Optimal Reconfiguration of Formation Flying Spacecraft--a Decentralized Approach

This paper introduces a hierarchical, decentralized, and parallelizable method for dealing with optimization problems with many agents. It is theoretically based on a hierarchical optimization theorem that establishes the equivalence of two forms of the problem, and this idea is implemented using DMOC (Discrete Mechanics and Optimal Control). The result is a method that is scalable to certain optimization problems for large numbers of agents, whereas the usual “monolithic” approach can only deal with systems with a rather small number of degrees of freedom. The method is illustrated with the example of deployment of spacecraft, motivated by the Darwin (ESA) and Terrestrial Planet Finder (NASA) missions

Discrete mechanics and optimal control: An analysis

The optimal control of a mechanical system is of crucial importance in many application areas. Typical examples are the determination of a time-minimal path in vehicle dynamics, a minimal energy trajectory in space mission design, or optimal motion sequences in robotics and biomechanics. In most cases, some sort of discretization of the original, infinite-dimensional optimization problem has to be performed in order to make the problem amenable to computations. The approach proposed in this paper is to directly discretize the variational description of the system's motion. The resulting optimization algorithm lets the discrete solution directly inherit characteristic structural properties from the continuous one like symmetries and integrals of the motion. We show that the DMOC (Discrete Mechanics and Optimal Control) approach is equivalent to a finite difference discretization of Hamilton's equations by a symplectic partitioned Runge-Kutta scheme and employ this fact in order to give a proof of convergence. The numerical performance of DMOC and its relationship to other existing optimal control methods are investigated

Cramer-Rao Lower Bound for Point Based Image Registration with Heteroscedastic Error Model for Application in Single Molecule Microscopy

The Cramer-Rao lower bound for the estimation of the affine transformation parameters in a multivariate heteroscedastic errors-in-variables model is derived. The model is suitable for feature-based image registration in which both sets of control points are localized with errors whose covariance matrices vary from point to point. With focus given to the registration of fluorescence microscopy images, the Cramer-Rao lower bound for the estimation of a feature's position (e.g. of a single molecule) in a registered image is also derived. In the particular case where all covariance matrices for the localization errors are scalar multiples of a common positive definite matrix (e.g. the identity matrix), as can be assumed in fluorescence microscopy, then simplified expressions for the Cramer-Rao lower bound are given. Under certain simplifying assumptions these expressions are shown to match asymptotic distributions for a previously presented set of estimators. Theoretical results are verified with simulations and experimental data

The Jacobi-Maupertuis Principle in Variational Integrators

In this paper, we develop a hybrid variational integrator based on the Jacobi-Maupertuis Principle of Least Action. The Jacobi-Maupertuis principle states that for a mechanical system with total energy E and potential energy V(q), the curve traced out by the system on a constant energy surface minimizes the action given by ∫√[2(E-V(q))] ds where ds is the line element on the constant energy surface with respect to the kinetic energy of the system. The key feature is that the principle is a parametrization independent geodesic problem. We show that this principle can be combined with traditional variational integrators and can be used to efficiently handle high velocity regions where small time steps would otherwise be required. This is done by switching between the Hamilton principle and the Jacobi-Maupertuis principle depending upon the kinetic energy of the system. We demonstrate our technique for the Kepler problem and discuss some ongoing and future work in studying the energy and momentum behavior of the resulting integrator

