# R. M. WoollandsUniversity of Illinois, Urbana-Champaign | UIUC · Department of Aerospace Engineering

R. M. Woollands

Doctor of Philosophy

## About

37

Publications

5,806

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297

Citations

Citations since 2016

Introduction

**Skills and Expertise**

## Publications

Publications (37)

Several million dust devil events occur on Mars every day. These events last, on average, about 30 minutes and range in size from meters to hundreds of meters in diameter. Designing low-cost missions that will improve our knowledge of dust devil formation and evolution, and their connection to atmospheric dynamics and the dust cycle, is fundamental...

Accurate orbit propagation for satellites in motion around a massive central body requires the inclusion of a high-fidelity gravity model for that central body. Including such a model significantly increases computational costs as a sufficiently large degree for the spherical harmonic series is required. The higher the degree of a specific series,...

Low thrust solar powered missions are challenging for their requirement of long duration missions with extended periods of thrusting. The complexity of the mission design and trajectory optimization is enhanced by the occurrences of eclipses when the solar arrays generate no power for the duration of the eclipse forcing the spacecraft to coast and...

A network of small satellites is designed to ferry data from Mars to Earth. The small satellites, or data mules, are assumed to have laser communicators and maintain cycler orbits. The concept exploits the fact that two nearby optical communicators can achieve extremely high data rates and that cycler orbits carry a satellite between Mars and Earth...

The endgame scenario that was explored in this analysis consisted of the part of the trajectory starting at the last Ganymede flyby and ending at the final Europa approach. The basic design components included computing the phasing for the final Ganymede encounter, computing the required intermediate Europa flybys, determining the required maneuver...

Model predictive control is a powerful methodology that involves repeatedly solving an optimization problem over a moving time horizon, using predictions of the system's future behavior and response. Model predictive control is especially useful for handling model and parameter uncertainty in real-world applications. It has become a widespread solu...

Designing long-duration lunar orbiter missions is challenging due to the Moon’s highly nonlinear gravity ﬁeld and the third-body perturbations induced by the Earth, Sun and other large bodies. The absence of a Lunar atmosphere has oﬀered the possibility for mission designers to search for extremely low-altitude, quasi-stable lunar orbits. In additi...

The presence of extremely low-altitude, lunar quasi-frozen orbits (QFOs) has given rise to interesting mission opportunities. These QFOs are ideal for close-range, high-resolution mapping of the lunar south pole, and their inherent stability translates into minimal station-keeping efforts. Despite the aforementioned desirable characteristics, desig...

Low-thrust propulsion technology and planetary gravity-assist maneuvers make a promising combination for deep space explorations. Hybrid optimal control methods have proven to be an excellent solution framework which exploits the advantages of both direct and indirect optimization methods, while alleviating their drawbacks. We employ a recently int...

We present a new methodology to incorporate shadow-and time-triggered constraints within the indirect optimization methods to solve low-thrust fuel-optimal orbit transfer problems. Such constraints could represent, for instance, zero thrusting during an eclipse or a time interval during which the thruster has to be shut down during a mission scienc...

The impact of Comet Shoemaker-Levy 9 (SL9) with Jupiter in 1994 was the ultimate confirmation of Eugene Shoemaker’s theory that impacts are a common, fundamental process in the Solar System. On Earth, asteroid impacts have produced several near extinction level events. We tend to visualise these collisions as billiard balls hitting one another. But...

We present the results of a comprehensive study in which the precision and efficiency of six numerical integration techniques, both implicit and explicit, are compared for solving the gravitationally perturbed two-body problem in astrodynamics. Solution of the perturbed two-body problem is fundamental for applications in space situational awareness...

We have developed a new method for solving low-thrust fuel-optimal orbit transfer problems in the vicinity of a large body (planet or asteroid), considering a high-fidelity spherical harmonic gravity model. The algorithm is formulated via the indirect optimization method, leading to a two-point boundary value problem (TPBVP). We make use of a hyper...

High precision propagation for satellites orbiting a large body with a highly nonlinear gravity field (planets, moons, asteroids) require accurate computation of the gravitational acceleration at each integration step. This is a computationally expensive operation that depends mainly on the orbit geometry and the accuracy to which the solution is r...

High precision propagation for satellites orbiting a large body with a highly nonlinear gravity field (planets, moons, asteroids) require accurate computation of the gravitational acceleration at each integration step. This is a computationally expensive operation that depends mainly on the orbit geometry and the accuracy to which the solution is r...

Design of long-duration lunar orbiter missions is challenging due to the Moon's highly non-linear gravity field and third-body perturbations induced by the Earth, Sun and other large bodies, on the orbiting spacecraft. The absence of a Lunar atmosphere, and hence the lack of orbital atmospheric drag, has encouraged mission designers to search for e...

An adaptive self-tuning Picard–Chebyshev numerical integration method is presented for solving initial and boundary value problems by considering high-fidelity perturbed two-body dynamics. The current adaptation technique is self-tuning and adjusts the size of the time interval segments and the number of nodes per segment automatically to achieve n...

