Aircraft Trajectory Planning Research Articles

Holistic Approach for Aircraft Trajectory Optimization Using Optimal Control

This paper deals with an optimal control approach for commercial aircraft trajectory planning, focusing on the vertical path and the minimization of the fuel burned. The main contribution is the optimization of the whole trajectory, also called the mission, without prior separation into different flight phases (climb, cruise, and descent), contrary to traditional approaches that consider the flight phases sequentially. The proposed optimal control problem (OCP) is formulated and then solved using a direct collocation method. Initial results yield optimal trajectories with a gradual climb during the cruise (climb cruise), which correspond to theoretical trajectories that minimize fuel consumption. Furthermore, a penalization is introduced to ensure vertical profiles featuring horizontal cruise levels on so-called flight levels, compliant with current air traffic management regulations. The use of direct methods to address this OCP induces large nonlinear optimization problems that are solved using an interior point method. This methodology is likely to lead to poor local optima, but a simple multistart heuristic shows that the solutions found for standard problems appear to be globally optimal. Such an approach does not need to impose a priori the cruise flight levels and is suitable for commercial aircraft flight planning purposes. It leads to fuel saving and subsequently to important improvements against environmental impact by reducing emissions.

The role of airspeed variability in fixed-time, fuel-optimal aircraft trajectory planning

With the advent of improved aircraft situational awareness and the need for airlines to reduce their fuel consumption and environmental impact whilst adhering to strict timetables, fixed-time, fuel-optimal routing is vital. Here, the aircraft trajectory planning problem is addressed using optimal control theory. Two variants of a finite horizon optimal control formulation for fuel burn minimization are developed, subject to arrival constraints, an aerodynamic fuel-burn model, and a data-driven wind field. In the first variant, the control variable is expressed as a set of position-dependent aircraft headings, with the optimal control problem solved through a reduced gradient approach at a range of fixed airspeeds. The fuel optimal result is taken as the lowest fuel use recorded. In the second variant, both heading angle and airspeed are controlled. Results from three months of simulated flight routes between London and New York show that permitting optimised en-route airspeed variations leads to fuel savings of 0.5% on an average day (and up to 4% on certain days), compared with fixed airspeed flights. We conclude that significant fuel savings are possible if airspeeds are allowed to vary en route to take optimal advantage of the wind field.

Fundamental Framework to Plan 4D Robust Descent Trajectories for Uncertainties in Weather Prediction

Aircraft trajectory planning is affected by various uncertainties. Among them, those in weather prediction have a large impact on the aircraft dynamics. Trajectory planning that assumes a deterministic weather scenario can cause significant performance degradation and constraint violation if the actual weather conditions are significantly different from the assumed ones. The present study proposes a fundamental framework to plan four-dimensional optimal descent trajectories that are robust against uncertainties in weather-prediction data. To model the nature of the uncertainties, we utilize the Global Ensemble Forecast System, which provides a set of weather scenarios, also referred to as members. A robust trajectory planning problem is constructed based on the robust optimal control theory, which simultaneously considers a set of trajectories for each of the weather scenarios while minimizing the expected value of the overall operational costs. We validate the proposed planning algorithm with a numerical simulation, assuming an arrival route to Leipzig/Halle Airport in Germany. Comparison between the robust and the inappropriately-controlled trajectories shows the proposed robust planning strategy can prevent deteriorated costs and infeasible trajectories that violate operational constraints. The simulation results also confirm that the planning can deal with a wide range of cost-index and required-time-of-arrival settings, which help the operators to determine the best values for these parameters. The framework we propose is in a generic form, and therefore it can be applied to a wide range of scenario settings.

Multiple-Aircraft-Conflict Resolution Under Uncertainties

A new method for efficient trajectory planning to resolve potential conflicts among multiple aircraft is proposed. A brief review of aircraft trajectory planning and conflict resolution methods is given first. Next, a new method is proposed that is based on a probabilistic conflict risk map using the predicted probability of conflict with the intention information of the intruders. The risk-map-based method allows the path planning algorithm to simultaneously account for many uncertainties affecting safety, such as positioning error, wind variability, and human errors. Following this, A* algorithm is used to find the cost-minimized trajectory for a single aircraft by considering all other aircraft as intruders. Search heuristic method is implemented to iterate the A* algorithm for all aircraft to optimize the trajectory planning. Convergence and computation efficiency of the proposed method are investigated in detail. Numerical examples are used to illustrate the effectiveness of the proposed method under several important scenarios for air traffic control, such as wind effects, non-cooperative aircraft, minimum disturbance of pilots, and deconflict with flight intent information. Several conclusions are drawn based on the proposed method.

