Trajectory optimization using TOMATO and COALA
Along the ambitious Single European Sky (SESAR) objectives which are a increase in capacity, environmental sustainability, and reduction in costs, air space users shall be freed from some of the numerous operational constraints during flight. In order to reach these targets, concepts as Trajectory Based Operations (TBO) and Reference Business Trajectories (RBT) enable air carriers to choose optimal and efficient flight profiles based on their individual requirements. Therefore, the Chair of Air Transport Technology and Logistics at Technische Universität Dresden developes models for the optimization of waypointless trajectories within a four-dimensional environment.
This is primarily the identification of the most eco-efficient flight path by a Shortest Path algorithm and a coupled calculation of an energy-optimal vertical profile by the COALA performance model (Compromised Aircraft Performance Model with Limited Accuracy). Both optimization modules and an additional assessment module iteratively improve the trajectory within the software platform TOMATO (TOolchain for Multicriteria Aircraft Trajectory Optimization). Figure 1 shows input and output data and the optimization process.
TOMATO and COALA are used and enhanced in the following projects:
- ProfiFuel: Improved planning and realization of flight profiles with the lowest ecological footprint and minimum fuel consumption
- UTOPIA II: Enhanced Flight Planning by introducing stochastic trajectory data
- CDO-Speedbrakes: Optimized CDO under uncertain environmental and mission conditions
- MEFUL: Minimizing Flight Emissions while Sustaining Guaranteed Operational Safety as a Contribution to an Environmental Friendly Air Transport System
Figure 1: Workflow of trajectory optimization and assessment with TOMATO
For the trajectory optimization, a flight performance model and a lateral pathfinding algorithm are used iteratively by the simulation environment TOMATO defining the input parameters for both models and assessing the trajectories regarding the KPIs. Figure 1 shows the iterative workflow and the interactions between input data, pathfinding module and flight performance model, as well as the trajectory assessment within TOMATO.
The input parameters are defined by weather data, city pairs and aircraft type together with information of the airspace structure and cost charges. Therewith, the pathfinding module calculates the lateral trajectory at cruising altitude, considering the global target function of the optimization (e.g. minimum costs). For lateral trajectory optimization, an efficient A* algorithm is used to find the shortest path between origin and destination under consideration of local restrictions (e.g. contrail sensitive regions) and wind vectors within the given weather scenario. Therefore, a cell based environment with a variable longitudinal resolution is simulated and rotated, such that the departure point represents a pole. The A* algorithm considers the best neighbored nodes to find the shortest path using a heuristic costs function. Time dependent parameters as weather can be considered as a function of estimated flown distance and average cruising speed.
The calculated route, the weather data and the aircraft and engine type is used by the aircraft performance model COALA to estimate the vertical trajectory considering the given cruising altitude. Additionally, COALA quantifies the engine emissions. Using the KPIs, TOMATO calculates all cost components and evaluates the trajectory. During the next iteration, TOMATO adjusts the input parameters for the pathfinding module and for COALA to iteratively converge to an optimal trajectory.
Figure 2: Flight from Barcelona to Helsinki as ATS restricted trajectory (black) based on recent AIRAC cylce and as waypointless optimized trajectory (yellow) at 04.08.2018, 01:00 p.m. Blue colored regions represent ice-supersatured regions resulting in condensation trails, which are considered in multi criteria optimization.
Along the ambitious SESAR objectives, new aircraft performance models are necessary to calculate and optimize free route aircraft specific trajectories considering real weather conditions. The aircraft performance model COALA meets these requirements. To consider constant changes in speed and acceleration, the dynamic equation of this unsteady system is solved analytically. Free variables are controlled by an aircraft specific proportional plus integral plus derivative controller. Therewith, the model is based solely on physical functions (except for the drag polar, which is approximated by BADA 4.1 [1]) and calculates only physically possible trajectories. Several aircraft and engine types are included, the aircraft specific behavior can be modeled in detail and emissions can be quantified. Figures 3 and 4 show for the flight Barcelona-Helsinki and the AIRAC and waypointless scenario each the optimized vertical profile. Blue regions represent ice supersatured regions, which are mostly avoided by vertical steps. Figure 5 and 6 show for the waypointless optimzied trajectory the target and actual air speeds, thrust, and fuel flow.
