Low-Thrust Nonlinear Guidance by Tracking Mean Orbital Elements

Finite Time Horizon Analysis of Launch Vehicles Under Mass and Thrust Uncertainty

An impulsive feedback control is developed to establish specie c relative orbits for spacecraft formation e ying. The relative orbit tracking errors are expressed in terms of mean orbit elements. The feedback control, based on Gauss’ s variational equations of motion, allows specie c orbit elements or orbit element sets to be controlled with minimal impact on the remaining osculating orbit elements. This is advantageous when J2-invariant orbits are to be controlled, where only the argument of perigee and mean anomaly will drift apart at equal and opposite rates. The advantage of this impulsive feedback control, compared to optimal control solutions, is that it can operate with little computational effort and in a near-optimal manner, whilerequiring only a marginal penalty in fuel cost. When applied to the spacecraft formation e ying problem, this control could also be used to perform general orbit corrections. Formulas are developed providing accurate estimates of the sensitivities of the mean semimajor axis and mean eccentricity with respect to the osculating inclination angle. With these sensitivities, the tracking error in semimajor axis, eccentricity, and inclination angle can be canceled within one orbit.

Gravitational and third-body perturbations can be modeled with sufficient precision for most applications in low Earth orbit. However, owing to severe uncertainty sources and modeling limitations, computational models of satellite aerodynamics and solar radiation pressure are bound to be biased. Aiming at orbital propagation consistent with observed satellite orbital dynamics, real-time estimation of these perturbations is desired. In this paper, a particle filter for the recursive inference and prediction of nongravitational forces is developed. Specifically, after assuming a parametric model for the desired perturbations, the joint probability distribution of the parameters is inferred by using a prescribed number of weighted particles, each consisting of one set of orbital elements and one set of parameters. The particle evolution is carried out by means of an underlying orbital propagator, and the Bayes rule is used to recursively update weights by comparing propagated orbital elements with satellite observations. The proposed formulation uses mean orbital elements as the only available measurements. This feature makes the algorithm a potentially valuable resource for space situational awareness applications, such as space debris trajectories prediction from two-line elements, or for onboard force estimation from Global Positioning System data. High-fidelity simulations show that nongravitational perturbations can be estimated with 20% accuracy.

Satellite navigation for meteorological purposes: Inverse referencing for NOAA-N and ERS-1 imagers with a 1 km nadir pixel size

Decomposition analysis of spacecraft relative motion with different inter-satellite ranges

A mission requirements-based configuration method of interferometric synthetic-aperture radar (InSAR) formation to design dual-satellite formation by mean orbital elements is derived. The configuration and initial orbital elements of two coordinated running satellites InSAR formation are designed when system parameters, such as the resolution of slant distance, latitude domain of ground coverage area, and the side-looking angle of the synthetic-aperture radar (SAR) beam center, are given.

The present paper describes a simple guidance strategy for the reentry mission of a generic Reusable Launch Vehicle. The guidance computation starts with a nominal feasible trajectory, which gets updated during actual reentry based on onboard measurements, using both incremental angle of attack and bank angle parameters. An analytical formulation for a modified predictor-corrector algorithm is developed, using angle of attack profile and bank angle reversal strategy. The guidance solution is arrived at under the heating rate and equilibrium glide constraints and the control actuation is implemented through the aerodynamic control surfaces. A scheme to improve the overall performance of the predictor-corrector algorithm is evolved, which is based on the determination of optimum perturbation levels of control variables. In addition, the control vector formulation is provided with a weighting option, for improving the overall terminal interface accuracy. Numerical results are obtained for the time histories of control variables and performance parameters, for a typical nominal trajectory, which show that proposed guidance scheme works well for a specified reentry mission. Results are also obtained for the optimum perturbation levels for the control parameters, which are used for estimating the sensitivity coefficients required in corrector algorithm. Lastly, the results are obtained for the trajectory parameters, by considering dispersions in the aerodynamic drag and lift coefficients, for establishing its robustness. The results clearly bring out the fact that the proposed reentry guidance algorithm is able to achieve the required terminal conditions, even in the presence of large perturbations in the aerodynamic coefficients.

A neighboring optimal guidance scheme for a nonlinear dynamic system is devised with stochastic inputs and perfect measurements as applicable to fuel optimal control of an aeroassisted orbital transfer vehicle. For the deterministic nonlinear dynamic system describing the atmospheric maneuver, a nominal trajectory is determined. Then, taking modeling uncertainties into account, a linear, stochastic, neighboring optimal guidance scheme is devised. Assuming the additive character of the stochastic effects, the optimal trajectory is approximated as the sum of the deterministic nominal trajectory and the stochastic neighboring optimal solution. Numerical results are presented for a typical aeroassisted orbital transfer vehicle.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A guidance strategy for generic 2D course correcting fuzes with canard control is developed using a perturbation approach. The starting point is a nominal trajectory which is computed before flight. During flight, only simple correction terms need to be calculated in order to form the guidance commands. The resulting strategy is of essentially predictive character but can be used with shorter prediction horizon than time-to-go, thereby effectively implementing a path following strategy. Simulations are provided to illustrate the effectiveness of the approach for a detailed model of a standard 155mm artillery shell in varying firing scenarios. It is shown that dispersion figures in the order of meters are possible to obtain with realistic values for errors in muzzle velocity, gun aiming and available control authority in the canard control system.

