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The purpose of this communication is to contribute to the development of a new trajectory management capability for an engine-out transportation aircraft. Engine-out is a dramatic situation for flight safety and this study focuses on the design of a management system for emergency trajectories at this special situation. First the gliding characteri...
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... a two level weighting has been adopted: V max , z max and J max are scaling parameters and O V , O z and O J with O V O z O J 1 are positive relative weightings. The above approach which has been developed is basically an open loop approach and requires a very large computational effort which is unlikely to be performed on board an aircraft which is already in a critical engine-out situation. Our proposal here, which should be developed in the near future is to take profit of the amount of data generated by the reverse dynamic programming search process, considering different situations and parameters such as aircraft initial flight level, altitude and mass, to train a neural network devise designed to generate pitch angle directives at each point along the descent so that the glide trajectory leads safely to the landing situation. Here the computational burden associated with reverse dynamic programming is taken into profit to generate the training data base for the neural network [15]. The generated pitch angle directives can be either sent to the autopilot when it is still operating or to a flight director. In that last case this will allow this maneuver to be performed efficiently in manual mode by the pilot. Observe that along the glide trajectory, each new solicitation of the neural network will generate new piloting directives in accordance with the current situation of the aircraft which is also the result of external perturbations such as wind. A simulation study has been performed using the RCAM wide body transportation aircraft model [16]. Then considering the case in which an engine failure occurs 150km away from a possible landing site, different glide trajectories obtained by reverse dynamic programming are displayed on Figures 5. and on Figure 6 according to different initial situations. It appears that if the aircraft has a large initial total energy, which means high speed and/or high altitude, the resulting glide trajectory is not be very smooth: the speed and altitude are subject to large and rapid changes so that the aircraft loses energy in excess sufficiently quickly to arrive to the landing site with acceptable flying parameters. When initial total energy is not too much excessive, the resulting glide trajectories result to be smoother. For example, for initial conditions with an Figure 7. and Figure 8. display an optimized glide trajectory in the case in which initial altitude is 10km (FL330) and initial airspeed is 200m/s (about 400 knot) . Figure 9. and Figure 10. display the landing range which can be reached safely by an aircraft whose initial glide conditions are an altitude of 10km and an airspeed of 180m/s (about 360 knot). The largest obtained glide range is about 137 km while the shortest obtained glide range is 116 km. Then in that case, the gliding aircraft can reach safely landing sites located between 116km and 137km away. Observe on these figures that, the shorter the range, the rougher is the trajectory. Comparing figures 7. and Figure 9. , it appears also that with a higher initial airspeed the gliding aircraft range is also higher. These numerical results indicate that reverse dynamic programming can be used to solve the glide trajectory generation problem and contribute to the design of a glide trajectory generator either off line or on ...
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... Due to various controversies, the idea of aerial gliding vehicles (GVs) has evolved and matured over the time. Developments in the aviation industry led to the creation of both powered and unpowered GVs, where an unpowered GV relies on the dynamic interaction of the air with its wings and tail for gliding, and the velocity regime determines whether an unpowered GV is subsonic, transonic, supersonic, or hypersonic [1][2][3][4]. Nowadays, to convert a general purpose bomb (MK series) to a subsonic unpowered GV (SUGV), a wing adaptation kit or range extension kit is installed [5,6]. Figure 1 displays a further illustration of an SUGV known as the joint stand-off weapon (JSOW) [7]. ...
