Engineering topics
How, Jonathan P.
Publications and source records attributed to How, Jonathan P..
Two-Stage Path Planning Approach for Designing Multiple Spacecraft Reconfiguration Maneuvers
The paper presents a two-stage approach for designing optimal reconfiguration maneuvers for multiple spacecraft. These maneuvers involve well-coordinated and highly-coupled motions of the entire fleet of spacecraft while satisfying an arbitrary number of constraints. This problem is particularly difficult because of the nonlinearity of the attitude dynamics, the non-convexity of some of the constraints, and the coupling between the positions and attitudes of all spacecraft. As a result, the trajectory design must be solved as a single 6N DOF problem instead of N separate 6 DOF problems. The first stage of the solution approach quickly provides a feasible initial solution by solving a simplified version without differential constraints using a bi-directional Rapidly-exploring Random Tree (RRT) planner. A transition algorithm then augments this guess with feasible dynamics that are propagated from the beginning to the end of the trajectory. The resulting output is a feasible initial guess to the complete optimal control problem that is discretized in the second stage using a Gauss pseudospectral method (GPM) and solved using an off-the-shelf nonlinear solver. This paper also places emphasis on the importance of the initialization step in pseudospectral methods in order to decrease their computation times and enable the solution of a more complex class of problems. Several examples are presented and discussed.
Multi-Objective Online Initialization of Spacecraft Formations
This paper extends a previously developed method for finding spacecraft initial conditions (ICs) that minimize the drift resulting from J2 disturbances while also minimizing the fuel required to attain those ICs. It generalizes the single spacecraft optimization to a formation-wide optimization valid for an arbitrary number of vehicles. Additionally, the desired locations of the spacecraft, separate from the starting location, can be specified, either with respect to a reference orbit, or relative to the other spacecraft in the formation. The three objectives (minimize drift, minimize fuel, and maintain a geometric template) are expressed as competing costs in a linear optimization, and are traded against one another through the use of scalar weights. By carefully selecting these weights and re-initializing the formation at regular intervals, a closed-loop, formation-wide control system is created. This control system can be used to reconfigure the formations on the fly, and creates fuel-efficient plans by placing the spacecraft in semi-invariant orbits. The overall approach is demonstrated through nonlinear simulations for two formations a GEO orbit, and an elliptical orbit.
GVE-Based Dynamics and Control for Formation Flying Spacecraft
Formation flying is an enabling technology for many future space missions. This paper presents extensions to the equations of relative motion expressed in Keplerian orbital elements, including new initialization techniques for general formation configurations. A new linear time-varying form of the equations of relative motion is developed from Gauss Variational Equations and used in a model predictive controller. The linearizing assumptions for these equations are shown to be consistent with typical formation flying scenarios. Several linear, convex initialization techniques are presented, as well as a general, decentralized method for coordinating a tetrahedral formation using differential orbital elements. Control methods are validated using a commercial numerical propagator.
Semimajor Axis Estimation Strategies
This paper extends previous analysis on the impact of sensing noise for the navigation and control aspects of formation flying spacecraft. We analyze the use of Carrier-phase Differential GPS (CDGPS) in relative navigation filters, with a particular focus on the filter correlation coefficient. This work was motivated by previous publications which suggested that a "good" navigation filter would have a strong correlation (i.e., coefficient near -1) to reduce the semimajor axis (SMA) error, and therefore, the overall fuel use. However, practical experience with CDGPS-based filters has shown this strong correlation seldom occurs (typical correlations approx. -0.1), even when the estimation accuracies are very good. We derive an analytic estimate of the filter correlation coefficient and demonstrate that, for the process and sensor noises levels expected with CDGPS, the expected value will be very low. It is also demonstrated that this correlation can be improved by increasing the time step of the discrete Kalman filter, but since the balance condition is not satisfied, the SMA error also increases. These observations are verified with several linear simulations. The combination of these simulations and analysis provide new insights on the crucial role of the process noise in determining the semimajor axis knowledge.
ORION-II: A True Formation Flying Mission in LEO
The final report for the Orion-II project is taken from Chapter 5 of "CDGPS-Based Relative Navigation for Multiple Spacecraft," a thesis by Megan Mitchell submitted to the MIT Department of Aeronautics and Astronautics, June 2004. This chapter begins with a comparison of the simulation architecture for the original and current simulation setups. Next, the changes made to the individual components of the navigation system are described. Finally, tests performed with a Spirent Simulator at NASA Goddard Space Flight Center (GSFC) are discussed. In addition to the development of the testbed components described, a new clean room facility was developed in the Orion Laboratory at MIT.
