Optimal 4D Trajectory Planning for Multiple Aircraft in Continuous Descent Operations (original) (raw)

Multiaircraft Optimal 4D Trajectory Planning Using Logical Constraints

International Journal of Aerospace Engineering, 2019

This paper studies the trajectory planning problem for multiple aircraft with logical constraints in disjunctive form which arise in modeling passage through waypoints, distance-based and time-based separation constraints, decision-making processes, conflict resolution policies, no-fly zones, or obstacle or storm avoidance. Enforcing separation between aircraft, passage through waypoints, and obstacle avoidance is especially demanding in terms of modeling efforts. Indeed, in general, separation constraints require the introduction of auxiliary integer variables in the model; for passage constraints, a multiphase optimal control approach is used, and for obstacle avoidance constraints, geometric approximations of the obstacles are introduced. Multiple phases increase model complexity, and the presence of integer variables in the model has the drawback of combinatorial complexity of the corresponding mixed-integer optimal control problem. In this paper, an embedding approach is employ...

Multiphase Mixed-Integer Optimal Control Approach to Aircraft Trajectory Optimization

Journal of Guidance, Control, and Dynamics, 2013

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 nonlinearprogramming-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 during the flight. The decision-making process arises in determining the optimal sequence of waypoints. The optimal times at which the waypoints are to be overflown are also to be determined. Numerical results are presented and discussed, showing the effectiveness of the approach.

4D Trajectory Optimization Satisfying Waypoint and No-Fly Zone Constraints

WSEAS Transactions on Systems and Control archive, 2016

This paper presents a model of an innovative Flight Management System (FMS) which is purposely developed to control a commercial airliner along an optimized 4-Dimensional Trajectory (4DT), respecting time and path constraints, while avoiding No-Fly Zones (NFZ). The optimum, expressed in terms of minimum fuel consumption, is optained by solving an Optimization Control Problem (OCP) by means of the Chebyshev Pseudospectral numerical direct collocation scheme. The OCP trajectory solution is a discrete sequence of optimal aircraft states, which guarantee the minimum-fuel trip between two waypoints. With the aim of controlling the aircraft along lateral, vertical and longitudinal axis, and in order to respect NFZ and waypoints constraints along the optimum 4DT, different guidance navigation and control techniques can be implemented. The effectiveness of the algorithms is evaluated through simulations performed in the Multipurpose Aircraft Simulation Laboratory (MASLab), on a Boeing 747-1...

Aircraft trajectory planning with collision avoidance using mixed integer linear programming

American Control Conference, 2002. …, 2002

Describes a method for finding optimal trajectories for multiple aircraft avoiding collisions. Developments in spacecraft path-planning have shown that trajectory optimization including collision avoidance can be written as a linear program subject to mixed integer constraints, known as a mixed-integer linear program (MILP). This can be solved using commercial software written for the operations research community. In the paper, an approximate model of aircraft dynamics using only linear constraints is ...

En-Route Optimal Flight Planning Constrained to Pass Through Waypoints using MINLP

In this paper we present a Mixed Integer Non-Linear Programming (MINLP) formulation for aircraft trajectory planning. As illustration, we study the en-route strategic flight planning of a commercial aircraft constrained to pass through a set of waypoints whose sequence is not predefined. This problem has been solved as an hybrid optimal control problem in which, given the dynamic model of the aircraft, the initial and final states, the path constraints constituting the envelope of flight, and a set of waypoints in the European air space, one has to find the control inputs, the switching times, the optimal sequence of waypoints and the corresponding trajectory of the aircraft that minimize the direct operating cost during the flight. The complete layout of waypoints in the European airspace is reduced and waypoints are gathered into a small number of clusters. The aircraft is constrained to pass through one waypoint inside every cluster of waypoints. The presence of multi point constraints makes the optimal control problem particularly difficult to solve. The hybrid optimal control problem is converted into a MINLP problem first making the unknown switching times part of the state, then introducing binary variable to enforce the constraint of passing through one waypoint inside every cluster, and finally applying a direct collocation method. The resulting MINLP problem has been solved using a branch and bound algorithm. The cases studied and the numerical results show the effectiveness, efficiency and applicability of this method for en-route strategic flight plans definition.

