Predictive Control of a Munition Using Low-Speed Linear Theory

Modified linear theory provides reasonable impact predictions at high speeds. However, for typical small UAS mission speeds, less than 20-m/s impact errors were substantial due to large angles of attack and pitch rates. Low-speed linear theory was developed by including higher-order terms involving w and q that modified linear theory neglects. As a result, the angle of attack, pitch, and yaw predictions are significantly improved, leading to accurate impact predictions even at very low speeds. A predictive control scheme was developed to reduce dispersion using control surfaces near the tail. The predictive controller uses low-speed linear theory to rapidly predict the impact error using the current state and control. Based on the estimated impact error, the control is iteratively found to minimize the predicted-impact error. For an example munition, it was shown that the maximum number of iterations during the control solution only impacted the initial control estimates. Limiting the guidance algorithm to a single iteration had little impact on the final accuracy and permitted a rapid solution. It was shown for the example munition that the predictive guidance significantly reduced the CEP from 14.1 to 2.7 and 2.2 m when the maximum iterations were 1 and 10. Furthermore, for a typical high- explosive 40-mm grenade, the percentage of impacts within a lethal radius was increased from 10 to 78% when the maximum iterations were both 1 and 10. In practical applications, errors in the target location must beincluded when considering the probability of impact within a lethal range of a target

The energy spectrum of metrics on surfaces

Let $(N,\rho)$ be a Riemannian manifold, $S$ a surface of genus at least two and let $f\colon S \to N$ be a continuous map. We consider the energy spectrum of $(N,\rho)$ (and $f$) which assigns to each point $[J]\in \mathcal{T}(S)$ in the Teichm\"uller space of $S$ the infimum of the Dirichlet energies of all maps $(S,J)\to (N,\rho)$ homotopic to $f$. We study the relation between the energy spectrum and the simple length spectrum. Our main result is that if $N=S$, $f=id$ and $\rho$ is a metric of non-positive curvature, then the energy spectrum determines the simple length spectrum. Furthermore, we prove that the converse does not hold by exhibiting two metrics on $S$ with equal simple length spectrum but different energy spectrum. As corollaries to our results we obtain that the set of hyperbolic metrics and the set of singular flat metrics induced by quadratic differentials satisfy energy spectrum rigidity, i.e. a metric in these sets is determined, up to isotopy, by its energy spectrum. We prove that analogous statements also hold true for Kleinian surface groups

Effects of Canopy-Payload Relative Motion on Control of Autonomous Parafoils

An 8 degree-of-freedom model is developed that accurately models relative pitching and yawing motion of a payload with respect to a parafoil. Constraint forces and moments are found analytically rather than using artificial constraint stabilization. A turn rate controller common in precision placement algorithms is used to demonstrate that relative yawing motion of the payload can result in persistent oscillations of the system. A model neglecting relative payload yawing failed to predict the same oscillations. It is shown that persistent oscillations can be eliminated by reduction of feedback gains; however, resulting tracking performance is poor. A reduced order linear model is shown to be able to adequately predict relative payload dynamics for the proposed turn rate controller on the full 8 degree-of-freedom system

De Novo Review Under the Freedom of Information Act: The Case Against Judicial Deference to Agency Decisions to Withhold Information

This Comment argues that courts should adhere to the de novo standard of review prescribed by Congress in the FOIA statute, and that this standard is necessary for FOIA to provide the public with the affirmative right to access government information. Part I of this Article examines the reasons why FOIA requires the de novo standard of review and why courts ignore the requirement. Part II discusses various standards of review used by courts reviewing agency actions outside FOIA litigation. Specifically, it compares the review of agency adjudications and rulemakings to review under FOIA. Part III analyzes the actual standards of review that are employed in cases involving Exemptions 1, 3, and 7(A) of FOIA and discusses how the de novo standard of review should be applied. Finally, Part IV provides suggestions for strengthening and clarifying the role of courts in reviewing agency determinations that information should be withheld for national security reasons

