Lorenzo Casalino

Optimal Design of Hybrid Rocket Motors for Microgravity Platform

A nested direct/indirect method is used to find the optimal design for a microgravity platform which is based on a hybrid sounding rocket. The direct optimization of the parameters that affect the motor design is coupled with the indirect trajectory optimization to maximize a given mission performance index. A gas-pressure feed system is used, with three different propellant combinations. The feed system exploits a pressurizing gas, namely, helium, when hydrogen peroxide or liquid oxygen is used as an oxidizer. The simplest blowdown design is compared with a more complex pressurizing system, which has an additional gas tank that allows for a phase with constant propellant tank pressure. Only self-pressurization is considered with nitrous oxide; two different models are used to describe the behavior of the tank pressurization. The simplest model assumes liquid/vapor equilibrium. A two-phase model is also proposed: Saturated vapor and superheated liquid are considered and the liquid/vapor mass transfer evaluation is based on the liquid spinodal line. Results show that the different tank-pressurization models yield minimal differences of the optimal motor characteristics. Performance differs slightly due to the different mass of the residual oxidizer. The propellant comparison for the present case shows better performance for hydrogen peroxide/ polyethylene with respect to liquid oxygen/hydroxyl-terminated polybutadiene, while nitrous oxide/hydroxyl-terminated polybutadiene remains attractive for system simplicity and low costs.

Indirect optimization of low-thrust capture trajectories

The theory of optimal control is used to find the best trajectories for the capture maneuver of an interplanetary probe, which employs electric propulsion. The thrust magnitude and direction are optimized to exploit the spacecraft continuous steering capabilities and maximize the spacecraft final mass. Strategies, which involve propelled and coast arcs, are analyzed. The influence on the optimal trajectories of some parameters, such as the thrust, the specific impulse, and the initial velocity, is also discussed

Hybrid Evolutionary Algorithm for the Optimization of Interplanetary Trajectories

A hybrid evolutionary algorithm is applied to the optimization of space missions with multiple impulses and gravity assists. The optimization procedure runs three different optimizers, based on genetic algorithms, differential evolution and particle swarm optimization, in parallel; the algorithms are used synergistically by letting the best individuals, found by each algorithm, migrate to the others at prescribed intervals. A mass mutation operator is also employed to diversify the population and avoid premature convergence to suboptimal solutions. A module based on an enhanced continuous tabu search algorithm is introduced in the initialization process to produce a good starting population for the optimization algorithm. The results show the good performance obtained with the hybrid algorithm and the improvement in terms of efficiency and computational cost which is provided, in most cases, by the tabu search initialization process.

Genetic Algorithm and Indirect Method Coupling for Low-Thrust Trajectory Optimization

A genetic algorithm is used to find suitable tentative solutions for an indirect optimization method for electric propulsion trajectories. The application of optimal control theory produces a boundary value problem; the genetic algorithm searches for the combination of unknown parameters that minimizes the error on the boundary conditions; the best (i.e., minimum-error) combination is then provided as a tentative guess to the indirect optimization code to obtain a converged solution. The procedure is tested by analyzing direct and multiple-gravity-assist missions to Mars; results show that the procedure is effective in finding many local optima and missions with different trip times in the case of direct trajectories, and does not require particular knowledge by the user; a simple technique must be used to find suitable initial guesses for more complex missions with planetary flybys.

Optimal Control Law for Interplanetary Trajectories with Nonideal Solar Sail

An indirect method is applied to minimize the trip time of interplanetary and escape missions using solar sails. A e at sail and specular ree ection of the incident radiation is assumed. The theory of optimal control provides the equation that gives the optimal orientation of the sail at each point of the trajectory. An analytical solution can be obtained in the ideal case (unit ree ectivity ) when all of the incident radiation is specularly ree ected. The equation is numerically solved when the incident radiation is partially absorbed (nonunit ree ectivity ). Once the ree ectivity has been assumed, the optimal trajectory only depends on the sail characteristic acceleration. The optimization procedure has been used to estimate the performance of different missions; the ine uence of the sail ree ectivity is in particular pointed out. Transfers to Mars and Mercury and escape from the solar system are presented.

