A renewed interest in the deployment of tethered satellites has motivated recent studies addressing the problem of the accurate identification, orbit determination, and motion prediction of a tethered satellite system (TSS). If the motion of a TSS is not analyzed accurately, a tethered satellite could be incorrectly identified as an object on a re-entry trajectory. Classical orbit determination methods do not possess the capabilities to determine whether or not a tracked satellite is part of a TSS. The problem of identification is compounded by the fact that this process must be performed quickly using a short arc of observational data. Once this "quick-look" identification is achieved, it is also important to have the capabilities to precisely determine the orbit of the TSS for future tracking and orbit prediction purposes. This paper presents a three-stage methodology which has been developed to address the accurate identification, orbit determination, and long-term orbit prediction of a TSS. The first stage uses recently developed preliminary orbit determination (POD) methods which have the capability to determine whether an observed satellite is part of a TSS or not using only a few observations. The second stage utilizes ridge-type estimation methods, which have been shown to be capable of obtaining a more accurate state of the observed satellite using a short arc of observational data. The third-stage analysis utilizes an enhanced tether satellite dynamical model suited for the long-term orbit determination and motion prediction. The effectiveness of this proposed three-stage method is demonstrated using both simulated tether satellite data and actual data obtained from the Tether Physics Survivability (TiPS) Experiment.

This paper investigates methods of detection and orbit determination for a two-satellite tethered system, given observation data for one of the satellites over a relatively short time. Such a task is more difficult when the system has a relatively short tether and/or significant libration. The estimation of the state of the system using the same information is also more difficult under these conditions, Two different formulations of the equations of motion of a tethered satellite system with a massless tether are used to see which results in the best performance of detection and state estimation algorithms. The two formulations involve the use of different state variables. In the first, the position and velocity of the observed satellite are used. In the second formulation, we use the position and velocity of the observed satellite and its position and velocity relative to the center of mass of the system as variables. The second formulation provides equations that may be solved approximately for small libration angles to obtain an analytical solution that describes the motion better than a similar solution based on the first formulation. However, both formulations provide essentially the same orbit determination results.

Covers advancements in spacecraft and tactical and strategic missile systems, including subsystem design and application, mission design and analysis, materials and structures, developments in space sciences, space processing and manufacturing, space operations, and applications of space technologies to other fields.

Since the launch of the first satellites, the coupling of translational and rotational motions of non-actively controlled objects moving in relatively low orbits about the Earth has been recognized as an important factor in the calculation of accurate orbits. In the case of debris objects, lack of knowledge of the objects' physical characteristics makes explicitly including the effects of rotational motion difficult. However, simulations based on six-degree-of-freedom models of generic types of debris objects can provide considerable insight into the effects of their rotational motions on their ballistic coefficients and hence their orbital motions. In this paper, we use some analytical models, a six-degree-of-freedom simulation, and a three-degree-of-freedom orbit determination program to study the effects of debris rotational motion on the prediction of the objects' time-varying ballistic coefficients and their orbits. First, uncoupled models for the rotational motion of rigid bodies and for orbital motion that includes the principal effects of the Earth's oblateness are used to demonstrate the variability of ballistic coefficients of objects with simple shapes due to the rotation of the object and the rotation of its orbit. Then, results obtained using the simulation and the orbit determination program are presented to illustrate how simulated and estimated ballistic coefficients differ and the errors produced by poor estimates.

PurposeThe purpose of this paper is to define and determine quantifiable measurements for head‐tilt and pilot fatigue by detecting and measuring the six degrees of freedom (6DOF) head motion of test subjects performing flight simulation operations.Design/methodology/approachFirst, a flight simulator that met the needs of the research project was designed and fabricated. Second, the tracking system was tested and deemed operable through a series of shakedown runs. Then, the head motion of test subjects was detected and measured using infrared technology. Finally, the data collected were used to establish definitions for head‐tilt and pilot fatigue.FindingsHead‐tilt and pilot fatigue were defined and evidence of their presence was observed in the head motion data.Practical implicationsThe goal of this research is to reduce aircraft accidents upon landing and take‐off for general, commercial, and military aviation to include unmanned aerial vehicles.Originality/valueLiterature which covers the definition and measurement of a pilot's head motion in flight is unclear. By defining the optokinetic phenomena of head‐tilt and precisely measuring pilot head motion and developing and using tests of pilots based on the results to screen for head‐tilt, the number of land aircraft veering off runways during both landing and takeoff can be reduced. Also, the number of aircraft overshooting the flight deck on an aircraft carrier can be reduced, as well as fewer crashes upon landing of unmanned aerial vehicles.