Strict plurisubharmonicity of the energy on Teichm\"uller space associated to Hitchin representations

Let $\Sigma$ be a closed surface of genus least two and $\rho \colon \pi_1(\Sigma) \to G$ a Hitchin representation into $G=\text{PSL}(n,\mathbb{R})$, $\text{PSp}(2n,\mathbb{R})$, $\text{PSO}(n,n+1)$ or $\text{G}_2$. We consider the energy functional $E$ on the Teichm\"uller space of $\Sigma$ which assigns to each point in $\mathcal{T}(\Sigma)$ the energy of the associated $\rho$-equivariant harmonic map. The main result of this paper is that $E$ is strictly plurisubharmonic. As a corollary we obtain an upper bound of $3 \cdot \text{genus}(\Sigma) -3$ on the index of any critical point of the energy functional.Comment: 10 pages. Comments welcom

Exponential convergence rate of the harmonic heat flow

We consider the harmonic heat flow for maps from a compact Riemannian manifold into a Riemannian manifold that is complete and of non-positive curvature. We prove that if the harmonic heat flow converges to a limiting harmonic map that is a non-degenerate critical point of the energy functional, then the rate of convergence is exponential (in the $L^2$ norm)

Basketball shooting performance is maximized by individual-specific optimal release strategies

This study investigated the relationship between optimal basketball release angles and individual release distributions and whether individuals seek their optimal or minimum velocity release strategy. Sixteen male basketball players (height 183 ± 9 cm, age 22.6 ± 7 years) were recorded shooting 75 three-point shots. Ball release angle and velocity estimates were used in a nonparametric kernel density estimator (KDE) to identify individual-specific release distributions and optimal release angles. Optimal releases varied among individuals and were 4.3 ± 2.1° higher than minimum velocity releases. Mean release angles were 3.9° higher than the minimum velocity angle (p \u3c 0.001) and only 0.4° below the optimal (p = 0.5). Participants skewed their probability density function (PDF) peaks 0.24° towards the optimal (p = 0.044) further indicating participants seek optimal rather than minimum velocity releases. Individual-specific optimal release angles were strongly correlated with their PDF covariance (r = 0.78, p \u3c 0.001) and weakly correlated to the principal axis aspect ratio (r = −0.40, p = 0.137). These findings illustrate that optimal releases varied among participants and performance may be maximized by each athlete matching their release strategy to their PDF characteristics rather than matching a predetermined optimal release angle

Natural maps in higher Teichmüller theory

In this thesis we consider harmonic maps and barycentric maps in the context of higher Teichmüller theory. We are particularly interested in how these maps can be used to study Hitchin representations. The main results of this work are as follows. Our first result states that equivariant harmonic maps into non-compact symmetric spaces that satisfy suitable non-degeneracy conditions depend in a real analytic fashion on the metric of the domain manifold and the representations they are associated to. For our second result we consider the energy functional on Teichmüller space that is associated to a Hitchin representation. We prove that this functional is strictly plurisubharmonic for Hitchin representations into either PSL(n, R), PSp(2n, R), PSO(n, n + 1) or G_2. In the third part of this thesis we examine the energy functional on Teichmüller space that is associated to a metric on a surface. We prove that the simple length spectrum of a non-positively curved metric is determined by its energy functional. We use this to prove that hyperbolic metrics and singular flat metrics induced by quadratic differentials are determined, up to isotopy, by their energy functional. Our next result concerns the harmonic heat flow for maps from a compact Riemannian manifold into a Riemannian manifold of non-positive curvature. We prove that if the harmonic heat flow converges to a harmonic map that is a non-degenerate critical point of the Dirichlet energy, then it converges exponentially fast. In the final part of this thesis we study the barycenter construction of Besson–Courtois–Gallot. We prove that for any Fuchsian representation and Hitchin representation into SL(n, R) there exists a natural map from the hyperbolic plane to SL(n, R)/SO(n) that intertwines the actions of the two representations. We put these maps forward as a new way to parametrise and study Hitchin components