The orthogonal Chebyshev polynomials are commonly used to approximate functions. The approximation accuracy is dependent on the nature of the approximated function, its domain, the Chebyshev series degree, and the number sampling nodes. In this paper, we show how to optimally choose the degree of Chebyshev expansion to achieve a prescribed accuracy...

We present an iterative five-element Lyapunov control for low thrust rendezvous that uses Modified Chebyshev Picard Iteration (MCPI), an iterative solver of linear and nonlinear ordinary differential equations (ODEs). MCPI uses Chebyshev polynomials to approximate the orbital trajectory and then uses Picard iteration to improve the approximation it...

This paper introduces a parallel-compiled tool that combines several of our recently developed methods for solving the perturbed Lambert problem using modified Chebyshev-Picard iteration. This tool (unified Lambert tool) consists of four individual algorithms, each of which is unique and better suited for solving a particular type of orbit transfer...

We present a new method for solving the multiple revolution perturbed Lambert problem using the method of particular solutions and modified Chebyshev-Picard iteration. The method of particular solutions differs from the well-known Newton-shooting method in that integration of the state transition matrix (36 additional differential equations) is not...

We unify and extend classical results from function approximation theory and consider their utility in astrodynamics. Least square approximation, using the classical Chebyshev polynomials as basis functions, is reviewed for discrete samples of the to-be-approximated function. We extend the orthogonal approximation ideas to n-dimensions in a novel w...

A novel application of Modified Chebyshev Picard Iteration (MCPI) to differential correction is presented. By leveraging the Chebyshev basis functions of MCPI, interpolation in 1 dimension may be used to target plane crossing events, instead of integrating the 42 dimensional variational equation required for standard step integrators. This results...

We present a method for performing low cost attitude estimation for CubeSat type missions. Our algorithm uses measurements from a custom built sun sensor, a star camera, and inertial measurements. These sensing measurements are supplied in real-time to an Multiplicative Kalman Filter for the purpose of generating continuous attitude estimates. The...

Modified Chebyshev Picard Iteration is an iterative numerical method for solving linear or non-linear ordinary differential equations. In a serial computational environment the method has been shown to compete with, or outperform, current state of practice numerical integrators. This paper presents several improvements to the basic method, designed...

This paper extends previous work on parallel-structured Modified Chebyshev Picard Iteration (MCPI) Methods. The MCPI approach iteratively refines path approximation of the state trajectory for smooth nonlinear dynamical systems and this paper shows that the approach is especially suitable for initial value problems of astrodynamics. Using Chebyshev...

A new approach for solving two-point boundary value problems and initial value problems using the Kustaanheimo-Stiefel transformation and Modified Chebyshev-Picard iteration is presented. The first contribution is the development of an analytical solution to the elliptic Keplerian Lambert problem based on Kustaanheimo-Stiefel regularization. This t...

A method is presented for solving boundary and initial value problems in celestial mechanics. In particular we consider the well-known Lambert TPBVP. The approach is quite general, however certain details in the transformed space boundary conditions pose challenges. We have been able to resolve these difficulties fully for the planar classical two-...

Over the last 40 years variations in the systemic velocity and the
observed minus computed time of first conjunction have been observed in
the RS Cha binary system. Our goal is to determine the probability for
the existence of a third body in this system, and to calculate an
orbital solution for this component. A total of 381 high-resolution
echell...

A combination of POAM III aerosol extinction and CHAMP RO temperature measurements are used to examine the role of atmospheric gravity waves in the formation of Antarctic Polar Stratospheric Clouds (PSCs). POAM III aerosol extinction observations and quality flag information are used to identify Polar Stratospheric Clouds using an unsupervised clus...

R Coronae Borealis (RCB) stars exhibit a unique variability whereby they
undergo enigmatic and rapid declines in brightness of up to several
magnitudes. The period of a decline may take several weeks, whereas the
recovery to maximum light may take months or even years. The accepted
wisdom for the cause of these enigmatic declines is a phenomenon wh...

This paper presents the initial results of a multi-site photometric programme to examine the extraordinary behaviour displayed by 18 R Coronae Borealis (RCB) stars in the Magellanic Clouds (MCs). RCB stars exhibit a unique variability whereby they undergo rapid declines of up to several magnitudes. These are thought to be caused by the formation of...

This study uses a combination of POAM III aerosol extinction measurements and CHAMP GPS/RO temperature measurements to examine the role of atmospheric gravity waves in Polar Stratospheric Cloud (PSC) formation in the Antarctic. POAM III aerosol extinction observations are used to identify Type I Polar Stratospheric Clouds using an unsupervised clus...

In recent years we have initiated and contributed to a number of campaigns to study non-radially pulsating objects. Our observing facility is the Mt John University Observatory 1.0 m telescope equipped with a high-efficiency and extremely stable echelle spectrograph, ideal for spectroscopic mode identification. Our current interests include delta S...

## Projects

Project (1)

Design algorithms to search for lunar frozen orbits and optimize station keeping efforts for extremely low altitude polar lunar missions.