Optimal explicit guidance for three-dimensional launch trajectory

T HE development of aircraft guidance, navigation, and control systems has been a long-standing research area. Numerous methods relating to the enhancement of aircraft performance under various mission parameters have been developed in response to a need for more reliable and robust guidance systems. Current guidance systems applied to commercial, civilian, and unmanned aircraft rely on the knowledge of a flight path, specified bywaypoints located in inertial space. Most missions are considered successful when the vehicle reaches the designatedwaypoint at which new commands are issued to the vehicle to proceed to the next waypoint. Two common types of conventional aircraft guidance are the direct-to-waypoint (DTW) and track-to-waypoint (TTW) methods in relation to pathfollowing between designated waypoints. The DTWmethod simply issues heading commands to the vehicle based on the angular difference between thewaypoint and vehicle.When thevehicle reaches the waypoint, the control system issues a new command to guide the aircraft to the next waypoint. The TTW method aims to follow the track betweenwaypoints. In this guidancemethod the control system aims to minimize the lateral offset between the prescribed flight path and the aircraft’s position, issuing heading commands that return the vehicle to the nominal flight path. The track method therefore places the additional constraint on a flight path that the vehicle must follow in order to reach the waypoint, rather than simply reaching the waypoint. However, both methods are far from optimal. This is evident in how the aircraft transitions between flight paths after reaching awaypoint. During theseflight-path transitions, the aircraft will often overshoot the desiredflight path to correct its track, particularlywhen the flight-path transition angle is acute. Various control strategies have been investigated to alleviate or minimize flight-path deviations. Such strategies include applyingmodern control methods such as receding-horizon control [1,2] and model predictive control [3] to anticipate flight-path changes and take control action before reaching a goal while maintaining adequate vehicle flight performance. Missile guidance and control systems operate on similar principles to commercial, civilian, and unmanned aircraft guidance and control algorithms. The primary mission for missile systems is to intercept a moving target using information about the relative position and velocity between the pursuer and target. One of thefirstmethods used in missile guidance was pursuit guidance (PG) [4–7]. The method operates by forcing the angular displacement error between a pursuer and its target to zero. Control commands scaled by a proportional factor of the current error are then issued to direct the pursuer along the line of sight (LOS) between the pursuer and target. PG solutions, however, do not consider the path taken or the levels of system performance required by the pursuer in reaching the target, resulting in a far-from-optimal solution. To address this problem of suboptimality, additional parameters have been introduced to enhance missile performance. One method includes taking into account the motion of the commanded line of sight between the pursuer and target [4,7–10], issuing lateral acceleration commands based on tracking error and tracking error rate to the target. This approach has been shown to improve overall interceptor performance compared with conventional PG [4,7]. Another suchmethod aims tomodify the level of control the guidance algorithm possesses over the vehicle by adjusting the level of proportional gain. This is achieved by gain scheduling [11] to select gain values based on current interceptor states. In addition to modifying internal missile guidance and control parameters such as variable gains and LOS rate estimation, mission performance can be enhanced by manipulating the trajectory taken by the pursuer to the targets. A good example of such a method is discussed in [12], in which a missile aims to exploit the aerodynamic benefits of high-altitude flight by tracking a virtual target at some initially high altitude that is not necessarily along the trajectory to the true target. This Note discusses the development of a guidance law fusing the virtual-target concepts with those of pursuit guidance for implementation into an aircraft guidance system. This Note develops a path-following aircraft guidance algorithm that pursues synthetic waypoints using only a small set of guidance parameters, extending the virtual-target concept to complete aircraft guidance. The path is defined by the track between a minimal set of waypoints at specified locations, removing the need for a smooth path to be defined or the need for complicated path-switching logic or trajectory planning when awaypoint is reached. The synthetic waypoint travels along the path between waypoints, with the trailing aircraft traveling a smooth path generated through its own dynamics in following the synthetic waypoint. The guidance law is tested by varying guidance parameters, thus assessing vehicle sensitivity to and overall system performance of parameter variations. The following sections discuss the basic concepts of missile and aircraft guidance and provide a detailed description of the structure of the synthetic-waypoint guidance algorithm. A discussion on the implementation of the algorithm into the underlying aircraft control system will also be presented, followed by an analysis of the performance of the guidance algorithm in nonlinear simulation. Received 30 June 2009; revision received 3 November 2009; accepted for publication 9November 2009.Copyright©2009 by theAmerican Institute of Aeronautics and Astronautics, Inc. All rights reserved. Copies of this paper may be made for personal or internal use, on condition that the copier pay the $10.00 per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923; include the code 0731-5090/10 and $10.00 in correspondence with the CCC. ∗Graduate Research Student, School of Aerospace, Mechanical and Mechatronic Engineering; e.medagoda@aeromech.usyd.edu.au. Senior Lecturer, School of Aerospace, Mechanical and Mechatronic Engineering; pwg@aeromech.usyd.edu.au. JOURNAL OF GUIDANCE, CONTROL, AND DYNAMICS Vol. 33, No. 2, March–April 2010

