Trajectory optimization using TOMATO and SOPHIA

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 SOPHIA performance model (Sophisticated Aircraft Performance Model). 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 SOPHIA are used and enhanced in the following projects:

TOMATO workflow — Figure 1: Workflow of trajectory optimization and assessment with TOMATO

Flight path optimization using 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 SOPHIA to estimate the vertical trajectory considering the given cruising altitude. Additionally, SOPHIA 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 SOPHIA 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.

Flight Performance Model SOPHIA

Along with 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 SOPHIA 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 the open-source aircraft performance model OpenAP [1]) and calculates only physically possible trajectories. Several aircraft and engine types are included, the aircraft-specific behaviour can be modelled in detail and emissions can be quantified. Figures 3 and 4 show the flight Barcelona-Helsinki and the AIRAC and waypointless scenario each the optimized vertical profile. Blue regions represent ice supersaturated regions, which are mostly avoided by vertical steps. Figures 5 and 6 show the waypointless optimized trajectory of the target and actual air speeds, thrust, and fuel flow.

SOPHIA 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 waypoints. However, target functions will always 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 SOPHIA will give all stakeholders the possibility to calculate the desired 4D trajectory and 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.

[1]	Sun, J.; Hoekstra, J.M.; Ellerbroek, J. OpenAP: An Open-Source Aircraft Performance Model for Air Transportation Studies and Simulations. Aerospace 2020, 7, 104. https://doi.org/10.3390/aerospace7080104

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Trajectory optimization using TOMATO and SOPHIA

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