The paper reviews the optimisation methods of the flight trajectory for airliners. In contrast to maritime navigation, where the shortest route (the orthodrome) is preferred, in air navigation, the brachistochrone is the optimal flight trajectory on the sphere or on the ellipsoid, considering the wind vector field (maximising the tail wind and minimising the head wind over the duration of the flight). The major impact of the wind on the flight trajectory results from the possible significant velocity at the normal cruise flight levels, which could reach 200 kts, or 40% of the aircraft true airspeed (TAS). Brachistochrone is independent of the flight performance optimisation (range versus speed), as computed by the flight management system. Whichever cost index (CI) is selected (and consequently, the cruise Mach number), the brachistochrone is the minimum time of flight trajectory at that target Mach number. In cruise flight, the minimum time of flight is also equivalent to the minimum fuel consumption. It concerns just the wind velocity field. All these qualify the brachistochrone as the greenest trajectory, the most fuel and emissions efficient solution relative to the atmosphere. The paper classifies the brachistochrone problems (2D, 3D and 4D brachistochrones, with or without flexible time of departure). Some numerical examples are provided. The overall optimal 4D trajectory considers many aspects, including safety, by minimisation of total costs and risks of the 4D trajectory.

Dynamic soaring improves the endurance of Unmanned Aerial Vehicles (UAVs) by obtaining energy from the horizontal wind shear gradient. The use of dynamic soaring in small solar UAVs can mitigate the trade-off between energy capacity and battery weight to achieve continuous all-day flight. The goal of this study is to determine the optimal energy acquisition methods for small solar UAVs using dynamic soaring and to decrease the battery weight to achieve all-day flight. A dynamic soaring UAV model that considers the influence of the wind shear gradient and a solar power energy model are established. The conditions to obtain a closed-loop energy system during daytime and nighttime flights are discussed, and the minimum mass of the energy system required for these conditions is determined. Simulations of single-cycle circular flights and a 72-h continuous flight of a small solar UAV are performed. The analyses and simulation results show that: (1) the combination of dynamic soaring and solar technology significantly reduces the energy consumption and reduces the required battery weight, (2) the flight speed and flight attitude angles have significant effects on the optimal total energy acquisition and (3) wind fields with a large horizontal gradient and strong solar illumination provide energy and load advantages.

This paper presents the results of a research performed at the Research Laboratory in Active Controls, Avionics and Aeroservoelasticty (LARCASE), at ÉTS, concerning optimisation strategies for cruise flight segments with imposed flight time (delimited by waypoints with required time of arrival constraints). Specifically, a new algorithm is presented that identifies the optimal vertical navigation profile (flight altitude and speed optimisation) for a cruise segment with imposed lateral navigation profile, bounded by two waypoints with required time of arrival constraints. The set of evaluated vertical navigation profiles are characterised by identical altitudes and speeds at their initial and final waypoints (at the beginning and the end of the cruise segment under optimisation), a maximum of one altitude step (relative to the initial altitude), and are flown at constant speed. This study investigates the flight performance increase (total cost reduction) for a flight along the optimal vertical navigation profile, relative to a flight at the optimal speed and initial cruise altitude. The evaluation was performed using a medium haul transport aircraft flight performance model, for three lateral navigation profiles and three wind profiles. The algorithm is targeted for Flight Management Systems platforms, to provide the optimal flight trajectory for the imposed lateral flight profile and time constraints.

Multicriteria trajectory optimisation is expected to increase aviation safety, efficiency and environmental compatibility, although neither the theoretical calculation of such optimised trajectories nor their implementation into today’s already safe and efficient air traffic flow management reaches a satisfying level of fidelity. The calibration of the underlying objective functions leading to the virtually best available solution is complicated and hard to identify, since the participating stakeholders are very competitive. Furthermore, operational uncertainties hamper the robust identification of an optimised trajectory. These uncertainties may arise from severe weather conditions or operational changes in the airport management. In this study, the impact of multicriteria optimised free route trajectories on the air traffic flow management is analysed and compared with a validated reference scenario which consists of real flown trajectories during a peak hour of Europe’s complete air traffic in the upper airspace. Therefore, the TOolchain for Multicriteria Aircraft Trajectory Optimisation (TOMATO) is used for both the multicriteria optimisation of txrajectories and the calculation of the reference scenario. First, this paper gives evidence for the validity of the simulation environment TOMATO, by comparison of the integrated reference results with those of the commercial fast-time air traffic optimiser (AirTOp). Second, TOMATO is used for the multicriteria trajectory optimisation, the assessment of the trajectories and the calculation of their integrated impact on the air traffic flow management, which in turn is compared with the reference scenario. Thereby, significant differences between the reference scenario and the optimised scenario can be identified, especially considering the taskload due to frequent altitude changes and rescinded constraints given by waypoints in the reference scenario. The latter and the strong impact of wind direction and wind speed cause wide differences in the patterns of the lateral trajectories in the airspace with significant influence on the airspace capacity and controller’s taskload. With this study, the possibility of a successful 4D free route implementation into Europe’s upper airspace is proven even over central Europe during peak hours, when capacity constraints are already reaching their limits.

The flatness of a six-degree-of-freedom (6DoF) aircraft model with conventional control surfaces – aileron, flap, rudder and elevator, along with thrust vectoring ability is established in this work. Trajectory optimisation of an aircraft can be cast as an inverse problem where the solution for control inputs that yield desired trajectories for certain states is sought. The solution to the inverse problems for certain systems is made tractable when they exhibit differential flatness. Flatness-based trajectory optimisation has a significant advantage over an equivalent collocation-based method in terms of computational efficiency and viability for real-time implementation. An application for the flatness of 6DoF aircraft is shown in the trajectory optimisation for dynamic soaring, and its connection with an equivalent 3DoF flatness-based implementation is also brought out. The results are compared with that from a collocation-based approach.

The increasing deployment of multiple unmanned vehicles systems has generated large research interest in recent decades. This paper therefore provides a detailed survey to review a range of techniques related to the operation of multi-vehicle systems in different environmental domains, including land based, aerospace and marine with the specific focuses placed on formation control and cooperative motion planning. Differing from other related papers, this paper pays a special attention to the collision avoidance problem and specifically discusses and reviews those methods that adopt flexible formation shape to achieve collision avoidance for multi-vehicle systems. In the conclusions, some open research areas with suggested technologies have been proposed to facilitate the future research development.

In this work, trajectory optimisation has been performed for a wing-body rocket assisted vehicle to compute the bestset of performance parameters including burn-out angle, angle-of-attack, bank-angle and throttle command that would result in optimal down-range and cross-range performance of the re-entry vehicle. An hp-adaptive Pseudospectral method has been used for the optimisation by combining the launch and rocket rocket-assisted re-entry stages. The purpose of the research is to compute optimal burn-out condition, angle-of-attack, bank-angle and optimal thrust segments that would maximise the down-range and cross-range performance of the hypersonic boost glide vehicle, under constrained heat rate environments. The variation of down-range/cross-range performance of rocket rocket-assisted hypersonic boost glide vehicle with bounds on diminishing heat rate has also been computed.