Flight trajectory design in the presence of contrails: Application of a multiphase mixed-integer optimal control approach

In this paper we study the 4D trajectory planning problem in a contrail sensitive environment. We identify the control inputs that steer the aircraft from the initial fix to the final fix following a horizontal route of waypoints while performing step climbs and descents, in order to minimize the overall flying cost of fuel consumption, CO2 emissions, passenger travel time, and persistent contrail formation. The optimal trajectory design problem is formulated as a multiphase mixed integer optimal control problem, which is converted into a mixed integer non-linear program by first making the unknown switching times part of the state, then applying a Hermite-Simpson direct collocation method, and finally introducing binary variables to model the decision making. We solve the mixed-integer nonlinear program using a branch-and-bound algorithm. The numerical results show the effectiveness of the approach.This research was carried out at NEXTOR, University of California at Berkeley, where Manuel Soler was a visiting scholar hosted by Prof. Mark Hansen. The authors would like to thank all members of NEXTOR at UC Berkeley for fruitful and interesting discussions. This work was partially financed by Universidad Rey Juan Carlos (URJC) encouraging mobility in PhD candidates with the following program: Programa propio de fomento y desarrollo de la investigación. This research was also partially sponsored by the NASA Ames-UC Santa Cruz, University Affiliated Research Center Aligned Research Program