Research on rapid planning of intelligent aircraft trajectory under multiple constraints

Intelligent aircraft trajectory planning is an important support to ensure the successful completion of the mission of the aircraft, and it is also a key component of the intelligent aircraft mission planning system. Due to system performance constraints and environmental constraints, the positioning system of the intelligent aircraft cannot be accurately positioned during flight, which will cause flight errors. Excessive flight errors will lead to the failure of the mission. Therefore, error correction plays an increasingly important role in trajectory planning. This paper studies the rapid trajectory planning of intelligent aircraft under the limitation of system positioning accuracy. Based on the optimization theory, with the error generation rules and correction rules of the intelligent aircraft in flight as constraints, establishes the optimization model, and uses the fast non-dominated multi-objective optimization algorithm (NSGA-II) with elite retention strategy. This paper corrects the vertical and horizontal errors during the flight, and finally designs a reasonable intelligent aircraft trajectory that meets the minimum trajectory length and the minimum number of corrections during the flight.

Metaheuristic Approach for Distributed Trajectory Planning for European Functional Airspace Blocks

The functional airspace block (FAB) concept is adopted by European airspace to allow cooperation between airspace users to manage the air traffic flow, while ensuring efficiency, safety, and fairness without the constraints of geographical boundaries. This integration of airspaces allows for flexibility in airspace management and aircraft trajectory planning. This paper proposes a distributed air traffic flow management model to address four-dimensional trajectory planning over the European FAB. The proposed method is based on a metaheuristic approach that uses a hybrid algorithm of simulated annealing and hill-climbing local search to separate a given set of aircraft trajectories in space and time domain (termed as flight interaction), by allocating an alternative flight plan (route and departure time) to each flight. An innovative data structure, termed as FAB–flight interaction matrix, captures the flight interaction information between and within FABs. The proposed distributed model is implemented and tested with two air traffic data sets comprising 4000 flights (3 h traffic) and 26,000 flights (one full day traffic data over the European airspace). The performance of the model is then compared with a centralized air traffic flow management model on scalability and interaction minimization. Results indicates that, though both approaches were able to achieve interaction-free trajectory planning within computational time acceptable for the operational context, the distributed model converges faster to an interaction-free solution as traffic size increases, which shows the viability of the distributed model for effective FAB implementation.

Robust Aircraft Trajectory Planning Under Wind Uncertainty Using Optimal Control

Uncertainty in aircraft trajectory planning and prediction generates major challenges for the future air traffic management system. Therefore, understanding and managing uncertainty will be necessary to realize improvements in air traffic capacity, safety, efficiency, and environmental impact. Meteorology (in particular, winds) represents one of the most relevant sources of uncertainty. In the present work, a framework based on optimal control is introduced to address the problem of robust and efficient trajectory planning under wind forecast uncertainty, which is modeled with probabilistic forecasts generated by ensemble prediction systems. The proposed methodology is applied to a flight planning scenario under a free-routing operational paradigm and employed to compute trajectories for different sets of user preferences, exploring the trade-off between average flight cost and predictability. Results show how the impact of wind forecast uncertainty in trajectory predictability at a pretactical planning horizon can be not only quantified, but also reduced through the application of the proposed approach.

Entropy Minimizing Curves with Application to Flight Path Design and Clustering

Air traffic management (ATM) aims at providing companies with a safe and ideally optimal aircraft trajectory planning. Air traffic controllers act on flight paths in such a way that no pair of aircraft come closer than the regulatory separation norms. With the increase of traffic, it is expected that the system will reach its limits in a near future: a paradigm change in ATM is planned with the introduction of trajectory based operations. In this context, sets of well separated flight paths are computed in advance, tremendously reducing the number of unsafe situations that must be dealt with by controllers. Unfortunately, automated tools used to generate such plannings generally issue trajectories not complying with operational practices or even flight dynamics. In this paper, a mean of producing realistic air routes from the output of an automated trajectory design tool is investigated. For that purpose, the entropy of a system of curves is first defined and a mean of iteratively minimizing it is presented.The resulting curves form a route network that is suitable for use in a semi-automated ATM system with human in the loop. The tool introduced in this work is quite versatile and may be applied also to unsupervised classification of curves: an example is given for the french traffic.

Optimization of Path-Constrained Systems using Pseudospectral Methods applied to Aircraft Trajectory Planning

Numerical optimal control techniques play an increasingly relevant role in trajectory planning for aerial vehicles. In the last decade, pseudospectral methods have been identified as a powerful alternative to other direct methods in numerical optimal control. We study the applicability and performance of pseudospectral methods when applied to problems involving systems with inequality path constraints such as aircraft trajectory optimization problems. We show that activation or deactivation of path constraints introduce non-smooth features in the solution that degrade the properties of pseudospectral methods, but proper reformulation of the problem as a multiphase problem preserves them. We finally propose an adaptive algorithm that automatically designs an appropiate multiphase reformulation of an optimal control problem. The results show that our method improves the accuracy of the numerical solution compared to direct application of the pseudospectral method.

