Optimal Flight Path Research Articles

Optimal Trajectories For Aircraft Using StateSpace Search

This paper presents a method for generating optimal flight paths across defended terrain. The terrain is described by a digital map specifying the elevation in each grid cell Threats are evaluated from line of sight calculations and the range to the threat The path of the vehicle is constrained by the physics of motion of the vehicle. The costs associated with the vehicle's motion are expressed by a multiobjective cost function that balances conflicting objectives. The solution procedure considers both hard obstacles such as the ground which cannot be passed through, and soft obstacles such as threats which can be passed through at increased cost. The problem was formulated using a state-space representation in which changing state, by moving the vehicle, corresponds to dynamically generating an arc of a graph. The cost associated with traversing each arc of the graph is a function of the terrain crossed, threats encountered, and the manoeuvre required to cause the change of state. The optimal trajectory is found using the A* algorithm. Unlike previous work using A* where solution optimality was given up to gain computational feasibility, optimality of solution was preserved by using knowledge to combine compound manoeuvres (effectively limited breath first search), search over regions of the map rather than over individual grid cells of the map and intelligent pruning of inferior states. Transactions on Information and Communications Technologies vol 2, © 1993 WIT Press, www.witpress.com, ISSN 1743-3517

Use of variational analysis in aerospacecraft design.

Useful procedures for the design of high-performance aerodynamic vehicles are outlined. Configuration variables, treated as special control variables, lead to development of corresponding influence-function relations. These relations utilize variational parameters and flight conditions from a reference optimum-flight path to 1) identify critical configuration (design) variables and 2) predict quantitative effects on the optimum performance (tradeoff factors) of configuration-variable perturbations. The procedures emphasize the use of simple methods to evaluate influence functions. Engineering estimates of configurationvariable effects on vehicle force characteristics (aerodynamic and propulsive) may be used for this evaluation. Examples use maximum-range and maximum-pay load flight paths for ramjet-powered hypersonic aircraft to demonstrate application of the design procedures. General configuration variables, such as wing thickness, engine-inlet area, and thrust incidence, are used in these examples. Results show good agreement between the effects on performance estimated from the integrated influence function and the computed effect obtained from the corresponding optimum solutions.

Navigation of the S.S.T.

As a general rule the navigational function is aimed at determining the position of the aircraft in order to resolve three types of problem:(1) To subject the aircraft's flight path to an optimum trajectory calculated before departure or progressively adapted in course of flight to the circumstances encountered.(2) To choose at each point of the selected flight path the flight system best adapted to the safety and economy of the flight.(3) Taking into account the presence of other aircraft in the airspace, to know and make known the actual position and the information allowing provision to be made for future positions, so as to permit effective air traffic control.Departures of the actual from the chosen flight path penalize the flight by a lowering of economy (in flying time or fuel consumption). It does not seem, however, that the problems raised from this point of view by S.S.T. are by nature or in difficulty any different from those which affect conventional aircraft. Taking into account the present-day precision of navigational aids there is every reason to believe that departures of the actual flight path from the optimum flight path will introduce a penalization which it is possible to ignore when compared with the penalization due to the inaccuracy of the knowledge of the elements (winds, temperatures, pressures) which have, in fact, served to determine this optimum flight path.

The effect of dry and fluid lubrication on instrument, ball-bearing torques at high speed : H. H. Mabie, Lubrication Eng., 21 (6) (1965) 242–249; 21 figs., 1 table

A review of the navigation, guidance, and control system of the Saturn launch vehicle includes the system analysis and design, signal flow diagrams, redundancy, and self-checking features used to obtain extreme reliability for crew safety.The iterative path adaptive guidance mode, featuring flight path optimization, is explained and presented in its computational form. Following the analytical considerations, the main guidance and control components are described. The navigation and control information is obtained inertinlly by a gyro-servo-stabilized, three-gimbal platform system with three mutually orthogonal pendulous-integrating gyro accelerometers; the single-degree-of-freedom gyros as well as the accelerometers use externally-pressurized gas bearings. Rate gyroscopes provide attitude staoilization; some vehicle configurations require additional accelerometer control to reduce wind loads. The digital computer system serves as the computation, central data, and onboard programing center, which ties in with the ground computer system during the prelaunch checkout of the overall system. The control signals are combined, shaped, attenuated, and amplified by an analog type control computer for engine actuator control.Results obtained in recent launchings of Saturn V vehicles are presented to confirm the adequacy of the navigation, guidance, and control system and its overall performance even under extreme flight perturbations.

Optimal control - A review of theory and practice.

