Regularization and the computation of optimal trajectories
Continuous thrust spacecraft optimal trajectory regularization, obtaining differential equations for three dimensional motion
Tapley, B. D.↗
SEARCH · Search NASA
Results for “Trajectory optimization”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Advanced launch system trajectory optimization using suboptimal control
The maximum-final mass trajectory of a proposed configuration of the Advanced Launch System is presented. A model for the two-stage rocket is given; the optimal control problem is formulated as a parameter optimization problem; and the optimal trajectory is computed using a nonlinear programming code called VF02AD. Numerical results are presented for the controls (angle of attack and velocity roll angle) and the states. After the initial rotation, the angle of attack goes to a positive value to keep the trajectory as high as possible, returns to near zero to pass through the transonic regime and satisfy the dynamic pressure constraint, returns to a positive value to keep the trajectory high and to take advantage of minimum drag at positive angle of attack due to aerodynamic shading of the booster, and then rolls off to negative values to satisfy the constraints. Because the engines cannot be throttled, the maximum dynamic pressure occurs at a single point; there is no maximum dynamic pressure subarc. To test approximations for obtaining analytical solutions for guidance, two additional optimal trajectories are computed: one using untrimmed aerodynamics and one using no atmospheric effects except for the dynamic pressure constraint. It is concluded that untrimmed aerodynamics has a negligible effect on the optimal trajectory and that approximate optimal controls should be able to be obtained by treating atmospheric effects as perturbations.
Shaver, Douglas A.↗
A man in the loop trajectory optimization program (MILTOP)
An interactive trajectory optimization program is developed for use in initial fixing of launch configurations. The program is called MILTOP for Man-In-the-Loop-Trajectory Optimization-Program. The program is designed to facilitate quick look studies using man-machine decision combinations to reduce the time required to solve a given problem. MILTOP integrates the equations of motion of a point-mass in 3-Dimensions with drag as the only aerodynamic force present. Any point in time at which an integration step terminates, may be used as a decision-break-point, with complete user control over all variables and routines at this point. Automatic phases are provided for different modes of control: vertical rise, pitch-over, gravity turn, chi-freeze and control turn. Stage parameters are initialized from a separate routine so the user may fly as many stages as his problem demands. The MILTOP system uses both interactively on storage scope consoles, or in batch mode with numerical output on the live printer.
Reinfields, J.↗
Properties of the optimal trajectories for coplanar, aeroassisted orbital transfer
The optimization of trajectories for coplaner, aeroassisted orbital transfer (AOT) from a high Earth orbit (HEO) to a low Earth orbit (LEO) is examined. In particular, HEO can be a geosynchronous Earth orbit (GEO). It is assumed that the initial and final orbits are circular, that the gravitational field is central and is governed by the inverse square law, and that two impulses are employed, one at HEO exit and one at LEO entry. During the atmospheric pass, the trajectory is controlled via the lift coefficient in such a way that the total characteristic velocity is minimized. First, an ideal optimal trajectory is determined analytically for lift coefficient unbounded. This trajectory is called grazing trajectory, because the atmospheric pass is made by flying at constant altitude along the edge of the atmosphere until the excess velocity is depleted. For the grazing trajectory, the lift coefficient varies in such a way that the lift, the centrifugal force due to the Earth's curvature, the weight, and the Coriolis force due to the Earth's rotation are in static balance. Also, the grazing trajectory minimizes the total characteristic velocity and simultaneously nearly minimizes the peak values of the altitude drop, dynamic pressure, and heating rate. Next, starting from the grazing trajectory results, a real optimal trajectory is determined numerically for the lift coefficient bounded from both below and above. This trajectory is characterized by atmospheric penetration with the smallest possible entry angle, followed by flight at the lift coefficient lower bound. Consistently with the grazing trajectory behavior, the real optimal trajectory minimizes the total characteristic velocity and simultaneously nearly minimizes the peak values of the altitude drop, the dynamic pressure, and the heating rate.
Miele, A.↗
An inverse dynamics approach to trajectory optimization for an aerospace plane
An inverse dynamics approach for trajectory optimization is proposed. This technique can be useful in many difficult trajectory optimization and control problems. The application of the approach is exemplified by ascent trajectory optimization for an aerospace plane. Both minimum-fuel and minimax types of performance indices are considered. When rocket augmentation is available for ascent, it is shown that accurate orbital insertion can be achieved through the inverse control of the rocket in the presence of disturbances.
Lu, Ping↗
Overview of optimal trajectories for flight in a windshear
Optimal flight trajectories for the B-727, B-737, and B-747 aircraft in the presence of wind shear are studied. The takeoff problem and the abort landing problem are considered with reference to flight in a vertical plane. In the former, optimal trajectories are computed by minimizing the peak deviation of the absolute path inclination from a reference value; in the latter, optimal trajectories are computed by minimizing the peak value of the altitude drop. Numerical computations show that, for both the problems under consideration, the optimal trajectories of the three aircraft show the same qualitative behavior. Hence, it appears that the near-optimal guidance schemes developed for the B-727 can be extended to the other two aircraft, albeit with some quantitative modification.