A novel trajectory planning strategy for aircraft emergency landing using Gauss pseudospectral method

To improve the survivability during an emergency situation, an algorithm for aircraft forced landing trajectory planning is proposed. The method integrates damaged aircraft modelling and trajectory planning into an optimal control framework. In order to deal with the complex aircraft flight dynamics, a solving strategy based on Gauss pseudospetral method (GPM) is presented. A 3-DOF nonlinear mass-point model taking into account the wind is developed to approximate the aircraft flight dynamics after loss of thrust. The solution minimizes the forced landing duration, with respect to the constraints that translate the changed dynamics, flight envelope limitation and operational safety requirements. The GPM is used to convert the trajectory planning problem to a nonlinear programming problem (NLP), which is solved by sequential quadratic programming algorithm. Simulation results show that the proposed algorithm can generate the minimum-time forced landing trajectory in event of engine-out with high efficiency and precision.

Aircraft Trajectory Planning Under Uncertainty by Light Propagation

In the SESAR framework (Single European Sky ATM Research), the need to increase the air traffic capacity motivated the 4D (space + time) aircraft trajectory planning. This paper deals with an important Air Traffic Management (ATM) problem that consists in generating sets of 4D conflict-free trajectories (the tactical planning problem). The Light Propagation Algorithm (LPA) was introduced in [1] to deal with this problem. LPA has recently been shown to manage successfully a full day of traffic over the French airspace, removing all conflicts while satisfying ATM constraints.In this paper, we adapt the LPA to take into account uncertainties in trajectory prediction. We introduce and test a new algorithm called u/LPA (LPA under uncertainty) on the same day of traffic. For some situations, uncertainties reduce so much the search space that the standard algorithm cannot guarantee conflict free situation. As a consequence, one must include some time constraints for few trajectories (so-called RTA points: Real Time of Arrival constraints) in order to remove the remaining conflicts. The goal of RTA points is to impose an aircraft to be at a specified position at some given time. This results into a new optimization formulation of the tactical trajectory planning problem involving the decision as to where/when RTA points should be imposed. In order to solve this new problem, here we are content with a simple heuristic that yields encouraging results.

A light-propagation model for aircraft trajectory planning

Predicted air traffic growth is expected to double the number of flights over the next 20 years. If current means of air traffic control are maintained, airspace capacity will reach its limits. The need for increasing airspace capacity motivates improved aircraft trajectory planning in 4D (space+time). In order to generate sets of conflict-free 4D trajectories, we introduce a new nature-inspired algorithm: the light propagation algorithm (LPA). This algorithm is a wavefront propagation method that yields approximate geodesic solutions (minimal-in-time solutions) for the path planning problem, in the particular case of air-traffic congestion. In simulations, LPA yields encouraging results on real-world traffic over France while satisfying the specific constraints in air-traffic management.

Hybrid Optimal Control for Aircraft Trajectory Design with a Variable Sequence of Modes

AbstractThe problem of aircraft trajectory planning is formulated as a hybrid optimal control problem. The aircraft is modeled as a switched system, that is, a class of hybrid dynamical systems. The sequence of modes, the switching times, and the inputs for each mode are the control variables. An iterative bi-level optimization algorithm is employed to solve the optimal control problem. At the lower level, given a pre-defined sequence of flight modes, the optimal switching times and the input for each mode are determined. This is achieved by extending the continuous state to include the switching times and then solving a conventional optimal control problem for the extended state. At the higher level, the algorithm modifies the mode sequence in order to decrease the value of the cost function. We illustrate the utility of the problem formulation and the solution approach with two case studies in which short horizon aircraft trajectories are optimized in order to reduce fuel burn while avoiding hazardous weather.

Hybrid Optimal Control Approach to Commercial Aircraft Trajectory Planning

CD = coefficient of drag CD0 = coefficient of parasite drag CL = coefficient of lift CLmax = maximum coefficient of lift CTc;4 = first thrust temperature coefficient CVmin = minimum speed coefficient D = drag force, 0:5 VSCD Gt = temperature gradient on maximum altitude GW = mass gradient on maximum altitude g = acceleration due to gravity h = altitude hM0 = maximum operating altitude hmax = maximum altitude at maximum takeoff weight under Instrument Society of America conditions hu = maximum dynamic altitude K = coefficient of induced drag L = lift force, 0:5 VSCL M = Mach number MM0 = maximum operating Mach number m = mass _ m = fuel flow mmax = maximum mass (maximum takeoff weight) mmin = minimum mass (operating empty weight) _ mmin = minimum fuel flow S = reference wing surface area T = thrust Tmax = maximum thrust V = true airspeed VCAS = calibrated airspeed VM0 = maximum operating calibrated airspeed Vstall = stall speed x = distance = angle of attack TISA = temperature deviation from International Standard Atmosphere = thrust specific fuel flow = flight-path angle = atmospheric density

Aircraft Trajectory Planning for Terrain Following Incorporating Actuator Constraints

The problem of navigating an aircraft over and through terrain is an important problem in trajectory planning. Typically, only two-dimensional motion of the aircraft (longitudinal aircraft control) is considered for such problems despite the fact that better terrain following may be achieved by following a three-dimensional trajectory. Furthermore, in collision avoidance maneuvers, pulling the aircraft up is not always the optimal method for avoiding terrain and climbing turns or lateral maneuvers must sometimes be considered. It is well recognized that terrain-following trajectories are important for many military aircraft in defense applications.