T objectives of this review are to summarize and to evaluate the present state of knowledge concerning optimal control synthesis. The primary areas of interest are flight mechanics and flight control. The design of optimal stabilization and control systems, the determination of optimal flight paths, and the calculation of optimal orbital transfers have a common mathematical foundation in the calculus of variations; this review is limited to problems requiring a variational treatment. The selection of optimum vehicle shapes and the determination of optimum staging and propellant loadings for rockets are not included in the scope of this work although they are variational problems. A general discussion of optimization techniques draws upon the accumulated experience and research results of many workers in different branches of engineering and applied mathematics. In recent years, there has been a confluence of control research in aeronautical, electrical, mechanical, and chemical engineering. The research efforts in specialized technical fields have produced results of general interest, but the splintering of the literature according to old traditions has sometimes retarded the application of the results. A principal task of this review is to discuss the synthesis of closed-loop optimal controllers. This review will not make a sharp distinction between optimal guidance and optimal control because the mathematical problems are nearly identical even though the time scales of the system being controlled may differ by several orders of magnitude. A synthesis procedure for an optimal system is a set of design rules whose application results in a closed feedback loop comprised by the system being controlled and a computer to process the output measurements and to determine the optimal control law. This is illustrated in Fig. 1, which is a block diagram encompassing a very wide range of diverse problems extending from the optimal correction of interplanetary trajectories to optimal flight controllers for airplanes. These two apparently dissimilar technical problems are nevertheless nearly identical from a system synthesis viewpoint. The same basic design steps are required in each case. These include the selection of a performance criterion, the estimation of the statistical properties of noise and random inputs, the determination of the system state from noisy data, and the computation of the optimal control law. Each of these items will be taken up again later on.

Some Problems in the Navigation of Supersonic Aircraft

This paper, which was presented at a meeting of the Deutsche Gesellschaft für Ortung und Navigation held in Berlin on 24 April 1963, briefly discusses some of the factors which will affect navigation and control of supersonic transport aircraft. Attention is directed to the special problems of determining optimum flight path and estimating position and E.T.A. during three phases of the flight: acceleration, supersonic cruise and deceleration.

Guidance theory and extremal fields

A guidance concept employing properties of optimal flight paths is developed on the basis of Jacobi's accessory minimum problem for the second variation. The analysis is equivalent to construction of a field of extremals in the neighborhood of a predetermined extremal serving as a nominal trajectory. In the absence of inequality constraints on the control variables, a linear terminal control scheme with time-varying gains is realized. The addition of inequality constraints leads to nonlinear control behavior. Certain propulsion system parameters are characterized as state variables as a convenient means for providing adaptive behavior in respect to in-flight changes in propulsion system performance. An application is given to an intercept problem sufficiently simple to allow analytical solution, and some numerical results comparing optimal and approximately optimal guidance in their effects on flight performance are presented. Treatment of a certain type of problem arising in rocket applications is discussed.

Application of Inequality Constraints to Variational Problems of Lifting Re-Entry

Inequality constraints are introduced into fhe variational formulation of the optimum re-entry problem for a lifting vehicle to prevent human and/or structural tolerances from being exceeded. These constraints consist of minimum and maximum angle of attack, maximum load factor, and maximum convective heat transfer (equilibrium temperature). The equations have been programed for the IBM 704 computer, and sample trajectories are presented for which the total heat transferred to certain critical areas on the windward surface of the vehicle is minimized. These trajectories indicate the dominant effect of the constraints on the optimum flight path, which is shown to consist of both unconstrained and constrained

Optimum Maneuvers for Launching Satellites Into Circular Orbits of Arbitrary Radius and Inclination

2 Miele, A., A Survey of the Problems of Optimizing Flight Paths of Aircraft and Missiles, ARS preprint 1219-60. 3 Breakwell, J. V., The Optimization of Trajectories, J. Soc. Indust. Appl. Math., vol. 7, no. 2, June 1959, pp. 215-247. 4 Kelley, H. J., Gradient Theory of Optimal Flight Paths, ARS preprint 1230-60. 5 Kulakowski, L. J. and Stancil, R. T., Boost Trajectories for Maximum Burn-Out Velocity, ARS JOURNAL, vol. 30, no. 7, July 1960, pp. 612-618. 6 Bliss. G. A., Lectures on the Calculus of Variations, University of Chicago Press, Chicago, First Ed., 1946, Chap. 7. 7 Cicala, C. and Miele, A., Brachistochronic Maneuvers of a Variable Mass Aircraft in a Vertical Plane, J. Aero. Sci., vol. 22, no. 8, Aug. 1955, pp. 577-578. 8 Wheelon, A. D., Free Flight of a Ballistic Missile, ARS JOURNAL, vol. 29, no. 12, Dec. 1959, pp. 915-926. 9 Leitmann, G., On a Class of Variational Problems in Rocket Flight, J. Aero/Space Sci., vol. 26, no. 9, 1959. 10 Leitmann, G., Minimum Transfer Time for a Power-Limited Rocket, XI Int. Astronautical Congress, Stockholm, 1960. 11 Fried, B. D., On the Powered Flight Trajectory of an Earth Satellite, J E T PROPULSION, vol. 27, no. 6, June 1957, pp. 641-643.