This paper discusses one of the state-of-the-art guidance laws developed for Satellite Launch Vehicles known as the Iterative Guidance Mode (IGM). The purpose of this paper is to compare the results of IGM with a benchmark optimal solution to check its optimality and to check whether it is implementable in real-time. SLVs are used to carry and inject payloads into their designated orbits. Since there can be many unpredictable disturbances during the flight such as variations in performance of the propulsion system, vehicle mass and atmospheric uncertainties, a guidance law is therefore necessary to ensure the successful injection of the payload into its orbit. In this paper, the IGM algorithm is implemented in its original form in an exo-atmospheric phase along a three-dimensional trajectory. The benchmark solution is developed using an indirect method from optimal control theory which uses Pontryagin’s minimum principle. Various assumptions are made in order to simplify the problem. The closed-loop guidance simulations are carried out in MATLAB/SIMULINK environment. The results and the comparison with benchmark solution show that IGM gives near-optimal results. A Monte-Carlo analysis is also performed to evaluate its performance in the presence of various perturbations and it is shown that IGM retains its optimality under nominal and off-nominal flight conditions and the execution time for a single guidance loop shows that IGM can be implemented in real-time.

Adaptive Impact Time Control Via Look-Angle Shaping Under Varying Velocity

The automatic landing guidance technology which meets the CAT III standard is the key technology to realize all-weather accurate landing, and it is an effective measure to reduce the accident rate in approach and landing stage. This paper proposed a generation of guidance errors and guidance instructions for automatic landing based on GPS-Aided ILS. Firstly, the glide path was defined by key points, and the mathematical description of the glide path was given in the form of vector. Then, a landing guidance errors calculation algorithm based on the spatial geometric relationship and a variable gain guidance instructions generation method based on the distance strategy were proposed. Finally, five hundred times stochastic simulations were conducted to evaluate the proposed guidance law under the condition of wind and sensors error disturbance, with the flight technical error, angle of localizer deviation and angle of glide slope deviation as indexes. It can be drawn from the results that the landing accuracy of the aircraft guided by the guidance algorithm given in this paper can meet the CAT III standard.KeywordsCAT IIIGPS-Aided ILSGuidance errorsGuidance instructionsMonte Carlo

Ascent trajectory optimization and explicit guidance problems for a satellite launch vehicle with yaw maneuver in a 3-dimension are considered. The trajectory optimization problem with boundary conditions is formulated as a nonlinear programming problem by parameterizing the inertial pitch and yaw attitude control variables, and is solved by using the SQP algorithm. The flight constraints such as gravity-turn and range safety conditions are imposed. An explicit inertial guidance algorithm in the exoatmospheric phase is also presented. The guidance algorithm provides steering command and time-to-go value directly using the current states of the vehicle and the desired orbit insertion conditions. The liquid propelled Delta 2910 launch vehicle is used as a numerical model.

On-line optimization design of sliding mode guidance law with multiple constraints

<p class="p1">Aiming at intercepting a hypersonic weapon in a hypersonic pursuit-evasion game, this paper presents a fractional calculus guidance algorithm based on a nonlinear proportional and differential guidance law. First, under the premise of without increasing the complexity degree of the guidance system against a hypersonic manoeuvering target, the principle that the differential signal of the line-of-sight rate is more sensitive to the target manoeuver than the line-of-sight rate is employed as the guidelines to design the guidance law. A nonlinear proportional and differential guidance law (NPDG) is designed by using the differential derivative of the line-of-sight rate from a nonlinear tracking differentiator. By using the differential definition of fractional calculus, on the basis of the NPDG, a fractional calculus guidance law (FCG) is proposed. According to relative motions between the interceptor and target, the guidance system stability condition with the FCG is given and quantitative values are also proposed for the parameters of the FCG. Under different target manoeuver conditions and noisy conditions, the interception accuracy and robustness of these two guidance laws are analysed. Numerical experimental results demonstrate that the proposed guidance algorithms effectively reduce the miss distance against target manoeuvers. Compared with the NPDG, a stronger robustness of the FCG is shown under noisy condition.</p>

In this paper, a new real-time collision avoidance scheme is proposed using Generalized Vector Explicit Guidance (GENEX) law, an optimal guidance algorithm that can simultaneously achieve design specifications on miss distance and final UAV–target relative orientation. Low computation, closed-form expression, and optimal derivation are the key features that make it a potential candidate for real-time applications. The guidance law has been tested through simulations for the two-dimensional scenario, and the results are very satisfactory.

