Marcus J. Holzinger

Texas A&M University, College Station, Texas, United States

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Publications (22)8.01 Total impact

  • Marcus J. Holzinger, Daniel J. Scheeres, John Hauser
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    ABSTRACT: The problem of optimal reachability set computation with alternate performance indices and independent parameters for smooth value functions is motivated and examined. A General Independent Parameter Hamilton Jacobi Bellman PDE formulation is derived and an independent parameter mapping function is defined. Performance index metric properties are leveraged to define Generalized Metric Range Sets. For Newtonian systems it is shown that singular independent parameter mappings can be circumvented using constants of motion. Finally, the motivating problem is solved using the central results of this technical note to generate free-time, $Delta v$-constrained orbital metric range sets.
    IEEE Transactions on Automatic Control 01/2015; 60(4):1099-1103. DOI:10.1109/TAC.2015.2391451 · 3.17 Impact Factor
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    ABSTRACT: 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.
    Journal of Guidance Control and Dynamics 04/2014; 37(3). DOI:10.2514/1.58002 · 1.15 Impact Factor
  • Marcus J. Holzinger, Daniel J. Scheeres, R. Scott Erwin
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    ABSTRACT: 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 J(2) perturbations. The derived optimal control policy reproduces known optimal free-time minimum Delta nu 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-fuel optimal maneuvers, and numerical examples of on-orbit operational range for low Earth orbits, geostationary transfer orbits, and geostationary Earth orbits are given. Applications to spacecraft operations are detailed.
    Journal of Guidance Control and Dynamics 03/2014; 37(2):608-622. DOI:10.2514/1.53861 · 1.15 Impact Factor
  • Marcus J. Holzinger, Jay W. McMahon
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    ABSTRACT: Sufficient stability conditions are derived for simultaneous uncoordinated impulsive maneuvers in distributed mean orbit element spacecraft formations. Lyapunov stability formalisms are used in conjunction with distributed mean orbit element spacecraft formation definitions. Special cases of the sufficient stability conditions are examined. Simulated results demonstrate the efficacy of the approach, and conclusions and future work are discussed.
    2013 American Control Conference (ACC); 06/2013
  • M.J. Holzinger, J.W. McMahon
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    ABSTRACT: Sufficient stability conditions are derived for simultaneous uncoordinated impulsive maneuvers in distributed mean orbit element spacecraft formations. Lyapunov stability formalisms are used in conjunction with distributed mean orbit element spacecraft formation definitions. Special cases of the sufficient stability conditions are examined. Simulated results demonstrate the efficacy of the approach, and conclusions and future work are discussed.
    American Control Conference (ACC), 2013; 01/2013
  • Marcus J. Holzinger, Daniel J. Scheeres, Kyle T. Alfriend
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    ABSTRACT: 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.
    Journal of Guidance Control and Dynamics 07/2012; 35(4):1312-1325. DOI:10.2514/1.53245 · 1.15 Impact Factor
  • Marcus J. Holzinger, Daniel J. Scheeres
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    ABSTRACT: 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.
    IEEE Transactions on Aerospace and Electronic Systems 04/2012; 48(2):1583-1600. DOI:10.1109/TAES.2012.6178080 · 1.39 Impact Factor
  • D.J. Scheeres, M.J. Holzinger
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    ABSTRACT: Changes in the orbit of a space-based object are a characteristic of a maneuver having occurred or of mismodeling of the state dynamics. This paper focuses on the former hypothesis to evaluate what constraints and inferences can be made on the actions of a vehicle given minimal information on its change in state. Such information can generally be used to evaluate whether a maneuver was likely, place constraints on the size of the maneuver, and can be used to reconstruct what form a maneuver took. This paper reviews what can be inferred from a difference in an object's orbital state through the definition and application of the control distance metric.
    Information Fusion (FUSION), 2012 15th International Conference on; 01/2012
  • Source
    M. Holzinger, D. Scheeres
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    ABSTRACT: History and methodology of ∆v range set computation is briefly reviewed, followed by a short summary of the ∆v optimal spacecraft servicing problem literature. Service vehicle placement is approached from a ∆v range set viewpoint, providing a framework under which the analysis becomes quite geometric and intuitive. The optimal servicing tour design problem is shown to be a specific instantiation of the metric- Traveling Salesman Problem (TSP), which in general is an NP-hard problem. The ∆v-TSP is argued to be quite similar to the Euclidean-TSP, for which approximate optimal solutions may be found in polynomial time. Applications of range sets are demonstrated using analytical and simulation results.
  • Marcus Holzinger
    AIAA Guidance, Navigation, and Control Conference; 08/2011
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    M.J. Holzinger, D.J. Scheeres
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    ABSTRACT: The track assignment problem in applications with large gaps in tracking measurements and uncertain boundary conditions is addressed as a Two Point Boundary Value Problem (TPBVP) using Hamiltonian formalisms. An L<sub>2</sub>-norm analog Linear Quadratic Regulator (LQR) performance function metric is used to measure the trajectory cost, which may be interpreted as a control distance metric. Distributions of the performance function are determined by linearizing about the deterministic optimal nonlinear trajectory solution to the TPBVP and accounting for statistical variations in the boundary conditions. The performance function random variable under this treatment is found to have a quadratic form, and Pearson's Approximation is used to model it as a chi-squared random variable. Stochastic dominance is borrowed from mathematical finance and is used to rank statistical distributions in a metric sense. Analytical results and approximations are validated and an example of the approach utility is given. Finally conclusions and future work are discussed.
