Marcus J. Holzinger

University of Colorado at Boulder , Boulder, CO, United States

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Publications (19)4.85 Total impact

  • Journal of Guidance Control and Dynamics 04/2014; 37(3). · 1.15 Impact Factor
  • Marcus J. Holzinger, Daniel J. Scheeres, R. Scott Erwin
    Journal of Guidance Control and Dynamics 03/2014; 37(2):608-622. · 1.15 Impact Factor
  • Marcus J. Holzinger, Daniel J. Scheeres, Kyle T. Alfriend
    Journal of Guidance Control and Dynamics 07/2012; 35(4):1312-1325. · 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. · 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
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    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.
    09/2011;
  • Marcus Holzinger
    AIAA Guidance, Navigation, and Control Conference; 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
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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
  • Marcus J. Holzinger, Daniel 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 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
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    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.
    01/2011;
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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.
    09/2010;
  • Marcus Holzinger, Daniel Scheeres
    AIAA Guidance, Navigation, and Control Conference; 08/2010
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    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
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    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.
    08/2009;
  • Marcus Holzinger, Daniel Scheeres
    AIAA Guidance, Navigation, and Control Conference; 08/2009
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    M. Holzinger, J. DiMatteo, J. Schwartz, M. Milam
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    ABSTRACT: 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.
    Decision and Control, 2008. CDC 2008. 47th IEEE Conference on; 01/2009