the optimal amount of departure fuel.

Employed Techniques
The flight planning problem can be regarded as a trajectory optimization problem. The trajectory optimization problem can be studied as an optimal control problem of a dynamic system in which the goal is to find the trajectory and the corresponding control inputs that steer the state of the system between two configurations satisfying a set of constraints on the state and/or control variables while minimizing an objective functional.

The use of these optimization techniques in flight planning allows a substantial fuel saving that is a strategic aspect for flight companies and has the additional positive effect of reducing CO2 emissions.

Relevant publications

  1. Commercial Aircraft Trajectory Planning based on Multiphase Mixed-Integer Optimal Control. PhD thesis.
    M. Soler. OMM Editorial, 2013. ISBN 978-84-941248-1-5.
  2. Multiphase Mixed-Integer Optimal Control Approach to Aircraft Trajectory Optimization.
    P. Bonami, A. Olivares, M. Soler, and E. Staffetti. Journal of Guidance, Control, and Dynamics. Vol. 36, No. 5 : pp. 1267-1277; September 2013. DOI 10.2514/1.60492
  3. Framework for Aircraft 4D Trajectory Planning Towards an Efficient Air Traffic Management.
    M. Soler, D. Zapata, A. Olivares, E. Staffetti. Journal of Aircraft. Vol. 49, No. 1, January-February 2012. DOI: 10.2514/1.C031490
  4. Hybrid Optimal Control Approach to Commercial Aircraft Trayectory Planning.
    M. Soler, A. Olivares and E. Staffetti. Journal of Guidance, Control, and Dynamics. Vol. 33, No. 3, May-June 2010. DOI: 10.2514/1.47458

Hypersonic Thermography :-(
Fig.1 Optimal and altitude and velocity profile for different flight planning concepts, namely: free-flight (green), optimized-procedured (orange), and fully-procedured (red). See Soler et al. Journal of Aircraft 2012.

Collision avoidance

Introduction, Motivation and Goal
The air traffic system is safety critical and large scale. Its operations are vulnerable to traffic fluctuations and weather hazard uncertainties. The Air Traffic Management (ATM) system has historically grown along highly structured airspace with various restrictions on aircraft trajectories in order to ensure safety, predictability and ease of control by human operators. With the projected increase in air traffic, it becomes critical to develop algorithms to ensure safety with respect to nearby aircraft and hazardous weather while optimizing performance of individual aircraft. The proposed Trajectory Based Operations (TBO) concept, pursued in Europe and the United States, will provide the capabilities, decision support tools and automation to manage aircraft movement by trajectory. Moreover it will give aircraft flexibility to fly trajectories that meet their own interests, such as minimizing fuel consumption, but always under the agreement of Air Traffic Control (ATC).

Employed tecnhiques
Automation tools need to be designed to fly optimal and accurate 4D (space and time) trajectories. The design process must consider that the trajectories are implemented under supervision of pilots and in communication with ATC. A hybrid optimal control framework is proposed, consistent with operations of air traffic controllers, pilots and autopilots, for strategic (20 minutes to one hour) de-conflicted trajectory planning.

The main contribution of this research line is that the conflict free trajectory planning can be formulated as a hybrid optimal control problem. By including accurate nonlinear aircraft dynamics and constraints 4D trajectories can be obtained while minimizing fuel consumption. In addition, by including hybrid modes of flight, the proposed method can be integrated with the current procedures implemented by pilots, autopilots and air traffic controllers.

Relevant publications

  1. Multiphase Mixed- Integer Optimal Control Framework for Aircraft Conflict Avoidance.
    M. Soler, M. Kamgarpour, C. J. Tomlin, and E. Staffetti, 51st IEEE Conference on Decision and Control (CDC 2012), December 8-11 2012, Maui, Hawaii, USA. pp 1740-1745.
  2. Hybrid Optimal Control for Aircraft Trajectory Design with a Variable Sequence of Modes.
    Maryam Kamgarpour, Manuel Soler, Claire J. Tomlin, Alberto Olivares and John Lygeros. Proocedings of the 18th IFAC World Congress; Milano, Aug. 29- Sep 2, 2011.ISBN: 978-3-902661-93-7.

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Fig.2 Sketch of 9 aircraft flying in the same control sector

Persistent contrails mitigation strategies

Introduction, Motivation and Goal
The goal of this research is thus to find contrail mitigation strategies with new flight planning concepts. CO2 is the most widely perceived greenhouse gas agent in aviation. However, emissions from aircraft engines include other constituents that contribute, via the formation or destruction of atmospheric constituents, to climate change. Another source of aviation-induced climate change comes from the formation of persistent contrails, which are composed of ice particles and formed in the wake of jet aircraft at high altitude where the ambient temperature is very low. Quantifying the climate impact of persistent contrails is an area that has attracted considerable research interests over the past decades. While consensus has yet to be achieved, the general conclusion is that the magnitude of contrail climate impact is non-negligible compared to that of CO2. Several strategies for persistent contrail mitigation have been studied. We focus herein on flight planning concepts for contrail mitigation. Further mitigation potential can be achieved by developing optimized aircrafts and jets for these alternative trajectories.

Employed tecnhiques
Mixed-integer linear programming allows many constraints to be considered and relatively large problems to be solved, permitting for instance the solution to realistic ATM de-conflicted, multi-aircraft scenarios. On the contrary, it is well-known that the most complete way of solving a trajectory optimization problem is to formulate it as an optimal control problem. Therefore, a bi-level algorithm is used pertaining:
- Optimal control to obtain the individual aircraft environmentally friendly trajectory.
- Mixed-integer linear programming algorithms to analyze the problem at a network level.
Moreover, Global Warming Potential theory is used to find metrics and thus quantify the impact of different climate impact sources.

Accounting for the formation of persistent contrails, therefore, should be indispensable when one wants to mitigate the overall aircraft induced climate impact. Preliminary results show that different optimal vertical profiles arise from different CO2-contrails trade offs.

Relevant publications

  1. Contrail Sensitive 4D Trajectory Planning with Flight Level Allocation using Multiphase Mixed-Integer Optimal Control.
    M. Soler, B. Zou, and M. Hansen, Proceedings of the AIAA Guidance, Navigation, and Control Conference, August 19-22, 2013. Boston, USA. Paper AIAA 2013-5179.
  2. Flight Trajectory Design in the Presence of Contrails: Application of a Multiphase Mixed-Integer Optimal Control.
    M. Soler, B. Zou, and M. Hansen. Submitted to Transportation Research Part C: Emerging Technologies.

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Fig.3 Persistent cortrails