Interplanetary Trajectory Optimization of Spacecraft Driven by Solar Electric Propulsion System with Cluster of Similar Thrusters

Аuthors

Woo S. W.

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

e-mail: sanukk@hanmail.net

Abstract

Interplanetary space missions often require large velocity increment leading to necessity to use the main solar electric propulsion systems (SEPS) with high specific impulse to decrease propellant consumption. Electric propulsion system with constant power consumption makes it necessary either excessive increase in the size and mass of the solar arrays or excessive decrease in the consumed power and thrust to provide SEPS operation at the greatest distance from the Sun. Therefore usage of non-adjustable thrusters leads to necessity of using a cluster of the thrusters in the composition of SEPS to permit most efficient power regulation of SEPS using maximum permissible number of operating thrusters depending on the available electric power. The interplanetary trajectory optimization of spacecraft driven by solar electric propulsion system with cluster of similar thrusters is considered. Fixed-time propellant minimization problem is considered. The technique uses Pontryagin maximum principle to reduce the optimal control problem to the boundary value problem and continuation method to reduce the boundary value problem to the initial value problem. Solution of the power-limited trajectory optimization problem is used as initial guess values for initial values of the costate variables. The power-limited trajectory optimization method does not require a user-supplied initial guess. The continuation parameter is introduced into right-hand parts of differential equations of optimal motion to provide the coincidence of these differential equations to the power-limited problem at zero value of the parameter and to the staircase-thrust problem when the parameter equals to one. The smoothed dependencies of the step function of thrust switching and staircase-thrust function are used to provide convergence of the continuation technique. Numerical experiments show good convergence and computational productivity of the presented technique. Presented numerical examples demonstrate importance of consideration the stepped thrust profile at early phases of mission design.

Keywords:

solar electric propulsion system, heliocentric trajectory, Pontryagin maximum principle, continuation technique

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