The role of electronics in national survival

This paper presents an adaptive path planner for unmanned aerial vehicles (UAVs) to adapt a real-time path search procedure to variations and fluctuations of UAVs’ relevant performances, with respect to sensory capability, maneuverability, and flight velocity limit. On the basis of a novel adaptability-involved problem statement, bi-level programming (BLP) and variable planning step techniques are introduced to model the necessary path planning components and then an adaptive path planner is developed for the purpose of adaptation and optimization. Additionally, both probabilistic-risk-based obstacle avoidance and performance limits are described as path search constraints to guarantee path safety and navigability. A discrete-search-based path planning solution, embedded with four optimization strategies, is especially designed for the planner to efficiently generate optimal flight paths in complex operational spaces, within which different surface-to-air missiles (SAMs) are deployed. Simulation results in challenging and stochastic scenarios firstly demonstrate the effectiveness and efficiency of the proposed planner, and then verify its great adaptability and relative stability when planning optimal paths for a UAV with changing or fluctuating performances.

Gyroscope research at the Franklin Institute

A review of the navigation, guidance, and control system of the Saturn launch vehicle includes the system analysis and design, signal flow diagrams, redundancy, and self-checking features used to obtain extreme reliability for crew safety.The iterative path adaptive guidance mode, featuring flight path optimization, is explained and presented in its computational form. Following the analytical considerations, the main guidance and control components are described. The navigation and control information is obtained inertinlly by a gyro-servo-stabilized, three-gimbal platform system with three mutually orthogonal pendulous-integrating gyro accelerometers; the single-degree-of-freedom gyros as well as the accelerometers use externally-pressurized gas bearings. Rate gyroscopes provide attitude staoilization; some vehicle configurations require additional accelerometer control to reduce wind loads. The digital computer system serves as the computation, central data, and onboard programing center, which ties in with the ground computer system during the prelaunch checkout of the overall system. The control signals are combined, shaped, attenuated, and amplified by an analog type control computer for engine actuator control.Results obtained in recent launchings of Saturn V vehicles are presented to confirm the adequacy of the navigation, guidance, and control system and its overall performance even under extreme flight perturbations.

Optimum Flight Paths

A condensed version of a paper presented to the Centre Beige de Navigation, Brussels, 9 January 1950.The fact that the most expeditious route between two points on the Earth's surface is not necessarily a great circle is no new discovery. In the days of sailing ships courses were set to take maximum advantage of the wind; the trade winds were so called because they made the voyages of the trading ships possible. To a large extent they dictated the sea lanes and it was not until the arrival of the steamship that more direct routes across the oceans could be followed.

Estimation of Cruising Air Speeds for Economic Analysis

In the course of investigation into the operating economics of transport aircraft, the cruising speed arises as a fundamental variable and a rapid method of correction of speed for variation of power, height and weight is frequently required. Other problems present themselves, such as the estimate of cruising speeds in the course of a new type design study, or the correction of a “one–point” published performance of a new aircraft to a standard operational condition differing in specified weight, altitude or power output for cruising.In this note no account will be taken of the block speed correction arising because of the modification of true air speed by the various factors, such as wind, climb and glide which distort the optimum flight path. The principle of the method here suggested involves the unique relationship of p, the ratio of thrust power required at any speed (V) to the thrust power at the minimum drag speed (u) at the same altitude, and n the wellknown speed ratio V/u.

Optimum Flight Path in Air Transport Operation

W ITH the introduction of the modern high performance airplane into the air transportation systems of the country, it has become increasingly necessary to make some study of the factors which influence the proper selection of flight paths for the efficient operation of the aircraft. In the past it has been the practice of the operators to make merely a rough estimate of the effect of the winds to determine the best altitude at which to fly on the course. There has been, in general, a complete neglect of the variations in the performance of the aircraft. I t is the purpose of this paper to present, in so far as possible, a means which is practical from the standpoint of the operator for determining the most efficient flight path. The problem, in general, is the following: To provide a means of quickly determining before the start of a flight the path which the pilot should follow in order to fly between any two points in the minimum possible time. Thus, for a given set of cruising specifications for the airplane, this path becomes the optimum not only with regard to elapsed time but also for economy of operation. First, it will be assumed that the flight will be restricted to the vertical plane, which includes the starting point and the destination. The flight path will then have two dimensions in which to vary, with an infinite number of possibilities from which to choose.