COALA uses target functions for the trajectory design and calculates the 4D trajectory for fixed time steps. For the definition of the Shared Business Trajectory (SBT) and the Reference Business trajectory (RBT) due to communication with the air traffic stakeholders the optimized 4D trajectory may have to be converted into way points. However, target functions will allways be closer to the optimum, especially under consideration of external influences. Without waypoints, the trajectory will not be predictable and difficult to control by Air Traffic Control (ATC). The flight performance model COALA will give all stakeholders the possibility to calculate the desired 4D trajectory and to investigate it with respect to conflicts with other stakeholders. For the RBT, ATC has to release the target function, not the waypoints.
Figure 3: Optimized vertical profile for the AIRAC scenario avoiding ice supersatured regions (blue). Head wind and tail wind components are shown as wind barbs.
Figure 4: Optimized vertical profile for the waypointless scenario avoiding ice supersatured regions (blue). Head wind and tail wind components are shown as wind barbs.
Figure 5: Target and Actual True Air Speed (m/s) for the waypointless optimized vertical profile.
Figure 6: Thrust (kN) and Fuel Flow (kg/min) for the waypointless optimized vertical profile.
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EUROCONTROL, (BADA) Base of Aircraft Data; 4, User Manual Family, 2012. |
- Judith Rosenow, Stanley Förster, Martin Lindner, Hartmut Fricke (2018): Multicriteria-Optimized Trajectories Impacting Today’s Air Traffic Density, Efficiency, and Environmental Compatibility, AIAA Journal, doi: https://arc.aiaa.org/doi/abs/10.2514/1.D0086
- Martin Lindner, Thomas Zeh, Hartmut Fricke (2018): Reoptimization of 4D-Flight Trajectories During Flight Considering Forecast Uncertainties, 67. DGLR Kongress, Friedrichshafen
- Judith Rosenow, David Strunck, Hartmut Fricke (2018): Trajectory Optimization in Daily Operations, 8th International Conference on Research in Air Transportation, Castelldefels
- Martin Lindner, Judith Rosenow, Hartmut Fricke (2018): Dynamically Optimized Aircraft Trajectories Affecting the Air Traffic Management, 8th International Conference on Research in Air Transportation, Castelldefels
- Judith Rosenow, Hartmut Fricke, Tanja Luchkova, Michael Schultz (2018): Minimizing contrail formation by rerouting around dynamic ice-supersaturated regions, Aeronautics and Aerospace Open Access Journal, Volume 2, Issue 3
- Judith Rosenow, Hartmut Fricke, Michael Schultz (2017): Air traffic simulation with 4D multi-criteria optimized trajectories, Winter Simulation Conference 2017, Las Vegas
- Judith Rosenow, Martin Lindner, Hartmut Fricke (2017): Impact of climate costs on airline network and trajectory optimization: a parametric study, CEAS Aeronautical Journal, Volume 8
- Judith Rosenow and Hartmut Fricke (2017): Impact of Multi-critica Optimized Trajectories on European Airline and Network Efficiency, Air Transport Research Society World Conference 2017, Antwerp
- Judith Rosenow, Stanley Förster, Martin Lindner, and Hartmut Fricke (2017): Impact of Multi-critica Optimized Trajectories on European Air Traffic Density, Efficiency and the Environment, Twelfth USA/Europe Air Traffic Management Research and Development Seminar (ATM2017), Seattle
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Judith Rosenow, Stanley Förster, and Hartmut Fricke (2016): Continuous Climb Operations with Minimum Fuel Burn, Sesar Innovation Days, Delft
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Stanley Förster, Judith Rosenow, Martin Lindner and Hartmut Fricke (2016): A toolchain for optimizing trajectories under real weather conditions and realistic flight performance , Greener Aviation, Brussels
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Martin Lindner, Stanley Förster, Judith Rosenow, and Hartmut Fricke (2016): Ecological Impact Of Air Traffic Control En-Route Charging Zones From Multi Criteria Optimized Flight Paths, Greener Aviation, Brussels
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Judith Rosenow and Hartmut Fricke (2016): Flight Performance Modeling to optimize Trajectories, DGLR Kongress, Braunschweig
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Judith Rosenow, Stanley Förster, Martin Lindner, and Hartmut Fricke (2016): Multi-objective trajectory optimization, International Transportation, Special Edition 1, Volume 68
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Judith Rosenow, Martin Lindner, and Hartmut Fricke (2015): Assessment of air traffic networks considering multi-criteria targets in network and trajectory optimization, DGLR Kongress, Rostock