This paper investigates a novel guidance algorithm for fixed-trim maneuverable entry vehicles with limited control authority. The previous work, which depends on simplified models, lacks effectiveness in addressing the limited control authority issue in the presence of disturbances. The contributions of this paper address this by developing a novel spinning guidance algorithm to steer the vehicle to the target with high precision and strong robustness in dynamic environments with notable uncertainties and disturbances. To this end, a pseudoactuator-limit framework is designed to resolve the inherent limited authority and disturbance issues. Based on this framework, an extended state observer is introduced from the active disturbance rejection control theory, and a new spinning guidance algorithm is proposed to consume the redundant lift through continuous rotation of the lift vector, instead of performing high-frequency bank reversals. Furthermore, an observer-based antiwindup scheme is developed to enhance the robustness and control capability of the algorithm. The convergence of the proposed guidance law is explored from a theoretical perspective. The accuracy and robustness of the proposed guidance algorithm are demonstrated through typical case simulations and Monte Carlo evaluations under a variety of dispersions. Simulation results show that the miss distance is reduced by about 90% when compared to the existing guidance laws.

Lunar soft-landing trajectory design methods using evolutionary strategies and differential correction are investigated. According to the launch site and vehicle of the Chinese Lunar Exploration Program, the general constraints and objectives of lunar soft-landing missions are given. The primary trajectory is calculated by evolutionary strategies based on patched conic model. Then the differential correction method is adopted to modify the error introduced by the inaccurate model. The trajectories of cislunar and lunar orbiter phase before the soft-landing are also simulated by the commercial software STK, and the feasibility of the methods delivered in this paper is confirmed by the comparison of results. The difference of parameters between the preliminary and accurate model indicates that the design based on evolutionary strategies gives a proper value for the differential correction. This approach will be significant for the lunar soft-landing trajectory design of Chinese Chang'E Mission.

In this paper, the performance of two distinct classes of feedback guidance algorithms is evaluated for a spacecraft rendezvous problem utilizing a continuous low-thrust propulsion system. They are the DG (Differential Geometric) and ZEM/ZEV (Zero-Effort-Miss/Zero- Effort-Velocity) feedback guidance algorithms. Even though these two guidance algorithms do not attempt to minimize the onboard fuel consumption or ΔV directly, the ΔV requirement is used as a measure of their orbital rendezvous performance for various initial conditions and a wide range of the rendezvous time (within less than one orbital period of the target vehicle). For the DG guidance, the effects of its guidance parameter and terminal time on the closed-loop performance are evaluated by numerical simulations. For the ZEM/ZEV guidance, its nearfuel- optimality is further demonstrated for a rapid, short-range orbital rendezvous, in comparison with the corresponding open-loop optimal solutions. Furthermore, the poor ΔV performance of the ZEM/ZEV guidance for a slow, long-range orbital rendezvous is remedied by simply adding an initial drift phase. The ZEM/ZEV feedback guidance algorithm and its appropriate variants are then shown to be a simple practical solution to a non-impulsive rendezvous problem, in comparison with the DG guidance as well as the open-loop optimal guidance.

An observation system using fast digital cameras was developed to measure a cryogenic hydrogen pellet’s cloud structure, trajectory, and velocity changes during its ablation in ASDEX Upgrade plasmas. In this article the system, the applied numerical methods, and the results are presented. The three-dimensional pellet trajectory and velocity components were reconstructed from images of observations from two different directions. Pellet acceleration both in the radial and toroidal directions was detected. The pellet cloud distribution was measured with high spatio-temporal resolution. The cloud surrounding the pellet was found to be elongated along the magnetic field lines. Its typical size is 5–7 cm along the field lines and 2 cm in the perpendicular directions. A cloud extension in the poloidal direction was also observed which may be related to the drift of the detached part of the cloud.

In this paper an explicit guidance law for the powered descent phase of the soft lunar landing is presented. The descent trajectory, expressed in polynomial form is fixed based on the boundary conditions imposed by the precise soft landing mission. Adapting an inverse model based approach, the guidance command is computed from the known spacecraft trajectory. The guidance formulation ensures the vertical orientation of the spacecraft during touchdown. Also a closed form relation for the final flight time is proposed. The final time is expressed as a function of initial position and velocity of the spacecraft (at the start of descent) and also depends on the desired landing site. To ensure the fuel minimum descent the proposed explicit method is extended to optimal guidance formulation. The effectiveness of the proposed guidance laws are demonstrated with simulation results.

Explicit VG Guidance Algorithm for a Solid Powered Closed Loop Guidance Mission

A new three-dimensional missile guidance law that guarantees the intercept of maneuvering targets in finite time is developed in this paper. The guidance law is designed via the finite-time input-to-state stability theory. It achieves a fast convergence rate and robustness to target maneuvers as well as an effective compensation for the missile autopilot dynamics. Distinct from the widely used sliding-mode-based guidance law design, prior knowledge of the upper bound of the target maneuver is not needed. The convergence time and convergence region can be controlled by adjusting the guidance parameters. The three-dimensional finite-time guidance law incorporating a first-order autopilot dynamics is designed by integrating the finite-time input-to-state stability theory with the backstepping method. Extensive simulation studies are provided to illustrate the advantages of the proposed guidance law over other guidance laws without the finite-time convergence property or without considering autopilot dynamics.