A Robust Finite Fourier Series (R-FFS) approach is developed for fast generation of Earth-Moon trajectories using continuous low thrust. Each component of the position vector is approximated using a finite Fourier series as a function of time; these approximations are then used to design a trajectory that satisfies the equations of motion and the constraints, at discrete points, as well as the problem boundary conditions. The R-FFS method leverages the three body problem characteristics to achieve all the required plane change without the use of propulsion. The trajectory is divided into phases. The phase of the trajectory near the L1 Lagrange point is designed first and is always a thrust-free phase. This thrust-free phase is optimized to achieve the required plane change, enabling planar trajectories in the other phases. The initial guess needed by the solver, in the escape and capture phases, is generated using an analytic approximation developed in this paper. The numerical results show that the R-FFS can generate three dimensional transfers to high lunar orbits, low lunar orbits, and Halo orbits, while meeting constraints on the maximum thrust level of the engine.

A method is presented for estimating frequency responses of multiple-input multiple-output bare-airframe dynamics from flight test data containing feedback control and/or mixing of control effectors. Orthogonal phase-optimized multisines are used to simultaneously excite each input with unique harmonic frequencies, at which frequency responses are computed as ratios of output-to-input Fourier transform data. The confounding effects of feedback and mixing are resolved by interpolation of the frequency responses. The analysis can be run in batch for post-flight analysis, or in real time as the aircraft is flying. The effectiveness of the method was verified using simulations of the subscale T-2 generic transport airplane with rate feedback. The method was also demonstrated using flight test data from the X-56A MUTT aeroelastic airplane, which was flown with both feedback control and mixing.

Project Link! is a NASA-led effort to study the feasibility of multi-aircraft aerial docking systems. In these systems, a group of vehicles physically link to each other during flight to form a larger ensemble vehicle with increased aerodynamic performance and mission utility. This paper presents a dynamic model and control architecture for a system of ftxed-wing vehicles with this capability. The dynamic model consists of the 6 degree-of-freedom ftxed-wing aircraft equations of motion, a spring-damper-magnet system to represent the linkage force between constituent vehicles, and the NASA-Burnham-Hallock wingtip vortex model to represent the close-proximity aerodynamic interactions between constituents before the linking occurs. The control architecture consists of a guidance algorithm to autonomously drive the constituents towards their linking partners and an inner-loop angular rate controller. A simulation was constructed from the model, and the flight dynamic modes of the linked system were compared to the individual vehicles. The main contributions of this work are twofold. First is the introduction of close-proximity aerodynamic effects to create a realistic simulation framework for this problem. Second is the application of a sophisticated leader-follower guidance algorithm to achieve in-air wingtip docking. Simulation results for both before and after linking are presented.

Many optimization methods require accurate partial derivative information in order to ensure efficient, robust, and accurate convergence. In this paper, analytic methods are developed for computing complex partial derivatives of two bounded-impulse trajectory models: the multiple gravity-assist low-thrust and the multiple gravity-assist with deep-space maneuvers using shooting transcriptions. Particular attention is paid to the match point defect constraint present in these models due to its complex functional dependencies, and the gradient computations presented are extended to allow for the computation of trajectory path constraints. A comet sample return mission design problem is solved that underscores the benefits of implementing analytic gradient equations for these trajectory models. The computational efficiency of the techniques presented is compared against other methods available for computing partial derivative information, including automatic differentiation and the method of finite differences.

Preliminary design of low-thrust interplanetary missions is a highly complex process. The mission designer must choose discrete parameters such as the number of flybys, the bodies at which those flybys are performed, and in some cases the final destination. In addition, a time-history of control variables must be chosen that defines the trajectory. There are often many thousands, if not millions, of possible trajectories to be evaluated, which can be a very expensive process in terms of the number of human analyst hours required. An automated approach is therefore very desirable. This work presents such an approach by posing the mission design problem as a hybrid optimal control problem. The method is demonstrated on hypothetical missions to Mercury, the main asteroid belt, and Pluto.

