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Morgan D.,University of Illinois at Urbana - Champaign | Chung S.-J.,University of Illinois at Urbana - Champaign | Blackmore L.,Jet Propulsion Laboratory | Blackmore L.,Guidance and Control Analysis Group | And 6 more authors.
Journal of Guidance, Control, and Dynamics | Year: 2012

This paper presents several new open-loop guidance methods for spacecraft swarms composed of hundreds to thousands of agents, with each spacecraft having modest capabilities. These methods have three main goals: preventing relative drift of the swarm, preventing collisions within the swarm, and minimizing the propellant used throughout the mission. The development of these methods progresses by eliminating drift using the Hill-Clohessy- Wiltshire equations, removing drift due to nonlinearity, and minimizing the J 2 drift. To verify these guidance methods, a new dynamic model for the relative motion of spacecraft is developed. These dynamics include the two main disturbances for spacecraft in low Earth orbit, J 2 and atmospheric drag. Using this dynamic model, numerical simulations are provided at each step to show the effectiveness of each method and to see where improvements can be made. The main result is a set of initial conditions for each spacecraft in the swarm, which provides the trajectories for hundreds of collision-free orbits in the presence of J2. Finally, a multiburn strategy is developed to provide hundreds of collision-free orbits under the influence of atmospheric drag. This last method works by enforcing the initial conditions multiple times throughout the mission, thereby providing collision-free trajectories for the duration of the mission. Copyright © 2012 by the American Institute of Aeronautics and Astronautics, Inc.


Blackmore L.,Jet Propulsion Laboratory | Blackmore L.,Guidance and Control Analysis Group | Acikmese B.,Jet Propulsion Laboratory | Acikmese B.,Guidance and Control Analysis Group | And 2 more authors.
Journal of Guidance, Control, and Dynamics | Year: 2010

To increase the science return of future missions to Mars and to enable sample return missions, the accuracy with which a lander can be delivered to the Martian surface must be improved by orders of magnitude. The prior work developed a convex-optimization-based minimum-fuel powered-descent guidance algorithm. In this paper, this convex-optimization-based approach is extended to handle the case when no feasible trajectory to the target exists. In this case, the objective is to generate the minimum-landing-error trajectory, which is the trajectory that minimizes the distance to the prescribed target while using the available fuel optimally. This problem is inherently a nonconvex optimal control problem due to a nonzero lower bound on the magnitude of the feasible thrust vector. It is first proven that an optimal solution of a convex relaxation of the problem is also optimal for the original nonconvex problem, which is referred to as a lossless convexification of the original nonconvex problem. Then it is shown that the minimum-landing-error trajectory generation problem can be posed as a convex optimization problem and solved to global optimality with known bounds on convergence time. This makes the approach amenable to onboard implementation for real-time applications.


Aldrich J.B.,Jet Propulsion Laboratory | Aldrich J.B.,Guidance and Control Analysis Group
Journal of Guidance, Control, and Dynamics | Year: 2014

Analytic formulas that guarantee a minimum level of disturbance-rejection performance are derived for a class of attitude control problems consisting of linear proportional-derivative quaternion feedback applied to a rigid-body spacecraft plant model. Specifically, a Lyapunov-based disturbance-rejection assessment tool is derived for a general class of perturbed nonlinear systems, and then it is specialized to the linear attitude control class. Although the tool accepts generic Lyapunov function candidates, this paper demonstrates that existing Lyapunov functions (that readily prove asymptotic stability for attitude control systems) are insufficiently parameterized for purposes of estimating disturbance-rejection capability via the proposed tool. In response to this shortcoming, two new Lyapunov functions are proposed, and they are evaluated in the context of two closed-form disturbance-rejection performance assessment algorithms. Both algorithms demonstrate that the magnitude of the allowable disturbance torque is proportional to 1) the magnitude of the allowable angular accuracy, 2) the square of the control bandwidth, and 3) the minimum eigenvalue of the spacecraft inertia matrix. Moreover, the constant of proportionality (coefficient of rejection) is shown to degrade gradually for larger angles, and it eventually goes to zero as the user-specified angular accuracy is increased to 180 deg (for a high-order Lyapunov function) and 12 deg (for a low-order quadratic Lyapunov function). Copyright © 2013 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

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