This paper describes the orbital dispersion problem for a fragmented asteroid in an elliptical orbit. The use of a state transition matrix derived from the general relative equation of motion for an elliptical orbit is emphasized in this paper. The state transition matrix is used to propagate the orbital dispersion. The Earth-impact probability is then computed to obtain a measure of the likelihood of impact with the Earth after the asteroid is fragmented with a high-energy fragmentation method. The state transition matrix approach is also compared with numerical integration approaches that use the two-body equation and the general relative equations of motion. The computational efficiency of such a state transition matrix approach is verified with accuracy equal to the numerical integration approaches. The employed state transition matrix, known as the Cochran, Lee and Jo (CLJ) state transition matrix, is also evaluated for the numerous fragments with data from the burst.

An integrated approach combining a state-dependent Ricatti equation (SDRE) and an extended Kalman filter (EKF) is applied to spacecraft formation flying for robust orbital and attitude maneuvers. The formation flying considered in this study is a two-spacecraft formation with a bounded out-of-orbit plane relative motion. The chaser is required to simultaneously perform large position and angle maneuvers with sufficient accuracy. The chaser is then required to maintain a relative orbit expressed in the local-vertical-local-horizontal frame with respect to the target and align its attitude with the target attitude for more than one orbital period. The controls of the chaser are formulated as a nonlinear optimal regulator problem using their highly nonlinear dynamics. To test the robustness of this integrated approach, highly nonlinear dynamics, including external disturbances, are employed as the truth plant that is then used to generate the measurements for an EKF. The tracking error is then computed between the true plant and the desired state. A six degrees-of-freedom simulation of a two-spacecraft flying formation is used to demonstrate the robustness of this integrated approach to external disturbances and plant uncertainties. The integrated approach also has an effect well under the large uncertainty of the chaser moment of inertia. DOI: 10.1061/(ASCE)AS.1943-5525.0000146. (C) 2012 American Society of Civil Engineers.

The dynamics of missile launcher systems are studied via digital simulations based on systems of flexible and rigid bodies. A digital computer program developed specifically to study the dynamic behavior of launchers containing several missiles is described. Particular attention is devoted to the handling of constraints between the bodies. Examples are presented that show some of the significant differences in the motions of missiles when the system is modeled as flexible as opposed to rigid.