Miele, A.↗
Properties of the optimal trajectories for coplanar, aeroassisted orbital transfer
The optimization of trajectories for coplanar, aeroassisted orbital transfer (AOT) from a high earth orbit (HEO) to a low earth orbit (LEO) is examined. In particular, HEO can be a geosynchronous earth orbit (GEO). During the atmospheric pass, the trajectory is controlled via the lift coefficient in such a way that the total characteristic velocity is minimized. First, an ideal optimal trajectory is determined analytically for lift coefficient unbounded. This trajectory is called a grazing trajectory. For the grazing trajectory, the lift coefficient varies in such a way that the lift, the contrifugal force due to the earth's curvature, the weight, and the Coriolis force due to the earth's rotation are in static balance. Also, the grazing trajectory minimizes the total characteristic velocity and simultaneously nearly minimizes the peak values of the altitude drop, dynamic pressure, and heating rate. Next, starting from the grazing trajectory results, a real optimal trajectory is determined numerically for the lift coefficient bounded from both below and above. This trajectory is characterized by atmospheric penetration with the smallest possible entry angle, followed by flight at the lift coefficient lower bound. The real optimal trajectory minimizes the total characteristic velocity and simultaneously nearly minimizes the peak values of the altitude drop, the dynamic pressure, and the heating rate.
Miele, A.↗
Refining Lucy Mission Delta-V During Spacecraft Design Using Trajectory Optimization Within High-Fidelity Monte Carlo Maneuver Analysis
Recent advances linking medium-fidelity trajectory optimization and high-fidelity trajectory propagation/maneuver design software with Monte Carlo maneuver analysis and parallel processing enabled realistic statistical delta-V estimation well before launch. Completing this high-confidence, refined statistical maneuver analysis early enabled release of excess delta-V margin for increased dry mass margin for the Lucy Jupiter Trojan flyby mission. By 3.3 years before launch, 16 of 34 TCMs had 1000 re-optimized trajectory design samples, yielding tens of m/s lower 99%-probability delta-V versus targeting maneuvers to one optimal trajectory. One year later, 1000 re-optimized samples of all deterministic maneuvers and subsequent flybys further lowered estimated delta-V.
Trojan↗
A fractional correction procedure for indirect trajectory optimization.
Fractional correction procedure for indirect trajectory optimization through extremal trajectory meeting boundary conditions
Winfield, D. H.↗
Optimal trajectories for the aeroassisted flight experiment, 1988-89
Research is summarized on optimal trajectories for the aeroassisted flight experiment, performed by the Aero-Astronautics Group of Rice University during the period 1988 through 1989. This research includes the following topics: (1) equations of motion in an Earth-fixed system; (2) equations of motion in an inertial system; (3) formultion of the optimal trajectory problem; (4) results on the optimal trajectory problem; and (5) guidance implications.
Miele, A.↗
Trajectory optimization and guidance for a hypersonic vehicle
The optimal ascent problem for a hypersonic vehicle is formulated as an inverse dynamic problem. This formulation is essential in solving the trajectory optimization problem via the nonlinear programming approach. Both minimum-fuel and minimax type of performance indices are considered. The results reveal important features of the optimal trajectory and controls, and they are subsequently used to construct a nonlinear feedback midcourse control law. This control law not only greatly simplifies the difficult constrained optimization problem and yields improved solutions, but is also suitable for onboard implementation. Finally, off-nominal trajectory guidance is addressed using combination of feedback compensation and onboard generation of control through the inverse dynamics approach.
Lu, Ping↗
Parallel solver for trajectory optimization search directions
A key algorithmic element of a real-time trajectory optimization hardware/software implementation is presented, the search step solver. This is one piece of an algorithm whose overall goal is to make nonlinear trajectory optimization fast enough to provide real-time commands during guidance of a vehicle such as an aeromaneuvering orbiter or the National Aerospace Plane. Many methods of nonlinear programming require the solution of a quadratic program (QP) at each iteration to determine the search step. In the trajectory optimization case, the QP has a special dynamic programming structure. The algorithm exploits this special structure with a divide- and conquer type of parallel implementation. The algorithm solves a (p.N)-stage problem on N processors in O(p + log2 N) operations. The algorithm yields a factor of 8 speed-up over the fastest known serial algorithm when solving a 1024-stage test problem on 32 processors.
Psiaki, M. L.↗
NBODY - a multipurpose trajectory optimization computer program
Documentation of the NBODY trajectory optimization program is presented in the form of a mathematical development plus a user's manual. Optimal multistage-launch ascent trajectories may be determined by variational thrust steering during the upper phase. Optimal low-thrust interplanetary spacecraft trajectories may also be calculated with solar power or constant power, all-propulsion or embedded coast arcs, fixed or optimal thrust angles, and a variety of terminal end conditions. A hybrid iteration scheme solves the boundary-value problem, while either transversality conditions or a univariate search scheme optimize vehicle or trajectory parameters.
