Manuel Soler

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

Multiphase Mixed-Integer Optimal Control Approach to Aircraft Trajectory Optimization

In this paper, an approach to aircraft trajectory optimization is presented in which integer and continuous variables are considered. Integer variables model decision-making processes, and continuous variables describe the state of the aircraft, which evolves according to differential-algebraic equations. The problem is formulated as a multiphase mixed-integer optimal control problem. It is transcribed into a mixed-integer nonlinear programming problem by applying a fifth degree Gauss–Lobatto direct collocation method and is then solved using a nonlinear-programming-based branch-and-bound algorithm. The approach is applied to the following en route flight planning problem: Given an aircraft point mass model, a wind forecast, an airspace structure, and the relevant flying information regions with their associated overflying costs, find the control inputs that steer the aircraft from the initial fix to the final fix, following a route of waypoints while minimizing the fuel consumption and overflying costs d...

Contrail sensitive 4D trajectory planning with flight level allocation using multiphase mixed-integer optimal control

In this paper we study the contrail sensitive 4D trajectory planning problem considering 0-1 binary variables to model decision-making processes. The problem we study can be described as follows: given an aircraft point mass dynamical model, a route composed by a sequence of waypoints, and the airspace’s flight level structure, find the control inputs that steer the aircraft from the initial fix to the final fix following the horizontal route of waypoints and performing the permitted step climbs to change flight level, while minimizing the fuel consumption, CO2 emissions, and contrail formation impact during the flight. The decision making process arises in determining the optimal allocation of flight levels for the flight. The times at which both the waypoints and the different flight levels are reached are also to be determined. The problem is formulated as a multiphase mixed-integer optimal control problem, which is converted into a mixed integer non linear programming problem first making the unknown switching times part of the state, then applying a 5th degree Gauss-Lobatto direct collocation method, and finally introducing binary variables to model the decision making process. The resulting mixed integer non linear programming problem has been solved using a nonlinear programming based branch and bound algorithm. The numerical results are presented and discussed, showing the effectiveness of the approach.

A Hybrid Optimal Control Approach to Fuel-Efficient Aircraft Conflict Avoidance

We formulate fuel-optimal conflict-free aircraft trajectory planning as a hybrid optimal control problem. The discrete modes of the hybrid system capture the air traffic procedures for conflict resolution, e.g., speed and turn advisories. To solve problems of realistic dimensions arising from air traffic sector planning, we formulate a numerically tractable approach to solve the hybrid optimal control problem. The approach is based on introducing binary functions for each mode, relaxing the binary functions and including a penalty term on the relaxation. The transformed and discretized problem is a nonlinear program. We use the approach on a realistic case study with seven aircraft within an air traffic control sector, in which we find minimum-fuel conflict-free trajectories.

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

Abstract The 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.

Multiphase mixed-integer optimal control applied to 4D trajectory planning in air traffic management

In this paper an approach to aircraft trajectory optimization is presented in which integer variables and continuous variables are considered. Integer variables model decision making processes, and continuous variables describe the state of the aircraft which evolves according to differential-algebraic equations. The problem is formulated as a multiphase mixed-integer optimal control problem. It is transcribed into a mixed integer nonlinear programming problem by applying a 5th degree Gauss-Lobatto direct collocation method and then solved using a nonlinear programming based branch-and-bound algorithm. The approach is applied to the following en-route flight planning problem: given an aircraft point mass model, a wind forecast, a 3D airspace structure, and the relevant flying information regions with their associated overflying costs, find the control inputs that steer the aircraft from the initial fix to the final fix following a route of waypoints and performing step climbs, while minimizing certain performance indexes in which fuel based, environmental based, time based, and overflying based costs are considered during the flight. The decision making process arises in determining the optimal sequence of waypoints and the optimal sequence of flight levels. The optimal times at which the step climbs are performed and the waypoints are to be overflown are also to be determined. Numerical results are presented and discussed, showing the effectiveness of the approach.

Collocation Methods to Minimum-Fuel Trajectory Problems with Required Time of Arrival in ATM

In the future air traffic management system, the trajectory becomes the fundamental element of a new set of operating procedures collectively referred to as trajectory-based operations. Trajectory-based operations require the air traffic management to introduce profound innovations to enable the envisioned changes. Some of these include collaborative decision-making processes, better data and information management, and advanced decision support tools to aid human operators. In particular, fast and accurate computation of optimal trajectories could certainly contribute to enhance trajectory management within the future air traffic management. The trajectory optimization problem can be solved using optimal control methods. In this paper, the existing methods for solving optimal control problems focusing on direct collocation are discussed. In particular, pseudospectral collocation methods have shown to be numerically more accurate and computationally much faster than other direct methods. A very relevant p...

Multiphase mixed-integer optimal control framework for aircraft conflict avoidance

This paper formulates the problem of aircraft conflict avoidance as a multiphase mixed-integer optimal control problem. In order to find optimal maneuvers, accurate models of aircraft nonlinear dynamics and flight envelop constraints are used. Wind forecast and obstacles in airspace due to hazardous weather are included. The objective is to design aircraft maneuvers that ensure safety while minimizing fuel consumption. The solution approach is based on conversion of the multiphase mixed-integer optimal control problem into a mixed-integer nonlinear programming problem. Two case studies for the Airbus 320 aircraft illustrate the approach.

Automated optimal flight planning based on the aircraft intent description language

The future air traffic management system is to be built around the notion of trajectory-based operations. It will rely on automated tools related to trajectory prediction in order to define, share, revise, negotiate and update the trajectory of the aircraft before and during the flight, in some case, in near real time. This paper illustrates how existing standards on trajectory description such as the aircraft intent description language can be enhanced including optimisation capabilities based on numerical optimal control. The Aircraft Intent Description Language is a formal language that has been created in order to describe aircraft intent information in a rigorous, unambiguous and flexible manner. It has been implemented in a platform for a modular design of the trajectory generation process. A case study is presented to explore its effectiveness and identify the requirements and needs to generate optimised aircraft intents with higher automation and flexibility. Preliminary results show the suitability of numerical optimal control to design optimised aircraft intents based on the aircraft intent description language.

On maximizing safety in stochastic aircraft trajectory planning with uncertain thunderstorm development

Abstract Dealing with meteorological uncertainty poses a major challenge in air traffic management (ATM). Convective weather (commonly referred to as storms or thunderstorms) in particular represents a significant safety hazard that is responsible for one quarter of weather-related ATM delays in the US. With commercial air traffic on the rise and the risk of potentially critical capacity bottlenecks looming, it is vital that future trajectory planning tools are able to account for meteorological uncertainty. We propose an approach to model the uncertainty inherent to forecasts of convective weather regions using statistical analysis of state-of-the-art forecast data. The developed stochastic storm model is tailored for use in an optimal control algorithm that maximizes the probability of reaching a waypoint while avoiding hazardous storm regions. Both the aircraft and the thunderstorms are modeled stochastically. The performance of the approach is illustrated and validated through simulated case studies based on recent nowcast data and storm observations.