In many aero gliding vehicles, achieving the maximum gliding range is a challenging task. A frequent example is the breakdown of an engine during flight or the use of unpowered stand-off weapons. When an unpowered stand-off weapon begins gliding at a given height, it eventually strikes the ground after some distance, and height is considered a stopping constraint in this general condition. To avoid the time-scaling approach for the free time optimal problem, the maximum stoppable time with a stopping constraint is addressed to attain the maximum glide range. This problem can be chosen as an optimal gliding range problem which can be solved by direct or indirect methods. In this paper, the inverted Y-tail joint stand-off weapon is selected as the subsonic unpowered gliding vehicle (SUGV). After being released from dispersion points, the SUGV has to face fluctuating gliding flight because of flight phase transition that causes gliding range reduction. To achieve a damped and steady gliding flight while maximizing the gliding range, we propose a non-uniform control vector parameterization (CVP) approach that uses the notion of exponential spacing for the time vector. When compared with the maximum step input and conventional uniform CVP approach, simulations of the proposed non-uniform CVP approach demonstrate that the SUGV exhibits superior damping and steady gliding flight, with a maximum gliding range of 121.278 km and a maximum horizontal range of 120.856 km.
... Helton J, Nie J applied the SDP to solve the trajectory optimization and optimal control problems. Hongying W, Nayibe Chio C, Bouadi H, Lunlong Z, Mora-Camino F [2] proposed a reverse DP based on the Bellman's principle solution technique to develop a new trajectory management capability for an engineout transportation aircraft. Colombo C, Vasile M, Radice G; Aziz J D, Parker J S, Scheeres D J and Englander J A applied the DDP method to calculate the rendezvous trajectory to near-Earth objects and solve the optimal problem relatively. ...
This work aims to review the proposed trajectory optimization algorithms and their applications in solving flight trajectory planning and optimal control problems. Beside the classification of trajectory optimization algorithms listed in Chai R, Savvaris A, Tsourdos A and Chai S such as the deterministic; the stochastic; and the multi-objective algorithms, this work adds in reviewing the effective and frequently-used approach for solving optimal problems— the hybrid/combined methods. The results of related works show that this hybrid approach is effective and can provide feasible solutions for solving the flight vehicle trajectory optimal design and control problems.
... Wu et al. (2012) studies an application on emergency flight, in which the gliding trajectory of a commercial aircraft under engine failure must be optimised. The objective was finding a flyable descent trajectory for the aircraft in order to achieve a safe landing with certain speed and flight attitude.Crispin (2016) proposes the use of balloon launched autonomous gliders for atmospheric research. ...
In recent years, employing Unmanned Aerial Vehicles (UAV) to collect data and making measurements has gained popularity. Often, the use of UAVs allows for a reduction in costs and improvements of other performance criteria. The academic routing community has acknowledged the interest of companies and organisations in adopting UAVs in their operations. However, constraints due to the flight dynamics of UAVs have often been neglected. Finding feasible trajectories for UAVs in a routing problem is a complex task, but it is necessary to ensure the feasibility of the routes. In this thesis we introduce the Unmanned Aerial Vehicle Routing and Trajectory Optimisation Problem (UAVRTOP), the problem of optimising the routes and trajectories of a fleet of UAVs subject to flight dynamics constraints. Motivated by a disaster assessment application, we propose a variant of the UAVRTOP, in which a fleet of autonomous aerial gliders is required to photograph a set of points of interest in the aftermath of a disaster. This problem is referred to as the Glider Routing and Trajectory Optimisation Problem (GRTOP). In this work, we propose a single-phase Mixed-Integer Non-linear Programming (MINLP) formulation for the GRTOP. Our formulation simultaneously optimises routes and the flight trajectories along these routes while the flight dynamics of the gliders are modelled as ordinary differential equations. We avoid dealing with non-convex dynamical constraints by linearising the gliders’ Equations of Motion (EOMs), reducing the proposed MINLP into a Mixed-Integer Second-Order Cone Programming (MISOCP) problem. Another contribution of this work consists of proposing a multi-phase MINLP formulation for a modified version of the GRTOP. We do not attempt to solve this formulation directly, instead we propose a hybrid heuristic method that is composed of two main building blocks: (i) a Sequential Trajectory Optimisation (STO) heuristic, designed to cope with the challenging task of finding feasible (flyable) trajectories for a given route; and (ii) a routing matheuristic, capable of generating routes that can be evaluated by STO. We perform computational experiments with real-life instances based on flood risk maps of cities in the UK as well as in a large number of randomly generated instances.
