Fuel-Optimal, Low-Thrust, Three-Dimensional Earth-Mars Trajectories

Abstract

Fuel-optimal three-dimensional trajectories from Earth to Mars for spacecraft powered by a low-thrust rocket with variable speci c impulse capability are presented. The problem formulation treats the spacecraft mass as a state variable, thus coupling the spacecraft design to the trajectory optimization. Gravitational effects of the sun, Earth, and Mars are included throughout an entire trajectory. To avoid numerical sensitivity, the trajectory is divided into segments, each de ned with respect to a different central body. These segments are patched at intermediate time points, with proper matching conditions on the states and costates. The optimization problem is solved using an indirect multiple shooting method. Details of trajectories for the outbound legs of crewed missions to Mars, with trip times of 145 and 168 days, are shown. Effects due to variations in the trip time, departure and arrival orbit inclinations, initial fuel mass, and power level are investigated.

Optimal low-thrust trajectories to asteroids through an algorithm based on differential dynamic programming

“…The overall trajectory is divided in a sequence of problems, each of them expressed in the primary body reference frame; different segments are then patched together, through boundary constraints at the edge of each segment (direct methods), or through conditions on states and costates (indirect methods). Many applications have been presented, making use of direct methods (Tang and Conway 1995;Herman and Spencer 2002;, indirect methods (Guelman 1995;Vadali et al 2000;Nah et al 2001;Ranieri and Ocampo 2005), or hybrid methods (Pierson and Kluever 1994;Kluever and Pierson 1995).…”

Parallelized Model of Low-Thrust Cargo Spacecraft Trajectories and Payload Capabilities to Mars

“…So regardless of how long it takes to reach Mars on a certain trajectory, the spacecraft needs the same amount of ∆ . Therefore the main optimizing objective is the time of flight of the transfer, which is mostly dependent on the locations of the planets at a given time [12]. Although there will be a limit to how fast the spacecraft can reach Mars due to the extremely low thrust of the ion engines, we still would like a reasonably quick transfer.…”

Minimum-Time Earth-to-Mars Interplanetary Orbit Transfer Using Adaptive Gaussian Quadrature Collocation

“…A great deal of research has been done previously on the design of low-thrust orbital transfers [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]. Refs.…”

“…Refs. [3,4,5,6] solved minimum-fuel optimal control problems by solving the Hamiltonian boundary-value problem (HBVP) arising from the calculus of variations. In particular, Ref.…”

“…In particular, Ref. [5] used an indirect multiple-shooting method to solve a three-dimensional minimum-fuel Earth-to-Mars orbital trajectory for a low-thrust spacecraft, while Ref. [6] transformed the HBVP into the Cauchy problem through the use of the continuation (homotopic) method.…”