A Treatise on the Analytical Dynamics of Particles and Rigid Bodies: THE GENERAL THEORY OF ORBITS

Feedback systems: Input-output properties

Stochastic Optimal Control

Space Vehicle Dynamics and Control, Second Edition

DOI: 10.2514/1.52476 This paper concerns the application of the homotopic approach, which solves the fuel-optimal problem of lowthrust trajectory by starting from the related and easier energy-optimal problem. To this end, some effective techniques are presented to reduce the computational time and increase the probability of finding the globally optimalsolution.First,theoptimalcontrolproblemismadehomogeneoustotheLagrangemultipliersbymultiplying the performance index by a positive unknown factor. Hence, normalization is applicable to restrict the unknown multipliersonaunithypersphere.Second,theswitchingfunction’s first-andsecond-orderderivativeswithrespectto time are derived to detect switching. The switching detection is embedded in the fourth-order Runge–Kutta algorithm with fixed step size to ensure integration accuracy for bang-bang control. Third, combined with the techniques of normalization and switching detection, the particle swarm optimization with well-chosen parameters considerably increases the probability of finding the approximate initial values of the globally optimal solution. Moreover, intermediate gravity assist, which brings complex inner constraints, is considered. To determine the approximate gravity assist date, analytical formulas are presented to evaluate the minimal maneuver impulse based on the results of Lambert problems. The first-order necessary conditions for gravity assist constraints are derived analytically.Theoptimalsolutioncanberapidlyobtainedbyapplyingthetechniquespresentedtosolvetheshooting function. The unknowns are far less than with direct methods, and the computational effort is also far lower. Two examples of fuel-optimal rendezvous problems from the Earth directly to Venus and from the Earth to Jupiter via Mars gravity assist are given to substantiate the perfect efficiency of these techniques.

Practical Techniques for Low-Thrust Trajectory Optimization with Homotopic Approach

The electric solar wind sail (E-sail) is a space propulsion concept that uses the natural solar wind dynamic pressure for producing spacecraft thrust. In its baseline form, the E-sail consists of a number of long, thin, conducting, and centrifugally stretched tethers, which are kept in a high positive potential by an onboard electron gun. The concept gains its efficiency from the fact that the effective sail area, i.e., the potential structure of the tethers, can be millions of times larger than the physical area of the thin tethers wires, which offsets the fact that the dynamic pressure of the solar wind is very weak. Indeed, according to the most recent published estimates, an E-sail of 1 N thrust and 100 kg mass could be built in the rather near future, providing a revolutionary level of propulsive performance (specific acceleration) for travel in the solar system. Here we give a review of the ongoing technical development work of the E-sail, covering tether construction, overall mechanical design alternatives, guidance and navigation strategies, and dynamical and orbital simulations.

http://www.electric-sailing.fi/paper9.pdf

Invited Article: Electric solar wind sail: Toward test missions

Solar-sail mission analysis and design is currently performed assuming constant optical and mechanical properties of the thin metalized polymer films that are projected for solar sails. More realistically, however, these properties are likely to be affected by the damaging effects of the space environment. The standard solar-sail force models can therefore not be used to investigate the consequences of these effects on mission performance. The aim of this paper is to propose a new parametric model for describing the sail film's optical degradation with time. In particular, the sail film's optical coefficients are assumed to depend on its environmental history, that is, the radiation dose. Using the proposed model, the optimal control laws for degrading solar sails are derived using an indirect method and the effects of different degradation behaviors are investigated for an example interplanetary mission.

Parametric model and optimal control of solar sails with optical degradation

 These values render the electric sail a potentially competitive propulsion means for future mission applications The aim of this paper is to provide a preliminary analysis of the electric sail performance and to investigate the capabilities of this propulsion system in performing interplanetary missions To this end, the minimum-time rendezvous/transfer problem between circular and coplanar orbits is considered, and an optimal steering law is found using an indirect approach The main differences between electric sail and solar sail performances are also emphasized

/pdf/electric-sail-performance-analysis-2zvt76d06l.pdf

Electric Sail Performance Analysis

Optimal Three-Dimensional Interplanetary Rendezvous Using Nonideal Solar Sail

Missions towards the boundaries of the Solar System require long transfer times and advanced propulsion systems. An interesting option is offered by electric sails, a new propulsion concept that uses the solar wind dynamic pressure for generating a continuous thrust without the need for reaction mass. The aim of this paper is to investigate the performance of such a propulsion system for obtaining escape conditions from the Solar System and planning a mission to reach the heliosphere boundaries. The problem is studied in an optimal framework, by minimizing the time to reach a given solar distance or a given hyperbolic excess speed. Depending on the value of the sail characteristic acceleration, it is possible that, in an initial mission phase, the sailcraft may approach the Sun to exploit the increased available thrust due to the growing solar wind electron density. The corresponding optimal trajectory is constrained to not pass inside a heliocentric sphere whose admissible radius is established by thermal constraints. Once the escape condition is met, the sail is jettisoned and the payload alone continues its journey without any propulsion system. A medium performance electric sail is shown to have the potentialities to reach the heliosheath, at a distance of 100 AU, in about fifteen years. Finally, the Interstellar Heliopause Probe mission is used as a reference mission to further quantify the electric sail capabilities for an optimal transfer towards the heliopause nose (200 AU).

/pdf/electric-sail-mission-analysis-for-outer-solar-system-3q25g5j6jp.pdf

Giovanni Mengali

Papers

Invited Article: Electric solar wind sail: Toward test missions

Parametric model and optimal control of solar sails with optical degradation

Electric Sail Performance Analysis

Optimal Three-Dimensional Interplanetary Rendezvous Using Nonideal Solar Sail

Electric Sail Mission Analysis for Outer Solar System Exploration