Human computational vision models that attempt to account for the dynamic perception of egomotion and relative depth typically assume a common three-stage process: first, compute the optical flow field based on the dynamically changing image; second, estimate the egomotion states based on the flow; and third, estimate the relative depth/shape based on the egomotion states and possibly on a model of the viewed surface. We propose a model more in line with recent work in human vision, employing multistage integration. Here the dynamic image is first processed to generate spatial and temporal image gradients that drive a mutually interconnected state estimator and depth/shape estimator. The state estimator uses the image gradient information in combination with a depth/shape estimate of the viewed surface and an assumed model of the viewer's dynamics to generate current state estimates; in tandem, the depth/shape estimator uses the image gradient information in combination with the viewer's state estimate and assumed shape model to generate current depth/shape estimates. In this paper, we describe the model and compare model predictions with empirical data.

A computational and experimental method is employed to provide an understanding of a critical human space flight problem, posture control following reduced gravity exposure. In the case of an emergency egress, astronauts' postural stability could be life saving. It is hypothesized that muscular gains are lowered during reduced gravity exposure, causing a feeling of heavy legs, or a perceived feeling of muscular weakness, upon return to Earth's 1 g environment. We developed an estimator-based model that is verified by replicating spatial and temporal characteristics of human posture and incorporates an inverted pendulum plant in series with a Hill-type muscle model, two feedback pathways, a central nervous system estimator, and variable gains. Results obtained by lowering the variable muscle gain in the model support the hypothesis. Experimentally, subjects were exposed to partial gravity (3/8 g) simulation on a suspension apparatus, then performed exercises postulated to expedite recovery and alleviate the heavy legs phenomenon. Results show that the rms position of the center of pressure increases significantly after reduced gravity exposure. Closed-loop system behavior is revealed, and posture is divided into a short-term period that exhibits higher stochastic activity and persistent trends and a long-term period that shows relatively low stochastic activity and antipersistent trends.

A more quantitative approach to the analysis of astronaut extravehicular activity (EVA) tasks is needed because of their increasing complexity, particularly in preparation for the on-orbit assembly of the International Space Station. Existing useful EVA computer analyses produce either high-resolution three-dimensional computer images based on anthropometric representations or empirically derived predictions of astronaut strength based on lean body mass and the position and velocity of body joints but do not provide multibody dynamic analysis of EVA tasks. Our physics-based methodology helps fill the current gap in quantitative analysis of astronaut EVA by providing a multisegment human model and solving the equations of motion in a high-fidelity simulation of the system dynamics. The simulation work described here improves on the realism of previous efforts by including three-dimensional astronaut motion, incorporating joint stops to account for the physiological limits of range of motion, and incorporating use of constraint forces to model interaction with objects. To demonstrate the utility of this approach, the simulation is modeled on an actual EVA task, namely, the attempted capture of a spinning Intelsat VI satellite during STS-49 in May 1992. Repeated capture attempts by an EVA crewmember were unsuccessful because the capture bar could not be held in contact with the satellite long enough for the capture latches to fire and successfully retrieve the satellite.

The notion and the theory of constructing planetary powered descent guidance laws based on fractional polynomials are introduced. Along the way a new perspective to the classical Apollo powered descent guidance designs is gained. As a foundation of this work, a theory is first developed on how to derive an explicit powered descent guidance law by selecting the feedback gains in a unique way in an implicit tracking guidance law. Then by employing a particular profile of the reference thrust acceleration in the tracking law with a special set of gains, a large family of powered descent guidance laws is obtained that offer the flexibility in trajectory shaping and thrust characteristics by two adjustable parameters. An equivalence theory is established to show that each in this family of guidance laws is actually the explicit guidance law from a fractional-polynomial thrust acceleration profile. This insight provides a perfect explanation to the predictable behavior and good targeting performance of these guidance laws. The well-known Apollo lunar descent guidance and E-guidance laws are revealed to be two members of this much broader class of fractional-polynomial powered descent guidance laws.