Citation: A. Gardi and R. Sabatini, “Outline of Multi-Objective Flight Trajectory Optimisatiuon Techniques for Environmental Impact Estimation and Mitigation.” Second International Symposium on Sustainable Aviation (ISSA 2016). Istanbul, Turkey. 29 May – 1 June 2016. OUTLINE OF MULTI-OBJECTIVE FLIGHT TRAJECTORY OPTIMISATION TECHNIQUES FOR ENVIRONMENTAL IMPACT ESTIMATION AND MITIGATION Alessandro Gardi and Roberto Sabatini RMIT University – School of Engineering PO Box 71, Bundoora, VIC 3083, Australia Authors' e-mails: roberto.sabatini@rmit.edu.au SUMMARY This paper presents the techniques available to optimise the trajectories of commercial transport aircraft with respect to multiple environmental criteria. The trajectory optimisation problem is formulated as an optimal control problem with boundary conditions, dynamic and path constraints and a variable performance index. Specific models for pollutant emissions, contrails and fuel consumption are integrated, together with apposite models for airspace and operational constraints. The pollutant emission models also allow for a quantitative estimation of the environmental impacts. Keywords: trajectory optimisation, aircraft emissions, optimal control, multi-objective, fuel burn, pseudospectral methods. INTRODUCTION More effective and comprehensive implementations of flight trajectory optimisation techniques are being considered as a very promising pathway to enhance the sustainability of aircraft operations both in short and long-haul travels. The fundamental proposition is not new, but state-of-the-art flight planning methods are still based on the optimised vertical planning techniques initially developed in the 1970s (Barman & Erzberger, 1976; Erzberger & Lee, 1978, 1980; Erzberger et al., 1975; Lee & Erzberger, 1980; Sorensen et al., 1979), and on lateral path planning based on optimal wind routing. The known limitations are associated to the limited set of optimality criteria (currently only fuel- and time- costs) and to the fact that the initial flight plan is the static entity assumed as a reference for every subsequent amendment. As a result, the limited initial optimality is progressively compromised when strategic or tactical Air Traffic Management (ATM) and Air Traffic Flow Management (ATFM) amendments are introduced. Suitably defined models can replicate the various operational and environmental aspects that depend on the flown aircraft trajectory, allowing for accurate Multi-Objective Trajectory Optimisation (MOTO) studies. PROBLEM FORMULATION Trajectory optimisation studies methods to determine the best possible trajectory of a dynamical system in a finite-dimensional manifold, in terms of specific objectives and adhering to given constraints and boundary conditions (Gardi et al., 2016). This definition corresponds to the definition of Optimal Control Problems (OCP), and consequently the most traditional and theoretically rigorous way to pose a Trajectory Optimisation Problem (TOP) is based on the optimal control theory. Most OCP solution methods are conventionally categorised as either direct methods if based on the transcription to a finite Non-Linear Programming (NLP) problem, or indirect methods if theoretical derivations based on the calculus of variation are implemented to formulate a Boundary-Value-Problem (BVP)