This paper presents an analysis of the precise soft landing problem for lunar missions focusing on the Decent & Landing (DL) trajectory optimization and the guidance scheme. The first step is the design of optimal solutions for different Descent & Landing strategies by evaluating the impact on the cost function (landed mass) of the problem relevant parameters. In addition, different optimal strategies are analyzed considering constraints from the navigation and hazard avoidance systems. The second step is to define an autonomous guidance scheme able to reach the desired landing site. The guidance strategy must cancel the deviations of the nominal trajectory due to the presence of execution errors and also be able to reach a new landing site (retargeting). A hybrid direct/indirect optimization scheme is implemented that can cope with different DL strategies and provides optimal DL trajectories defined by a reduced number of parameters easily flyable. The algorithm includes a continuation method for initial guess computation and is very fast and robust to compute sensitivity and off-nominal analyses. The guidance algorithm is based on an analytical approach for initial guess computation that is also used for analysis and definition of the guidance strategy. In the unconstrained problem, the guidance strategy is such that the guidance algorithm solves a non-linear system of equations. If navigation constraints are included, the guidance algorithm becomes a hybrid direct/indirect optimization algorithm that optimizes the final landed mass fulfilling the boundary conditions and some path constraints.

Robustness analysis method for orbit control

We report on the improved ephemerides for the irregular Jovian satellites. We used a combination of numerically integrated equations of motion and a weighted least-squares algorithm to fit the astrometric measurements. The orbital fits for 59 satellites are summarized in terms of state vectors, post-fit residuals, and mean orbital elements. The current data set appears to be sensitive to the mass of Himalia, which is constrained to the range of GM = 0.13–0.28 km3 s−2. Here, GM is the product of the Newtonian constant of gravitation, G and the body's mass, M. Our analysis of the orbital uncertainties indicates that 11 out of 59 satellites are lost owing to short data arcs. The lost satellites hold provisional International Astronomical Union (IAU) designations and will likely need to be rediscovered.

In this paper, a novel approach is introduced to estimate the North American Aerospace Defense Command (NORAD)-type two-line elements (TLE) data based on the invasive weed optimization (IWO) method, which is a stochastic numerical optimization algorithm inspired by colonizing weeds. Many satellite applications use the NORAD Simplified General Perturbations model 4 (SGP4) for satellite position prediction. The input of SGP4 consists of TLEs which are published via NORAD freely through the worldwide web. Since it is generated irregular, a new TLE which is independent of NORAD is required to access data about the satellite location each time. An alternative to independent computation of TLE can be made feasible by the existing emersion of GPS receivers in the space project and using IWO. Using this stochastic algorithm increases the success probability to find a more accurate TLE. The estimation is performed for six Keplerian orbital elements and SGP4 drag term ( B*) by using the satellite position data achieved from the GPS receiver. Also, the feasibility study of the concept is performed by using the actual GPS data of CHAMP and corresponding NORAD TLE. The time length of the GPS data used in the estimation is studied for practical application purposes. The results show that 500 samples of position data, with 1-min time intervals, are sufficient to keep the position error within 10 km in 3 days after epoch time in orbital elements with known drag term estimation. Moreover, for orbital elements with drag term estimation, 1000 samples of position, with 1-min time intervals, are sufficient to keep the position error within 15 km in 3 days after epoch time. If there is no considerable constraint for position-data time-length or time available for performing numerical computations, the estimated TLE can be more accurate than corresponding NORAD TLE.

This paper investigates a reliability-based trajectory optimization method for the design of soft landing trajectory on an irregular shape asteroid with highly uncertain gravitational field. First, the gravitational field of the irregular asteroid is described by the finite particle model. Second, to avoid the singularity and reduce the sensitivity, the original finite particle model is modified to an “N-body/two-body” switching dynamic model. The trajectory optimization problem in the switching dynamic model is summarized as an optimal control problem and is then transformed into a two-point boundary value problem by Pontryagin’s maximum principle. By solving the two-point boundary value problem with a homotopic continuation procedure, the nominal optimal trajectory is obtained. Third, the uncertainty caused by the nonuniform mass distribution of the asteroid is considered. With high uncertainty, the deterministic optimal control problem becomes a parameter optimization problem with reliability constraints. This problem is then solved by a sequential optimization and reliability assessment, and the parallel computation technique is adopted. Finally, two soft landing trajectories are optimized using the proposed method to demonstrate the effectiveness of the technique.

This paper researches the fuel‐optimal geocentric orbit transfer problem using a low‐thrust, electric propulsion. First, the transfer trajectory is divided into N burn‐coast arcs via introducing (N−1) intermediate orbits between the initial and the target orbits. By restricting the time duration of each burn, the changes in orbital states caused by one time of ignition can be represented by a discrete velocity impulse; therefore, a considerable large N, a great many optimization variables, and a months and revolutions long trajectory will be calculated to solve the optimization problem. By proposing a new transfer coordinate system, the performance index is analytically calculated, and strict constraints derived from the continuous condition between adjacent orbits are removed from the mathematical optimization model. Meanwhile, an improved particle swarm optimization (PSO) method and a mesh refinement method are proposed to address the optimization problem. The mesh refinement algorithm begins with a simple bi‐impulse transfer problem, automatically increases/decreases N, and finally converges to the optimal solution. Numerical simulation shows the efficiency of the method with some classical and representative scenarios.