Cultivating Acute Care Rehabilitation Team Collaboration Using the Kawa Model

Purpose: Effective healthcare team collaboration is imperative for quality client-centered care, job satisfaction, and overall morale. Rehabilitation team collaboration can be impacted by high productivity demands, differing backgrounds of individual team members, and the unpredictable healthcare environment. The Kawa (river) model, a culturally-neutral model of occupational therapy practice, has been shown to improve communication and collaboration with its use of metaphors, but its utility in various contexts to enhance collaborative practice is still being explored. The purpose of this study was to implement an evidence-based teambuilding intervention with use of the Kawa model to investigate the impact on acute care rehabilitation team collaboration. Method: A 5-week pretest-posttest study was completed with a group of eight rehabilitation team members, consisting of occupational therapists, physical therapists, and a speech language pathologist, in an acute care setting. Pre and post-surveys were utilized to gather quantitative and qualitative data on perceptions of team collaboration, knowledge of the Kawa model, and the model’s utility for collaboration. Results: Outcomes showed overall mean improvements in agreement that the Kawa model provides a common method of communication, and 100% of the participants agreed or strongly agreed that use of the Kawa model can improve acute care rehabilitation team collaboration. Qualitative post-survey responses indicated an enhanced understanding of the components of effective team collaboration. Conclusions & Recommendations: Team collaboration was cultivated with use of the Kawa model. The model provided a successful method for the acute care team to openly discuss and collaboratively problem-solve how to maximize their team flow. Further study of the Kawa model’s utility to improve collaboration in various contexts with broader participant groups is recommended, as well as study of longitudinal effects of a teambuilding intervention with use of the Kawa model

Trajectory Design Combining Invariant Manifolds with Discrete Mechanics and Optimal Control

A mission design technique that combines invariant manifold techniques, discrete mechanics, and optimal control produces locally optimal low-energy trajectories. Previously, invariant manifolds of the planar circular restricted three-body problem have been used to design trajectories with relatively small midcourse change in velocity ΔV. A different method of using invariant manifolds is explored to design trajectories directly in the four-body problem. Then, using the local optimal control method DMOC (Discrete Mechanics and Optimal Control), it is possible to reduce the midcourse ΔV to zero. The influence of different boundary conditions on the optimal trajectory is also demonstrated. These methods are tested on a trajectory that begins in Earth orbit and ends in ballistic capture at the moon. Impulsive DMOC trajectories require up to 19% less ΔV than trajectories using a Hohmann transfer. When applied to low-thrust trajectories, DMOC produces an improvement of up to 59% in the mass fraction and 22% in travel time when compared with results from shooting methods

The Dynamic Use of the Kawa Model: A Scoping Review

Background: The Kawa model, a framework to guide culturally relevant occupational therapy, has gained recognition and become more widely used in practice. Research on the model thus far, while still relatively sparse, provides guidance for the model’s use, including its strengths and facets that require further exploration to support its use and effectiveness in dynamic ways. Method: A scoping review was completed to gather, organize, appraise, and synthesize the current research evidence on use of the model. Results: Findings support the Kawa model’s culturally flexible application and its capacity to garner client-centered qualitative information, as well as to build therapeutic relationships in a variety of settings. Challenges to the model’s use include therapists’ inexperience limiting effectiveness and the need for additional quantitative assessment measures to supplement the qualitative findings gathered during use of the Kawa. Limitations to this review include author preconceptions, homogeneity among the authors, and inclusion of non-peer-reviewed theses. Conclusion: The Kawa model is an adaptable tool to examine and enhance well-being. It may be most effective when used by experienced therapists and in conjunction with other relevant tools. Further research is recommended to continue to evaluate its dynamic use

Factor analysis of the Dissertation Barriers Scale: Evidence for dimensionality and construct validity.

The research participants consisted of 319 graduate students from APA-approved doctoral programs. Five instruments were administered for this study: Dissertation Barriers Scale (DBS), Self-Efficacy in Research Measure (SERM), Advisor Working Alliance Inventory---Student Version (AWAI-S), Multidimensional Scale of Perceived Social Support (MSPSS), and a demographic questionnaire. The findings of this study indicated a 5-factor solution for the DBS and provided some evidence of reliability and validity. Also, multiple regression analyses revealed relationships between the DBS components and various subscales of the SERM, AWAI-S, and the MSPSS and the DBS total score and select demographic variables. Advisors and department chairs can use the information provided by the DBS to plan coursework, review advisor/advisee relationship characteristics, and highlight practical considerations in the personal lives of students