... max A solution of this problem using optimality conditions from optimal control theory (Minimum Principle) appears improbable considering that this optimal control problem is over constrained. However, since the initial state is totally specified, it appears that Direct Dynamic Programming applied to a spatial discretization of this problem can provide straightforwardly a numerical solution [4], [5]. The optimal trajectory can then be summarized by: ...
The purpose of this communication is to investigate the interest of using a spatial reference for performing first aircraft trajectory generation and then trajectory tracking while overfly or arrival time constraints are imposed. The adoption of a space reference leads us to rewrite the aircraft flight dynamics. Then an aircraft trajectory optimization problem, including time constraints, is formulated and discussed. Then a new nonlinear control structure for trajectory tracking based on spatial reference is developed and simulation results are displayed.
When encountering atmospheric or exo-atmospheric spacecraft flight, a well-designed trajectory is essential for making the flight stable and enhancing the guidance and control of the vehicle. Much research has focused on how to design suitable spacecraft trajectories available for various mission profiles. To optimize the flight trajectory, researchers have designed numerous useful tools successfully. Nevertheless, it is only in the last five years that the interest in how to plan flight trajectories and consider numerous mission goals and different model errors/uncertainties simultaneously has grown greatly. Note that for various practical guidance, navigation and control systems for spacecraft, during the trajectory planning process, the frequent consideration of multiple performance indices and various forms of uncertainty is necessary. Consequently, the multi-objective spacecraft trajectory optimization methods and stochastic spacecraft trajectory optimization algorithms are successfully proposed with the help of the requirements mentioned above. The core aim of this chapter is to provide a wide overview of current developments in numerical multi-objective trajectory optimization algorithms and stochastic trajectory planning approaches for spacecraft flight operations. First, we will briefly describe the process of how the problem is formulated mathematically. Then several optimization strategies for addressing spacecraft trajectory planning problems, such as gradient-based methods, convexification-based methods, and evolutionary/metaheuristic methods, are discussed. Besides, we will overview the formulation process of the multi-objective spacecraft trajectory optimization problem, as well as multiple types of multi-objective optimization algorithms. The significant features, for example, the merits and demerits of the newly-proposed multi-objective approaches, are summarized. Furthermore, we will pay some attention to the extension of the original deterministic problem to a stochastic form. To handle the stochastic trajectory planning formulation, several robust optimization algorithms are also outlined. Additionally, applications of the optimized trajectory proposed recently will be especially focused on. Finally, we will draw some conclusions and discuss further research about strategies for multi-objective and stochastic trajectory optimization.
This chapter aims to broadly review the state-of-the-art development in spacecraft trajectory optimization problems and optimal control methods. Specifically, the main focus will be on the recently proposed optimization methods that have been utilized in constrained trajectory optimization problems and multi-objective trajectory optimization problems. An overview regarding the development of optimal control methods is first introduced. Following that, various optimization methods that can be effective for solving spacecraft trajectory planning problems are reviewed, including the gradient-based methods, the convexification-based methods, the evolutionary/metaheuristic methods, and the dynamic programming-based methods. In addition, a special focus will be given on the recent applications of the optimized trajectory. Finally, the multi-objective spacecraft trajectory optimization problem, together with different classes of multi-objective optimization algorithms, is briefly outlined at the end of the chapter.