Strack, W. C.↗
Wind-Optimal Trajectories for Multirotor eVTOL Aircraft on UAM Missions
Distributed electric propulsion powered electric vertical takeoff and landing aircraft are expected to enable urban air mobility. Low specific energy of onboard lithium-ion polymer batteries and wind conditions impose constraints on flight endurance. Therefore, from the safety and efficiency perspective, planning and flying minimum energy trajectories are important.The primary motivation for this paper is to determine if there is an operational benefit to flying wind-optimal trajectories for short flights (less than 60 miles) in the urban environment. This study employs wind-optimal trajectories for a NASA-proposed conceptual multirotor aircraft flight in the urban environment. The optimal control model presented includes a wind model for quantifying the effect of wind on the trajectory. The optimal control problem is numerically solved using the direct method. Energy consumption and flight duration flying wind-optimal trajectories between origins and destinations in a metropolitan area are compared with energy consumption and flight duration flying on the great-circle paths between the same origin and destination pairs to determine the operational benefit of wind-optimal routing for short flights.The flight duration results for different scenarios are validated using a simulation tool designed and developed by NASA for exploring advanced air traffic management concepts. In summary,this research study suggests that for short flights in an urban environment, the wind-optimal trajectories have a very slight (insignificant) operational advantage over the great-circle trajectories in terms of energy consumption and flight duration. As expected, headwinds and tailwinds along the route of flight have a significant impact on energy consumption and flight duration.
Urban Air Mobility↗
Trajectory optimization for the National Aerospace Plane
The primary objective of this research is to develop an efficient and robust trajectory optimization tool for the optimal ascent problem of the National Aerospace Plane (NASP). This report is organized in the following order to summarize the complete work: Section two states the formulation and models of the trajectory optimization problem. An inverse dynamics approach to the problem is introduced in Section three. Optimal trajectories corresponding to various conditions and performance parameters are presented in Section four. A midcourse nonlinear feedback controller is developed in Section five. Section six demonstrates the performance of the inverse dynamics approach and midcourse controller during disturbances. Section seven discusses rocket assisted ascent which may be beneficial when orbital altitude is high. Finally, Section eight recommends areas of future research.
Lu, Ping↗
A new method for treating optimal trajectories with restricted segments
New method for treating optimal trajectories
EULER EQUATION↗
Algorithm for fixed-range optimal trajectories
An algorithm for synthesizing optimal aircraft trajectories for specified range was developed and implemented in a computer program written in FORTRAN IV. The algorithm, its computer implementation, and a set of example optimum trajectories for the Boeing 727-100 aircraft are described. The algorithm optimizes trajectories with respect to a cost function that is the weighted sum of fuel cost and time cost. The optimum trajectory consists at most of a three segments: climb, cruise, and descent. The climb and descent profiles are generated by integrating a simplified set of kinematic and dynamic equations wherein the total energy of the aircraft is the independent or time like variable. At each energy level the optimum airspeeds and thrust settings are obtained as the values that minimize the variational Hamiltonian. Although the emphasis is on an off-line, open-loop computation, eventually the most important application will be in an on-board flight management system.
Lee, H. Q.↗
Singular perturbation analysis of AOTV-related trajectory optimization problems
The problem of real time guidance and optimal control of Aeroassisted Orbit Transfer Vehicles (AOTV's) was addressed using singular perturbation theory as an underlying method of analysis. Trajectories were optimized with the objective of minimum energy expenditure in the atmospheric phase of the maneuver. Two major problem areas were addressed: optimal reentry, and synergetic plane change with aeroglide. For the reentry problem, several reduced order models were analyzed with the objective of optimal changes in heading with minimum energy loss. It was demonstrated that a further model order reduction to a single state model is possible through the application of singular perturbation theory. The optimal solution for the reduced problem defines an optimal altitude profile dependent on the current energy level of the vehicle. A separate boundary layer analysis is used to account for altitude and flight path angle dynamics, and to obtain lift and bank angle control solutions. By considering alternative approximations to solve the boundary layer problem, three guidance laws were derived, each having an analytic feedback form. The guidance laws were evaluated using a Maneuvering Reentry Research Vehicle model and all three laws were found to be near optimal. For the problem of synergetic plane change with aeroglide, a difficult terminal boundary layer control problem arises which to date is found to be analytically intractable. Thus a predictive/corrective solution was developed to satisfy the terminal constraints on altitude and flight path angle. A composite guidance solution was obtained by combining the optimal reentry solution with the predictive/corrective guidance method. Numerical comparisons with the corresponding optimal trajectory solutions show that the resulting performance is very close to optimal. An attempt was made to obtain numerically optimized trajectories for the case where heating rate is constrained. A first order state variable inequality constraint was imposed on the full order AOTV point mass equations of motion, using a simple aerodynamic heating rate model.
Calise, Anthony J.↗