Jennifer Hudson

Reduction of Low-Thrust Continuous Controls for Trajectory Dynamics

A novel method to evaluate the trajectory dynamics of low-thrust spacecraft is developed. The thrust vector components are represented as Fourier series in eccentric anomaly, and Gausss variational equations are averaged over one orbit to define a set of secular equations. These secular equations are a function of only 14 of the thrust Fourier coefficients, regardless of the order of the original Fourier series, and are sufficient to accurately determine a low-thrust spiral trajectory with significantly reduced computational requirements as compared with integration of the full Newtonian problem. This method has applications to low-thrust spacecraft targeting and optimal control problems.

Mission Analysis for a Micro RF Ion Thruster for CubeSat Orbital Maneuvers

The performance of a micro RF ion thruster is analyzed for several CubeSat orbital maneuver strategies. Mission simulations are performed for various types of trajectory control, including thrust at perigee only; intermittent thrust for a passive, magnetically stabilized spacecraft; and constant and pulsed thrust along the velocity vector. For each case, the propulsion system efficiency and maximum orbit change are evaluated. Constraints on power, fuel mass, and mission duration are considered. The most effective combinations of thruster operational modes and trajectory control strategies are discussed.

Orbital Targeting Using Reduced Eccentric Anomaly Low-Thrust Coefficients

A method to evaluate the trajectory dynamics of low-thrust spacecraft is applied to targeting and optimal control problems. Averaged variational equations for the osculating orbital elements are used to estimate a spacecraft trajectory over many spiral orbits. Fourteen Fourier coefficients of the thrust acceleration vector represent the fundamental trajectory dynamics. Spacecraft targeting problems are solved using the averaged variational equations and a general cost function represented as a Fourier series. The resulting fuel costs and dynamic fidelity of the targeting solutions are evaluated. The goal of the method is not precise targeting, but easy reconstruction of the basic elements of the thrusting trajectory and control law.

Iterative model and trajectory refinement for launch optimization of automotive powertrains

Abstract A recently proposed iterative model and trajectory refinement (IMTR) approach is applied to launch control of an automotive powertrain with a turbocharged gasoline engine and a dual-clutch transmission. The optimal clutch torque trajectory is determined by a piecewise linear in time function that minimizes a cost function while meeting multiple constraints on vehicle acceleration and engine speed. A high-fidelity model of the powertrain and a simplified physics-based model are used iteratively to refine solutions. The iterative method converges on a solution that meets target performance metrics with efficient execution time.

Trajectory optimization using the reduced eccentric anomaly low-thrust coefficients

A method to evaluate the trajectory dynamics of low-thrust spacecraft is refined and applied to targeting and optimal control problems. The original method uses averaged variational equations for the osculating orbital elements with 14 Fourier coefficients of the thrust acceleration vector to estimate a spacecraft trajectory over many spiral orbits. The accuracy of this method is improved by correction of any offset of the averaged trajectory from the true trajectory due to non-trivial periodic components. Spacecraft targeting problems are then solved using the corrected averaged variational equations and a general cost function represented as a Fourier series. A method for reducing the cost of a transfer by selection of acceleration Fourier coefficients beyond the 14 that appear in the averaged equations is described.

Mission Analysis for CubeSats with Micropropulsion

The orbital maneuver capabilities of several CubeSat propulsion systems are analyzed using trajectory simulations. Properties of several types of developmental micropropulsion systems are reviewed, and ΔV capabilities are compared. Mission simulations are used to analyze the relationship between thrust arc length and orbit change capability in a low-thrust spiral trajectory. Constraints on power, fuel mass, and mission duration, as well as system-level constraints, are considered. Feasible CubeSat architectures and mission designs are developed for three electric propulsion systems. The most effective combinations of thruster operational modes and trajectory control strategies are discussed.

Integration of micro electric propulsion system for cubesat orbital maneuvers

Attitude and trajectory control strategies are developed for a CubeSat with electric propulsion. The thrust capabilities of a micro RF ion thruster are characterized using ion source measurements to estimate thrust vectoring performance. Trajectory simulations are used to determine feasible orbit-raising maneuvers from low-Earth orbit. A PID controller is developed to determine attitude control torques for circular and elliptical orbit cases. Thrust vectoring to allow thruster pointing at a variable angle with respect to the CubeSat body is simulated.

A Linear Model for Low-Thrust Spiral Orbits and Optimal Control

This paper proposes a linear model to approximate the Newtonian equations of motion for low-thrust spiral orbits. The problem formulation consists of Keplerian orbital elements and fourteen Fourier thrust coe cients. The proposed linear model represents the spiral orbital dynamics more accurately than a rst-order linearizaton of the system. Using this linear formulation, linear quadratic optimal control is used to generate approximate solutions for low-thrust spiral orbit targeting problems.

Fourier Coefficient Selection for Low-Thrust Control Shaping

a = semimajor axis E = eccentric anomaly e = eccentricity F = thrust acceleration FR;W;S = radial, normal, and circumferential thrust acceleration i = inclination M = mean anomaly r = radial unit vector ŵ = normal unit vector α k = cosine coefficient, Fourier series of thrust acceleration β k = sine coefficient, Fourier series of thrust acceleration ΔV = velocity increment λ = angle of thrust acceleration Ω = longitude of the ascending node ω = argument of periapsis

Equivalent Average Trajectory Dynamics Using the Reduced Low-Thrust Coefficients

Calculation of low-thrust control laws with equivalent average trajectory dynamics but dierent thrust proles is studied using an averaged method based on Fourier series representation of the thrust control. Fourier coecients of order 2 and higher are used to transform variable-magnitude controls into controls with constant thrust arcs, which can be implemented more easily by low-thrust propulsion systems. Fuel cost reduction through selection of higher-order Fourier coecients is also discussed.