Optimization of DV-Earth-Gravity-Assist Trajectories

An analysis of delta-velocity Earth-gravity-assist (D V-EGA) trajectories is carried out by using an indirect optimization method. In comparison to previous literature, the eccentricity of the Earth’ s orbit is taken into account, and simplifying assumptions, concerning the position and direction of velocity impulses, are removed. However, the focus is on the application of the theory of optimal control to complex interplanetary missions and D V-EGA trajectories are only illustrative examples. In particular, it is shown that the optimization of this kind of mission, according to the patched-conic approximation, can be obtained by considering only the two-body problem equations in the heliocentric frame. The necessary optimum conditions for the Earth e yby are extended to consider a minimum-height constraint, which is frequently required in this maneuver. The procedure is also capable of recognizing when a numerical solution is only suboptimal and a powered e yby could improve the mission.

Improved Edelbaum's Approach to Optimize Low Earth/Geostationary Orbits Low-Thrust Transfers

Edelbaums approach to the optimization of low-thrust transfers is revisited and some simplifications are removed. The variation of the spacecraft mass due to the propellant consumption is considered in the case of constant thrust, and the corresponding numerical result is compared with Edelbaums solution. The approach is then extended to consider variable specific impulse and thrust magnitude with constant power level. The payload increment is first computed maintaining Edelbaums suboptimal control strategy (i.e., constant-thrust direction during each half-revolution). An analytical solution of the quasi-circular one-revolution transfer is then found using the optimal control of both the thrust direction and magnitude. The very-low-thrust multirevolution problem is easily solved by assembling many one-revolution basic trajectories; in particular, the transfer from a 28.5 deg inclined low Earth orbit to the equatorial geostationary orbit is considered. Exact numerical solutions for both constant and variable specific impulse have also been obtained using an indirect optimization method: the accuracy of the solution based on the quasi-circular approximation has been verified

Missions to Asteroids Using Solar Electric Propulsion

Abstract Future interplanetary missions will use conventional rockets to leave the Earths sphere of influence, and solar electric propulsion to carry out deep-space maneuvers. Optimization of this kind of mission is the subject of the paper. Attention is mainly paid to a mission concept that exploits high specific impulse and steering capabilities of electric propulsion to obtain a gravity assist from the Earth about a year after spacecraft departure. Missions to several near Earth objects are considered and their common features are highlighted. The analysis suggests useful criteria to define the initial solution required to start the optimization process. Guidelines are also given to select, from the large number of near Earth bodies, the asteroids that may profitably be the targets of this class of trajectories.

Oxidizer control and optimal design of hybrid rockets for small satellites

The parameters that affect the design of a hybrid rocket for small satellites are highlighted, and the benefit of the oxidizer flow rate control is analyzed. A single-port circular-section polyethylene grain is considered; the oxidizer is 85% hydrogen peroxide. The engine design is optimized to search for the minimum engine mass when the initial satellite mass and the required velocity increment are assigned. First, the simplest blowdown feed system is considered. The analysis shows that the optimal design depends on a lower limit for the regression rate and sometimes on a further constraint, which is related to the occurrence of thermal choking. The initial values of the mixture ratio, the thrust level and the initial port area to the throat area ratio seem to be the most important parameters for an optimal design. As far as the oxidizer flow rate control is concerned, several control strategies, namely, constant mixture ratio, repressurization, constant combustion chamber pressure, and constant propellant tank pressure, are compared to the simplest blowdown system. The constant mixture ratio control is the worst case, as the mass and volume are similar to the blowdown case, while a large thrust variation occurs. Repressurization reduces the thrust variation. Constant pressure controls (both combustion chamber and tank pressures) guarantee a quasi-constant thrust and reduce engine dimensions, with a limited mass penalty.

Optimization of Hybrid Upper-Stage Motor with Coupled Evolutionary/Indirect Procedure

Upper-stage motors used in small launchers constitute an application where hybrid rocket motors may be competitive. A coupled optimization of motor design and trajectory is needed for such an application due to mission characteristics and motor features. The present article presents a cooperative evolutionary method nested with an indirect approach to perform the coupled optimization of hybrid rocket motor and trajectory for an upper stage. The evolutionary method optimizes the parameters that affect the motor design (e.g., grain geometry) and feed system, whereas the indirect method optimizes the trajectory (i.e., thrust direction and motor switching times) for a given motor and mission. A mission profile based on the Vega launcher is considered and the performance index is the payload inserted into the final orbit. The hybrid rocket motor powers the third and last stage and has a pressurizing feed system that is partially regulated. The characteristics of the first and second solid rocket motor stages a...