1,720,999 research outputs found
Optimal space trajectories with multiple coast arcs using modified equinoctial elements
Full text linkThe detection of optimal trajectories with multiple coast arcs represents a significant and challenging problem of practical relevance in space mission analysis. Two such types of optimal paths are analyzed in this study: (a) minimum-time low-thrust trajectories with eclipse intervals and (b) minimum-fuel finite-thrust paths. Modified equinoctial elements are used to describe the orbit dynamics. Problem (a) is formulated as a multiple-arc optimization problem, and additional, specific multipoint necessary conditions for optimality are derived. These yield the jump conditions for the costate variables at the transitions from light to shadow (and vice versa). A sequential solution methodology capable of enforcing all the multipoint conditions is proposed and successfully applied in an illustrative numerical example. Unlike several preceding researches, no regularization or averaging is required to make tractable and solve the problem. Moreover, this work revisits problem (b), formulated as a single-arc optimization problem, while emphasizing the substantial analytical differences between minimum-fuel paths and problem (a). This study also proves the existence and provides the derivation of the closed-form expressions for the costate variables (associated with equinoctial elements) along optimal coast arcs
Optimal low-thrust hyperbolic rendezvous for interplanetary missions
No full textEarth-Mars cycling spacecraft have been proposed as a valuable option for the future exploration of Mars. Cycler mission architectures consider the use of a large space vehicle that cycles continuously between Earth and Mars, describing a near-ballistic path that includes flybys at the two planets. While this large spacecraft can be equipped with the life support system appropriate for a long interplanetary flight with a crew, taxi vehicles of reduced size are sufficient to ensure the connection between the interplanetary vehicle and each planet. This research addresses the determination of the optimal low-thrust transfer trajectories for a pair of taxi vehicles aimed at transferring a crew or an inert payload from and toward a large Earth-Mars cycling spacecraft. The problem is solved through the indirect heuristic method, which uses the necessary conditions for optimality together with a heuristic technique, i.e. the particle swarm algorithm. The use of the indirect heuristic approach for low-thrust paths may be affected by hypersensitivity with respect to the initial values of the costate. This phenomenon is mitigated through a judicious choice of the equations of motion that govern the spacecraft dynamics. The solution method proposed in this work proves to be effective and very accurate, and definitely leads to determining the minimum-time low-thrust paths for a pair of taxi vehicles traveling from and toward a large cycling spacecraft
Optimal hyperbolic rendezvous trajectories for cycler missions
No full textCycler mission architectures are based on the joint use of a large spacecraft that cycles continuously between Earth and Mars, and small taxi vehicles, aimed at connecting each planet with the cycling vessel. The latter describes a hyperbolic path relative to the Earth. This work considers the problem of optimizing the trajectory of the taxi leading to rendezvous with the cycler. Propellant minimizing transfers have been found for both impulsive (short-duration, high-thrust) and low-thrust hyperbolic rendezvous. For the impulsive case, two, three, or four velocity changes are proven to be optimal for performing the rendezvous. If the time of flight can be large, the most fuel efficient rendezvous path is composed of four velocity impulses, and ends at the farthest allowed point along the cycler hyperbola. The optimal low-thrust rendezvous trajectory is found as well, using nonsingular equinoctial elements, in conjunction with the indirect heuristic method
Particle swarm optimization of ascending trajectories of mulstistage rockets
No full textMultistage launch vehicles are commonly employed to place spacecraft and satellites in their operational orbits. If the rocket characteristics are specified, the optimization of its ascending trajectory consists of determining the optimal control law that leads to maximizing the final mass at orbit injection. The numerical solution of a similar problem is not trivial and has been pursued with different methods, for decades. This paper is concerned with an original approach based on swarming theory. The particle swarm optimization technique represents a heuristic population-based optimization method inspired by the natural motion of bird flocks. Each individual (or particle) that composes the swarm corresponds to a solution of the problem and is associated with a position and a velocity vector. The formula for velocity updating is the core of the method, and is composed of three terms with stochastic weights. As a result, the population migrates toward different regions of the search space taking advantage of the mechanism of information sharing that affects the overall swarm dynamics. At the end of the process the best particle is selected and corresponds to the optimal solution to the problem of interest. In this work the three-dimensional trajectory of the multistage rocket is assumed to be composed of four arcs: (i) first stage propulsion, (ii) second stage propulsion, (iii) coast arc (after release of the second stage), and (iv) third stage propulsion. The Euler-Lagrange equations and the Pontryagin minimum principle, in conjunction with the Weierstrass-Erdmann corner conditions, are employed to express the thrust angles as functions of the adjoint variables conjugate to the dynamics equations. The use of these analytical conditions coming from the calculus of variations leads to obtaining the overall rocket dynamics as a function of seven parameters only, namely the unknown values of the initial state and costate components, the coast duration, and the upper stage thrust duration. In addition, a simple approach is introduced and successfully applied with the purpose of satisfying exactly the path constraint related to the maximum dynamical pressure in the atmospheric phase. The basic version of the swarming technique, which is used in this research, is extremely simple and easy to program. Nevertheless, the algorithm proves to be capable of yielding the optimal rocket trajectory with great numerical accuracy. Copyright© (2012) by the International Astronautical Federation
Lunar ascent and orbit injection via locally-flat near-optimal guidance and nonlinear reduced-attitude control