Agent Based Software for the Autonomous Control of Formation Flying Spacecraft
Distributed satellite systems is an enabling technology for many future NASA/DoD earth and space science missions, such as MMS, MAXIM, Leonardo, and LISA [1, 2, 3]. While formation flying offers significant science benefits, to reduce the operating costs for these missions it will be essential that these multiple vehicles effectively act as a single spacecraft by performing coordinated observations. Autonomous guidance, navigation, and control as part of a coordinated fleet-autonomy is a key technology that will help accomplish this complex goal. This is no small task, as most current space missions require significant input from the ground for even relatively simple decisions such as thruster burns. Work for the NMP DS1 mission focused on the development of the New Millennium Remote Agent (NMRA) architecture for autonomous spacecraft control systems. NMRA integrates traditional real-time monitoring and control with components for constraint-based planning, robust multi-threaded execution, and model-based diagnosis and reconfiguration. The complexity of using an autonomous approach for space flight software was evident when most of its capabilities were stripped off prior to launch (although more capability was uplinked subsequently, and the resulting demonstration was very successful).
Robust controllers for the Middeck Active Control Experiment using Popov controller synthesis
Recent work in robust control with real parameter uncertainties has focused on absolute stability and its connections to real mu theory. In particular, the research has investigated the Popov stability criterion and its associated Lur'e-Postnikov Liapunov functions. State space representations of this Popov stability analysis tests are included in an H2 design formulation to provide a powerful technique for robust controller synthesis. This synthesis approach uses a state space optimization procedure to design controllers that minimize an overbound of an H2 cost functional and satisfy stability analysis tests based on the Popov multiplier. The controller and stability multiplier coefficients are optimized simultaneously, which avoids the iteration and curve-fitting procedures required by the D-K algorithm of mu synthesis. While previous work has demonstrated this synthesis approach on benchmark control problems, the purpose of this paper is to use Popov controller synthesis to design robust compensators for the Middeck Active Control Experiment (MACE).
Robust control design with real parameter uncertainty using absolute stability theory
The purpose of this thesis is to investigate an extension of mu theory for robust control design by considering systems with linear and nonlinear real parameter uncertainties. In the process, explicit connections are made between mixed mu and absolute stability theory. In particular, it is shown that the upper bounds for mixed mu are a generalization of results from absolute stability theory. Both state space and frequency domain criteria are developed for several nonlinearities and stability multipliers using the wealth of literature on absolute stability theory and the concepts of supply rates and storage functions. The state space conditions are expressed in terms of Riccati equations and parameter-dependent Lyapunov functions. For controller synthesis, these stability conditions are used to form an overbound of the H2 performance objective. A geometric interpretation of the equivalent frequency domain criteria in terms of off-axis circles clarifies the important role of the multiplier and shows that both the magnitude and phase of the uncertainty are considered. A numerical algorithm is developed to design robust controllers that minimize the bound on an H2 cost functional and satisfy an analysis test based on the Popov stability multiplier. The controller and multiplier coefficients are optimized simultaneously, which avoids the iteration and curve-fitting procedures required by the D-K procedure of mu synthesis. Several benchmark problems and experiments on the Middeck Active Control Experiment at M.I.T. demonstrate that these controllers achieve good robust performance and guaranteed stability bounds.
Finite element model and identification procedure
Viewgraphs on finite element model and identification procedure are presented. Topics covered include: interferometer finite element model; testbed mode shapes; finite element model update; identification procedure; shaker locations; data analysis; modal frequency and damping comparison; computational procedure; fit comparison; residue analysis; typical residues; identification/FEM residual comparison; and pathlength control using isolation mounts.
The application of controlled structures technology to adaptive optics
Viewgraphs on the application of controlled structures technology (CST) to adaptive optics are presented. Topics covered include: a typical large optical system (LDR); overview of current optical programs; typical adaptive optics system; actuation approaches for deforming a mirror; control approach comparison; control structure interaction (CSI) control bandwidth limitations; applications of CST concepts to optics; distributed control approaches; quasistatic error correction; low authority control (LAC); and high authority control (HAC) design methodology.