MILP and NLP Techniques for centralized trajectory planning of multiple unmanned air vehicles

2006 American Control Conference, 2006

We consider the problem of optimal cooperative three-dimensional conflict resolution involving multiple Unmanned Air Vehicles (UAVs) using numerical trajectory optimization methods. The conflict problem is posed as an optimal control problem of finding trajectories that minimize a certain objective function while maintaining the safe separation between each UAV pair. We assume the origin and destination of the UAV are known and consider UAV models with simplified linear kinematics. The main objective of this report is to compare two different approaches to the solution of the problem. In the first approach, the optimal control is converted to a finite dimensional Nonlinear Program (NLP) by using collocation on finite elements and by reformulating the disjunctions involved in modeling the protected zones by using continuous variables. In the second approach the optimal control is converted to a finite dimensional Mixed Integer Linear Program (MILP) using Euler discretization and reformulating the disjunctions involved with the protected zones by using binary variables and Big-M techniques. Based on results of extensive random simulations, we compare time complexity and optimality of the solutions obtained with the MILP approach and the NLP approach. NLPs are essential to enforce flyability constraints on more detailed UAV models. The main objective of this paper is to open the route to the use of MILP solutions (based on simple linear UAV models) in order to initialize NLP solvers which allow the use of dynamic UAV models at any desired level of detail.

A Modified Dynamic Programming Approach for 4D Minimum Fuel and Emissions Trajectory Optimization

Aerospace, 2021

4D flight trajectory optimization is an essential component to improve flight efficiency and to enhance air traffic capacity. this technique not only helps to reduce the operational costs, but also helps to reduce the environmental impact caused by the airliners. This study considers Dynamic Programming (DP), a well-established numerical method ideally suited to solve 4D flight Trajectory Optimization Problems (TOPs). However, it bears some shortcomings that prevent the use of DP in many practical real-time implementations. This paper proposes a Modified Dynamic Programming (MDP) approach that reduces the computational effort and overcomes the drawbacks of the traditional DP. In this paper, two numerical examples with fixed arrival times are presented, where the proposed MDP approach is successfully implemented to generate optimal trajectories that minimize aircraft fuel consumption and emissions. Then the obtained optimal trajectories are compared with the corresponding reference c...

Synthesis of conflict-free aircraft flight trajectories using multi-criteria dynamic programming

Aviation

The paper discusses the problem of flight trajectory synthesis that is conducted to prevent potential conflict situations between two aircraft in air traffic. A method of multi-objective sequential synthesis of conflict-free flight trajectories is developed. This method provides the synthesis of Pareto conflict-free trajectories using multi-criteria dynamic programming and selection of the optimal trajectory. The paper also considers the principles of discretization concerning states and controls to apply dynamic programming. An analysis of the proposed method is performed using computer simulation.

Objective Function for 4D Trajectory Optimization in Trajectory Based Operations

AIAA Guidance Navigation and …, 2009

In the future Air Traffic Management (ATM) implementations based on 4D trajectories, both the ATM problems (safe separation, sequencing for the best runway utilization) and the flight management problems (best fuel efficiency) may be solved together using a multidisciplinary optimization of all aircraft 4D trajectories. The paper presents advancements on 4D navigation based on an objective function for the optimization process, which effectively models the total costs and risks of air navigation. The resulted gate-to-gate 4D trajectories generated by a dynamic model flight simulator for the specific type of aircraft with the individual initial Flight Management System data are "flyable", and they present the best cost-risks trade-offs. The paper also reveals results on some simulated experiments using genetic algorithms to minimize the objective function presented.