    American Control Conference (ACC), 2011; 08/2011
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    M.J. Holzinger, D.J. Scheeres, J. Hauser
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    ABSTRACT: 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.
    American Control Conference (ACC), 2011; 08/2011
  • Marcus J. Holzinger, Daniel J. Scheeres
    [Show abstract] [Hide abstract]
    ABSTRACT: The track assignment problem in applications with large gaps in tracking measurements and uncertain boundary conditions is addressed as a Two Point Boundary Value Problem (TPBVP) using Hamiltonian formalisms. An L2-norm analog Linear Quadratic Regulator (LQR) performance function metric is used to measure the trajectory cost, which may be interpreted as a control distance metric. Distributions of the performance function are determined by linearizing about the deterministic optimal nonlinear trajectory solution to the TPBVP and accounting for statistical variations in the boundary conditions. The performance function random variable under this treatment is found to have a quadratic form, and Pearson's Approximation is used to model it as a chi-squared random variable. Stochastic dominance is borrowed from mathematical finance and is used to rank statistical distributions in a metric sense. Analytical results and approximations are validated and an example of the approach utility is given. Finally conclusions and future work are discussed.
    2011 American Control Conference; 06/2011
  • Marcus J. Holzinger, Daniel J. Scheeres, John Hauser
    [Show abstract] [Hide abstract]
    ABSTRACT: 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.
    2011 American Control Conference; 06/2011
  • Source
    Marcus J. Holzinger
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    ABSTRACT: There are currently more than 19,000 trackable objects in Earth orbit, 1,300 of which are active. With so many objects populating the space object catalog and new objects being added at an ever increasing rate, ensuring continued access to space is quickly becoming a cornerstone of national security policies. Space Situational Awareness (SSA) supports space operations, space flight safety, implementing international treaties and agreements, protecting of space capabilities, and protecting of national interests. With respect to objects in orbit, this entails determining their location, orientation, size, shape, status, purpose, current tasking, and future tasking. For active spacecraft capable of propulsion, the problem of determining these characteristics becomes significantly more difficult. Optimal control techniques can be applied to object correlation, maneuver detection, maneuver/spacecraft characterization, fuel usage estimation, operator priority inference, intercept capability characterization, and fuel-constrained range set determination. A detailed mapping between optimal control applications and SSA object characterization support is reviewed and related literature visited. Each SSA application will be addressed starting from first-principles using optimal control techniques. For each application, several examples of potential utility are given and discussed.
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    M.J. Holzinger, D.J. Scheeres
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    ABSTRACT: Computational savings in reachability set subspace computation are realized by carefully applying transversality conditions to trajectory samplings of the full reachability set. Differential constraints on the initial state and initial constraint Lagrange multiplier are developed that enforce the necessary conditions of optimality as total trajectory duration increases. Results are validated against known linear analytical results and an example is given where a 1-dimensional subspace of a 6-dimensional nonlinear problem is computed.
    Decision and Control and European Control Conference (CDC-ECC), 2011 50th IEEE Conference on; 01/2011
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    M. Holzinger, D. Scheeres
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    ABSTRACT: Object correlation and maneuver detection 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 both correlate object tracks and detect maneuvers using Uncorrelated Tracks (UCTs), real-time sensor measurement residuals, and prior state uncertainty. State and measurement uncertainty are incorporated into the computation, and distributions of optimal control usage are computed. Both UCT correlation as well as maneuver detection are demonstrated in several scenarios Potential avenues for future research and contributions are summarized.
  • Marcus Holzinger, Daniel Scheeres
    AIAA Guidance, Navigation, and Control Conference; 08/2010
  • Source
    M.J. Holzinger, D.J. Scheeres
    [Show abstract] [Hide abstract]
    ABSTRACT: Existing reachability theory and optimal control theory are applied to a class of nonlinear systems with ellipsoidal initial reachability sets, reflecting information typically provided by industry-standard optimal estimation methods. Analytical expressions for position-and velocity-extrema are developed, yielding necessary conditions for reachability as well as tools for significant reduction in reachability computation requirements. 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.
    Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conference. CDC/CCC 2009. Proceedings of the 48th IEEE Conference on; 01/2010
  • Source
    Marcus Holzinger, Daniel Scheeres
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    ABSTRACT: 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-configuration 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. 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. Examples for both circular and eccentric orbits are examined and compared. Weaknesses with the current implementation are discussed and future numerical improvements and analytical efforts are discussed.

Publication Stats

19 Citations
8.01 Total Impact Points

Institutions

  • 2014
    • Texas A&M University
      College Station, Texas, United States
  • 2011–2014
    • University of Colorado at Boulder
      • Department of Aerospace Engineering Sciences (AES)
      Boulder, Colorado, United States
  • 2013
    • Georgia Institute of Technology
      • School of Aerospace Engineering
      Atlanta, Georgia, United States
  • 2009
    • Northrop Grumman
      Falls Church, Virginia, United States