Marcus J. Holzinger

Object Correlation, Maneuver Detection, and Characterization Using Control-Distance Metrics

Object correlation, maneuver detection, and maneuver characterization are persistent problems in space surveillance and space object catalog maintenance. This paper demonstrates the utility of using control effort as a rigorously defined metric with which to correlate object observations, detect maneuvers, and characterize maneuvers given dynamical systems with boundary-condition uncertainty. Uncorrelated tracks and new object measurements are incorporated into the control-distance metric framework and corresponding control-distance distributions are computed. Approaches are given with which to rank control-distance distributions and hypothesis testing is used to detect possible maneuvers in the presence of system uncertainty. Simulated examples of the approaches are given and implications are discussed. Potential avenues for future research and contributions are summarized.

Incorporating Uncertainty in Admissible Regions for Uncorrelated Detections

Admissible region methods for initial orbit determination are generally implemented without considering the contributions of uncertainty in observations or observer state when computing the admissible region. In this paper, a generalization of the admissible region approach is introduced that more accurately accounts for uncertainty in the constraint hypothesis parameters used to generate the admissible region. Considering the uncertainty to have Gaussian distributions, the proposed relationship between provided information uncertainty and admissible region uncertainty results directly in an analytical probability distribution function. The methodology is extended to account for admissible regions with multiple overlapping constraint hypotheses. The proposed approach is applied to an example optical detection to demonstrate the quality of the approximation and the sensitivity of the resulting distribution to typical errors.

Passively safe Receding Horizon Control for satellite proximity operations

Recent on-orbit mission performance illustrates a pressing need to develop passively safe formation flight trajectories and controllers for multiple satellite proximity operations. A receding horizon control (RHC) approach is formulated that directly relates navigation uncertainty and process noise to non-convex quadratic constraints, which enforce passive safety in the presence of a large class of navigation or propulsion system failures. Several Keplerian simulations are executed to examine increased ¿v usage incurred by adding passive safety constraints, the corresponding reduction in collision probability, and resulting passively safe formation flight geometries. Results show that modest cross-track motion significantly reduces collision probability, and that once a passively safe relative orbit is achieved, steady-state ¿v usage rates are comparable to usage rates without passive safety constraints. Navigation uncertainty and process noise are found to be significant ¿v usage drivers for passively safe proximity operations. Onorbit autonomous RHC control with passive safety constraints applied to proximity operation missions enables trajectory generation and control that reduces collision probability to acceptable levels while minimizing ¿v usage.

Reachability Results for Nonlinear Systems with Ellipsoidal Initial Sets

Existing reachability and optimal control theory are applied to a class of nonlinear systems with ellipsoidal initial reachability sets. Analytical expressions for general state partition extrema are developed, yielding necessary conditions for reachability as well as tools for significant reduction in reachability computation. Similar relations for position and velocity reachability set surface computation are also developed and the computation implications discussed. Several examples are worked to illustrate results, and finally directions for future work are discussed.

Photometric Attitude Estimation for Agile Space Objects with Shape Uncertainty

The problem of estimating attitude for actively maneuvering or passively rotating space objects with unknown mass properties/external torques and uncertain shape models is addressed. To account for agile space object maneuvers, angular rates are simply assumed to be random inputs (e.g., process noise), and model uncertainty is accounted for in a bias state with dynamics derived using first principles. Bayesian estimation approaches are used to estimate the resulting severely non-Gaussian and multimodal state distributions. Simulated results are given, conclusions regarding performance are made, and future work is outlined.

Robust Feature Detection, Acquisition and Tracking for Relative Navigation in Space with a Known Target

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On-Orbit Operational Range Computation Using Gauss’s Variational Equations with J2 Perturbations

Aircraft operational range, the distance an aircraft can travel with a fixed quantity of fuel, is an intuitive measure that provides strategic and tactical insight to the end user. Currently, there is no rigorously defined and derived operational range measure for on-orbit spacecraft operations with which to inform strategic decisions and planning. This paper illustrates how operational range may be computed in the context of orbital motion using optimal control theory and how existing results in reachability set computation may be leveraged. The solution method presented incidentally solves the free-time minimum-impulse full orbit-element transfer problem under J2 perturbations. The derived optimal control policy reproduces known optimal free-time minimum Δv basis maneuvers. The methodology presented is shown to have the capability to exactly capture the minimum-fuel free-time operational range volumes, although numerical solution algorithm errors persist. The approach is validated using known minimum-fu...

Object Correlation, Maneuver Detection, and Maneuver Characterization using Control Effort Metrics with Uncertain Boundary Conditions and Measurements

Object correlation, maneuver detection, and maneuver characterization are persistent problems in space surveillance and space object catalog maintenance. This paper demonstrates the utility of using quadratic trajectory control cost, an analog to the trajectory L2-norm in control, as a distance metric with which to correlate object observations, detect maneuvers, and characterize maneuvers using real-time sensor measurement residuals and prior state uncertainty. An object track correlation approach is investigated that frames the Two-Point Boundary Value Problem (TPBVP) with uncertain boundary conditions in terms of the control distance metric framework. Also, information typically available to operators such as propagated state uncertainty, measurement uncertainty, and real-time measurement residuals are also incorporated into the control distance metric framework. Careful inclusion of these uncertainties enables conservative maneuver detection and characterization. Simulated examples of the approaches are given and implications are discussed. Potential avenues for future research and contributions are summarized.

Applied Reachability for Space Situational Awareness and Safety in Spacecraft Proximity Operations

Several existing and emerging applications of Space Situational Awareness (SSA) relate directly to spacecraft Rendezvous, Proximity Operations, and Docking (RPOD) and Formation / Cluster Flight (FCF). Observation correlation of nearby objects, control authority estimation, sensor-track re-acquisition, formation re-conguration feasibility, ‘stuck’ thrusters, and worst-case passive safety analysis are some areas where analytical reachability methods have potential utility. Existing reachability theory is applied to RPOD and FCF regimes. An optimal control policy is developed to maximize the reachability set and optimal control law discontinuities (switching) are examined. Necessary conditions for maximum position reachability are developed, allowing for a reduction in reachable set computation dimensionality. The nonlinear relative equations of Keplerian motion are introduced and used for all reachable position set determinations. The linearized ClohessyWiltshire equations of motion are normalized to accentuate relative control authority for spacecraft propulsion systems at both Low Earth Orbit (LEO) and Geostationary Earth Orbit (GEO). Several examples with traditional and low thrust propulsion systems in LEO and GEO are explored to illustrate the eects of relative control authority on the timevarying reachability set surface using the nonlinear equations of motion. Both monopropellant spacecraft at LEO and Hall thruster spacecraft at GEO are shown to be strongly actuated while Hall thruster spacecraft at LEO are found to be weakly actuated. Weaknesses with the current implementation are discussed and future numerical improvements and analytical eorts are discussed.

Optimal reachability sets using Generalized Independent Parameters

The problem of free-time optimal reachability set computation with alternate integral constraints is motivated and examined. Specific examples of such systems are optimal spacecraft, aircraft and automobile free-time, fuel-limited range computation. An alternate Hamilton Jacobi Bellman PDE formulation is derived using a Generalized Independent Parameter (GIP) associated with the integration constraint and GIP mapping function with respect to time is defined. Necessary conditions on the GIP mapping function are identified and discussed. Singular independent parameter mapping functions, often found in astrodynamics optimal control problems, are shown to be challenging to solve using a simple change of integration variable, motivating an approach to transform such problems before solving. Several short illustrations are used to emphasize theoretical cases of interest, and two simple fully-worked examples are given to demonstrate the potential utility of this approach.