Full text linkThis work deals with an explicit guidance and control architecture for autonomous lunar ascent and orbit injection, i.e., the locally-flat near-optimal guidance, accompanied by nonlinear reduced-attitude control. This is a new explicit guidance scheme, based on the local projection of the position and velocity variables, in conjunction with the real-time solution of the associated minimum-time problem. A recently-introduced quaternion-based reduced-attitude control algorithm, which enjoys quasi-global stability properties, is employed to drive the longitudinal axis of the ascent vehicle toward the desired direction. Actuation, based on thrust vectoring, is modeled as well. Extensive Monte Carlo simulations prove the effectiveness of the guidance, control, and actuation architecture proposed in this study for precise lunar orbit insertion, in the presence of nonnominal flight conditions
Optimal low-thrust trajectories using nonsingular equinoctial orbit elements
No full textLow-thrust propulsion was proven to allow substantial propellant savings with respect to high-thrust systems, at the price of increasing the time of flight. This work addresses low-thrust orbit transfer optimization, which consists in finding the thrust direction time history that minimizes the time of flight. The indirect heuristic method is outlined and employed. It is based on the joint use of a heuristic technique and the necessary conditions associated with the optimization problem. If this is formulated using the polar coordinates for position and velocity, a major drawback resides in hypersensitivity on the initial values of the adjoint variables associated with the dynamics equations. This research proves that the use of nonsingular equinoctial elements allows overcoming this serious difficulty, by mitigating hypersensitivity. Two interesting low-thrust orbit transfer problems are considered, i.e. (a) from a circular, equatorial low Earth orbit to a geostationary orbit, and (b) between a circular, low Earth orbit and a hyperbolic trajectory. In both cases, the minimum-time transfer path is found with great accuracy
Low-thrust lunar capture leveraging nonlinear orbit control
Full text linkNonlinear orbit control with the use of low-thrust propulsion is proposed as an effective strategy for autonomous guidance of a space vehicle directed toward the Moon. Orbital motion is described in an ephemeris model, with the inclusion of the most relevant perturbations. Unfavorable initial conditions, associated with weak, temporary lunar capture, are considered, as representative conditions that may be encountered in real mission scenarios. These may occur when the spacecraft is released in nonnominal flight conditions, which would naturally lead it to impact the Moon or escape the lunar gravitational attraction. To avoid this, low-thrust propulsion, in conjunction with nonlinear orbit control, is employed, to drive the space vehicle toward two different, prescribed, lowaltitude lunar orbits. Nonlinear orbit control leads to identifying a saturated feedback law (for the low-thrust magnitude and direction) that is proven to enjoy global stability properties. The guidance strategy at hand is successfully tested on three different mission scenarios. Then, the capture region is identified, and includes a large set of initial conditions for which nonlinear orbit control with low-thrust propulsion is effective to achieve lunar capture and final orbit acquisition
Nonlinear orbit control for earth satellites using low-thrust propulsion
No full textThis research is focused on the definition, analysis, and numerical testing an effective orbit control strategy tailored to compensating orbit perturbations, as well as possible errors at orbit injection of low-Earth-orbit microsatellites. A general, systematic approach to real-time orbit control is presented, under the assumption that the satellite of interest is equipped with a low-thrust propulsion system. Two different operational orbits are considered: (a) very-low-altitude Earth orbit and (b) sunsynchronous orbit. A feedback control law based on Lyapunov stability theory is proposed and tested. A steerable, throttleable low-thrust propulsion system with an upper bound on the thrust magnitude is considered. The stability properties and the overall performance over 5 years are investigated for cases (a) and (b). For case (a), the effect of satellite eclipsing on available electrical power is considered as well. Suitable tolerances on the desired (nominal) conditions allow substantial savings in terms of propellant requirements
Deployment strategies of a satellite constellation for polar ice monitoring
No full textThis research considers a constellation of 16 satellites equipped with SAR sensors and tailored to monitoring the polar ice evolution, with a suitable revisit time over the regions of interest. Satellite deployment includes three phases: (i) orbit injection, performed by the upper stage of the launch vehicle, (ii) orbit plane selection, and (iii) orbit phasing. This work is primarily focused on phase (ii). Carrier spacecraft are proposed as a valuable option to place the majority of satellites in their orbits. Two distinct strategies are proposed to complete this task. The first strategy is based on the use of chemical propulsion, combined with the perturbing action due to Earth oblateness. The second strategy considers the use of low-thrust electric propulsion, in conjunction with nonlinear orbit control. A comparison between these two approaches is drawn, in terms of deployment time and final mass ratio of the carrier. Orbit phasing concludes the constellation deployment, and is carried out by each satellite. A tradeoff is proven to exist between phasing time and propellant expenditure
A new guidance and control architecture for accurate orbit injection
Full text linkAccurate orbit injection represents a crucial issue in several mission scenarios, e.g. for spacecraft orbiting the Earth or for payload release from the upper stage of an ascent vehicle. This work considers a new guidance and control architecture based on the combined use of (i) the variable-time-domain neighboring optimal guidance technique (VTD-NOG), and (ii) the constrained proportional-derivative (CPD) algorithm for attitude control. More specifically, VTD-NOG & CPD is applied to two distinct injection maneuvers: (a) Hohmann-like finite-thrust transfer from a low Earth orbit to a geostationary orbit, and (b) orbit injection of the upper stage of a launch vehicle. Nonnominal flight conditions are modeled by assuming errors on the initial position, velocity, attitude, and attitude rate, as well as actuation deviations. Extensive Monte Carlo campaigns prove effectiveness and accuracy of the guidance and control methodology at hand, in the presence of realistic deviations from nominal flight conditions
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