For most atmospheric or exo-atmospheric spacecraft flight scenarios, a well-designed trajectory is usually a key for stable flight and for improved guidance and control of the vehicle. Although extensive research work has been carried out on the design of spacecraft trajectories for different mission profiles and many effective tools were successfully developed for optimizing the flight path, it is only in the recent five years that there has been a growing interest in planning the flight trajectories with the consideration of multiple mission objectives and various model errors/uncertainties. It is worth noting that in many practical spacecraft guidance, navigation and control systems, multiple performance indices and different types of uncertainties must frequently be considered during the path planning phase. As a result, these requirements bring the development of multi-objective spacecraft trajectory optimization methods as well as stochastic spacecraft trajectory optimization algorithms. This paper aims to broadly review the state-of-the-art development in numerical multi-objective trajectory optimization algorithms and stochastic trajectory planning techniques for spacecraft flight operations. A brief description of the mathematical formulation of the problem is firstly introduced. Following that, various optimization methods that can be effective for solving spacecraft trajectory planning problems are reviewed, including the gradient-based methods, the convexification-based methods, and the evolutionary/metaheuristic methods. The multi-objective spacecraft trajectory optimization formulation, together with different class of multi-objective optimization algorithms, is then overviewed. The key features such as the advantages and disadvantages of these recently-developed multi-objective techniques are summarised. Moreover, attentions are given to extend the original deterministic problem to a stochastic version. Some robust optimization strategies are also outlined to deal with the stochastic trajectory planning formulation. In addition, a special focus will be given on the recent applications of the optimized trajectory. Finally, some conclusions are drawn and future research on the development of multi-objective and stochastic trajectory optimization techniques is discussed.
This paper proposes an optimal control framework for the climb and descent economy modes of a flight management system (FMS) yielding a solution that can be implemented in real-time flights below the drag divergence Mach number. The problem is formulated as the optimization of a functional that trades off the fuel- and time-related costs of a flight as a function of a (crew-supplied) parameter called the cost index. The work builds on previous research of the authors for the cruise phase and extends it to the climb and descent phases of flight. More specifically, for both climb and descent, it is found that suboptimal solutions can be obtained as the positive real roots of a fifth-degree polynomial lying inside the flight envelope, which can be found using fast-converging algorithms such as Newton's method. The main contributions of this work are threefold. First, the proposed method gives physical insight because there is an analytical expression for each coefficient of the polynomial. Second, this approach eliminates the need to have a performance database in the system, thus making its implementation faster in real-time. Third, the solution exhibits the same behavior of airborne FMS units as a function of the cost index, which is justified in this paper based on Bellman's principle of optimality. This justification is an important theoretical contribution of the paper. A validation of the approximate solution is obtained using the shooting method to compute the optimal trajectories and compare them against the proposed suboptimal solution. Simulation results show that, for an Airbus A320 model and for a Gulfstream-IV aircraft model, the relative error of the suboptimal trajectories when compared to the optimal trajectories is small for climb and descent trajectories, respectively.
Engine-out is an undoubted critical situation for flight safety. The objective of this thesis is to improve the management of emergency manoeuvres for transportation aircraft once all engines go out at a given point during the flight. Here we consider the evolution of the gliding aircraft along a vertical plane possibly leading directly to a safe landing place. The gliding qualities of standard transportation aircraft are first analyzed and reachable areas from given initial situations are established. Once a safe reachable area exists the problem which is tackled here is to develop design principles for a guidance system which makes the aircraft perform a feasible glide trajectory towards such landing area. Reverse dynamic programming is used to build backwards sets of feasible trajectories leading to final conditions compatible with engine-out landing. To get an on-line device to produce efficient directives for the autopilot or the human pilot (through a flight director), a neural network is built from the generated database. Then simulation results are analyzed for validation and further improvements of the proposed approach are considered
The purpose of this communication is to contribute to the development of an emergency trajectory management capability for an engine-out transportation aircraft. First a representation of the flight dynamics of an engine-out aircraft is proposed where the space variable is chosen as independent parameter instead of the time variable. This allows to propose a spatial formulation of the corresponding trajectory optimization problem and to develop a reverse dynamic programming solution technique which generates data for the training of a neural network whose function is to generate feasible and safe reference values for the vertical guidance of the gliding aircraft. Simulation results are displayed and new development perspectives are discussed. © 2012 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.