U NMANNED aerial vehicles (UAVs) are now widely used in antiterrorism activities and intelligence gathering to enhance mission performance and maximize safety. The susceptibility of these UAVs in hostile environments raises requirements for flight path planning. Path planning strategies in hostile environments are normally composed of two phases [1,2]. The first phase is a Voronoi graph search, which will generate polygonal graphs and will optimize a safety performance index. The second is to use the virtual forces emanated from the virtual field of each surveillance radar site to refine the generated Voronoi graphs. These virtual forces provide information that can be used to reduce the vertices of the Voronoi polygonal and greatly improve the UAV performance. But the curvature continuity of the refined graphs, which plays an important role in the stability of the UAVs’ turning maneuvers, often does not meet the requirements for a continuously flyable path. Many kinds of curves have been studied and designed for UAVs to accomplish their mission [3–5]. Dubins curves, first applied in robotics path planning, are curves along which the UAV can move forward. This kind of circle–line–circle curve has a jump discontinuity in curvature at the connection points between the circle and the line that will cause a robot to stop at these connection points when traveling through the whole path. Other curves, such as the Reeds– Shepp curves [6,7], also have curvature discontinuities at their joint points. An alternative choice, the composite clothoid–line–clothoid curves, can be well designed with curvature being zero at the joint points to eliminate the discontinuities. This allows one to generate a continuous-curvature path by using different kinds of simply shaped curves, although, under most circumstances, we are expecting more flexibility in the curve shape that will allow more space for change. Shanmugavel et al. [3–5]. proposed quintic Pythagorean hodograph (PH) curves for a flyable path, with ten parameters representing each curve. The PH curves are flexible in design and their curvatures are expressed in continuous polynomials. The parameter calculation of a PH curve is an iterative process in order to satisfy different constraints. Such kinds of curves can be further simplified with fewer parameters and a more efficient optimization algorithm. All the methods discussed leave room for improvement in the area of continuous-curvature path planning. The Cornu sprial (CS) [8,9], also known as a clothoid or Euler’s spiral, has wide application in highway and railroad construction, since it can be used to design gradual and smooth transitions in highway entrances or exits. Kelly and Nagy [10] used a parametric CS model to generate real-time nonholonomic trajectories for robotics to minimize the terminal posture error. Here, we consider this CSmodel for use in UAV path planning and investigate how this parametric CS curve works under different constraints. To generate a flyable and safe path with given starting and ending points for UAVs passing through areas covered, at least partially, by several radar sites, the path constraints considered here include 1) minimum accumulative exposure to all radar sites; 2) continuous curvature throughout its length, which will ensure a flyable path’ 3) maximum curvature corresponding to the maximum achievable lateral turn rate; and 4) initial and final boundary constraints. Unlike other path planning problems, including that of moving objects finding the final path, which normally result in motion planning or trajectory planning with system dynamics [11], the path considered here is in a static object environment without dynamic constraints. The work in this paper is based on the developed Voronoi graph; it refines the graph by proposing a generalized CS curve along with a simplified parameter-identification procedure. Most papers on the topic of path planning do not include the information about dynamic state variables of UAVs flying along the planned path. For control purposes, it is beneficial to estimate these state variables to construct complete information of the flight. Kalman filtering [12] has been widely used as an efficient tool in optimal filtering and prediction, especially in the field of state estimation of UAVs performing designated missions [13–17]. For example, Grillo and Vitrano [13] used an extended Kalman filter (EKF) to estimate the state variables and wind velocity for a nonlinear UAV model with Global Positioning System (GPS) measurements. Abdelkrim et al. [14] used an EKF and an H1filter to estimate the localization of UAVs for which the position, velocity, and attitude aremeasured by an inertial navigation system. Campbell andOusingsawat [15] used two different estimators to provide online state and parameter estimation for path planning in uncertain environments. The state estimations in these studies have a commonality, because the UAVs in both cases have sensors or other instruments to provide useful measurement information. If all of the Voronoi points on the initial path are fixed and expected to be followed as closely as possible, they can be assumed asmeasurement points. The generated CS curve is then treated as the reference solution so that the state variables can be estimated by the EKF. The following sections present the procedure for the pathinformation construction in three parts. The first part is the initial rough path of the Voronoi graph and the dynamic programming search algorithm. In the second part, CS curve expression and properties are introduced and different constraints and their mathematical expression are explained. This is followed by the systematicsolution nonlinear programming (NLP) solver. In the last part, the state variables are estimated based on the generated Voronoi points and the refined reference path generated in the first two parts. Simulation results are presented in each part separately.

The operational airspace of aerospace vehicles, including airplanes and unmanned aerial vehicles, is often restricted so that constraints on three-dimensional climbs, descents, and other maneuvers are necessary. In this paper, the problem of determining constrained, three-dimensional, minimum time-to-climb, and minimum fuel-to-climb trajectories for an aircraft in an airspace defined by a rectangular prism of arbitrary height is considered. The optimal control problem is transformed to a parameter optimization problem. Because a helical geometry appears to be a natural choice for climbing and descending trajectories subject to horizontal constraints, helical curves are chosen as starting trajectories. A procedure for solving the minimum time-to-climb and minimum fuel-to-climb problems by using the direct collocation and nonlinear programming methods including Chebyshev pseudospectral and Gauss pseudospectral discretization is discussed. Results obtained when different constraints are placed on airspace and state variables are presented to show their effect on the performance index. The question of "optimality" of the numerical results is also considered.

In this paper, a group of cooperative planning paths for simultaneous starting and arriving Unmanned Aerial Vehicles (UAVs) are generated by parameterized Cornu-Spirals (CSs). The continuity and smoothness requirements for the designed flyable paths are achieved by the continuous curvature characteristics of CSs. The final curves are minimized in length with the least number of parameters representing the polynomial expression of the path curvature, while satisfying the maximum curvature constraints, equal length constraints, and collision avoidance constraints. The paths are integrated from initial points to final points by a trapezoidal integration algorithm. A nonlinear programming solver is used to calculate the optimized parameters. Simulation results for four simultaneous UAV paths are presented with designated initial and final positions and attitudes.

A Haar wavelet technique is discussed as a method for discretizing the nonlinear system equations for optimal control problems. The technique is used to transform the state and control variables into nonlinear programming (NLP) parameters at collocation points. A nonlinear programming solver can then be used to solve optimal control problems that are rather general in form. Here, general Bolza optimal control problems with state and control constraints are considered. Examples of two kinds of optimal control problems, continuous and discrete, are solved. The results are compared to those obtained by using other collocation methods.

In this paper, a simple method for modeling the relative orbital motion of multiple spacecraft and their formation-keeping control strategy is presented. Power series and trigonometric functions are used to express the relative orbital motion between the member spacecraft. Their coefficients are obtained using least square regression such that the difference between the exact numerically integrated position vector and the approximate vector obtained from the closed-form propagator is minimized. Then, this closed-form orbit propagator and optimization technique is used to plan a series of impulsive maneuvers which maintain the formation configuration within a specified limit. As an example, formation-keeping of four spacecraft is investigated. The motion projected onto the local horizontal plane (along- and cross-track plane) is a circle with the leader satellite located at its center and follower satellites positioned circumferentially. The radial distance between the leader and the followers, and the relative phase angles between the followers are controlled. Results from the nonlinear simulation are presented.

Dynamic-inversion has been shown to be an effective control structure for the nonlinear and multi-bodied dynamics of a flight motion simulator. This paper investigates the robustness of dynamic-inversion control to perturba tions in the dynamics model. In particular, actuator dynamics and viscous friction are considered, and a dynamic-inversion controller is compared to a conventional controller with proportional-derivative plus acceleration feedback. Results indicate the dynamic -inversion controller reduces the angular position error while accepting a larger bandwidth o f motion compared to the conventional controller.

Dynamic-inversion is an effective alternative control structure when compared to a conventional proportional-derivative structure for the nonlinear dynamics of a flight motion simulator. Results indicate the dynamic-inversion controller significantly reduced the lag and motion errors in system response while accommodating a larger bandwidth of motion. Perturbations affected the dynamic-inversion performance, however, dynamic-inversion is recommended over the conventional proportional-derivative controller.

uThe use of integrals of certain reference satellite motions has played an important role in many classical investigations. As a principal example, the solution to the two-body problem is the foundation of Lagrange's planetary equations. The two-body solution has also been used to find solutions that satisfy the Associated linear differential "variational" equations that form the basis of certain guidance schemes without additional integration by expanding the solution about a nominal trajectory. These guidance equations have traditionally been written in a nonrotating coordinate system. Recently, solutions to the two-body (and the perturbed two-body) variational equations written in a rotating coordinate system have been found by linearizing solutions to nonlinear equations of relative motion obtained from the two two-body problem solutions. In those solutions, classical and modified orbital elements are varied. Here, the general problem of finding solutions to the variational equations of dynamical systems that are completely integrable is first considered. Then, an alternate solution for linear relative motion of a satellite with respect to another satellite moving in an elliptic orbit is obtained in the form of an analytical state transition matrix by varying the initial polar coordinates, the inclination, and the right ascension of the ascending node of the reference orbit in the analytical solution to the nonlinear equations. Only the inverse of a relatively simple matrix is required at initial time and the new transition matrix is valid for arbitrary elliptic orbits. Examples of relative motion, obtained by evaluating the analytical solution, are presented and are compared with numerical results.