Optimal Feedback Guidance Research Articles

Cooperative trajectory optimization of UAVs in approaching stage using feedback guidance methods

This paper mainly studies the problem of using UAVs to provide accurate remote target indication for hypersonic projectiles. Based on the optimal trajectory trends and feedback guidance methods, a new cooperative control algorithm is proposed to optimize trajectories of multi-UAVs for target tracking in approaching stage. Based on UAV kinematics and sensor performance models, optimal trajectory trends of UAVs are analyzed theoretically. Then, feedback guidance methods are proposed under the optimal observation trends of UAVs in the approaching target stage, producing trajectories with far less computational complexity and performance very close to the best-known trajectories. Next, the sufficient condition for the UAV to form the optimal observation configuration by the feedback guidance method is presented, which guarantees that the proposed method can optimize the observation trajectory of the UAV in approaching stage. Finally, the feedback guidance method is numerically simulated. Simulation results demonstrate that the estimation performance of the feedback guidance method is superior to the Lyapunov guidance vector field (LGVF) method and verify the effectiveness of the proposed method. Additionally, compared with the receding horizon optimization (RHO) method, the proposed method has the same optimization ability as the RHO method and better real-time performance.

Autonomous Entry Guidance for Hypersonic Vehicles by Convex Optimization

Advanced entry guidance systems could potentially enable future vehicles to generate feasible/optimal flight trajectories onboard for the latest mission requirements and track the new trajectories under uncertainties. To this end, an autonomous entry guidance algorithm is proposed for hypersonic vehicles using convex optimization methods. Based on previous sequential convex programming methods for entry trajectory optimization, a different successive procedure is developed for the online generation and tracking of reference trajectories from the current location to a desired target. In each guidance cycle, a new reference trajectory is generated by solving a second-order cone programming problem, and an optimal feedback guidance law is designed using a quadratically constrained quadratic programming method to track this reference trajectory. Because these two problems are convex, they are expected to be solved by state-of-the-art interior-point methods very efficiently. To demonstrate the effectiveness and performance of the proposed entry guidance algorithm, an offline convex entry guidance method is also designed for comparison based on a predetermined reference trajectory. Numerical simulations are presented for both offline and online approaches, which show that the proposed autonomous entry guidance algorithm is robust and efficient for potential future onboard guidance applications.

Collision avoidance ZEM/ZEV optimal feedback guidance for powered descent phase of landing on Mars

A novel zero-effort-miss (ZEM)/zero-effort-velocity (ZEV) optimal feedback guidance is proposed in order to rule out the possibility of Martian surface collision caused by the classical ZEM/ZEV optimal feedback guidance. The main approach is to add a collision avoidance term, which has self-adjustment capacity to ensure the near fuel optimality. Its main improvement is that it can not only successfully avoid collisions with the thruster constraint but also guarantee the near fuel optimality, and both of them are pivotal performances in Mars landing missions. Simulations are made to show the effectiveness of the proposed guidance and the parameters effects are simulated as well to analyze the properties of the proposed guidance.

Optimal nonlinear feedback guidance algorithm for Mars powered descent

In this paper, an optimal nonlinear feedback guidance algorithm with complex state and control constraints is developed for Mars powered decent. The analysis of the optimal control problem for Mars powered descent is undertaken firstly. Then based on the real-time sampling optimal feedback control theory, the Mars powered descent guidance (PDG) algorithm is designed and analysed. A practical method is also proposed to solve the problem of the initialization of the PDG algorithm. Numerical simulations are performed to evaluate the effectiveness of the proposed PDG algorithm. The effects of the sampling period and the prediction errors on landing errors are studied in the numerical simulations. The fuel consumption performances of the proposed PDG algorithm and the Apollo guidance algorithm are also studied and compared. The simulation results show that the less fuel consumption is obtained with the proposed PDG algorithm. Monte Carlo simulation verifies the high landing precision of the proposed PDG algorithm.

Improved ZEM/ZEV feedback guidance for Mars powered descent phase

An improved zero-effort-miss (ZEM) and zero-effort-velocity (ZEV) optimal feedback guidance algorithm is proposed in this paper for Mars powered descent phase, which has taken into account the no-subsurface constraints when designing the guidance law. Detailed descriptions have been given to this algorithm. The main advantage of this optimal guidance law is that it can successfully avoid collision to the Martian surface, at the same time preserving high landing precision and fuel optimality. For future Mars landing mission, the thrust-limited engine is most likely to be used. We propose a simulation method to study and determine the optimal final time which can minimize the fuel usage while ensuring precision landing and no-subsurface constraints. Monte Carlos are run to test the robustness and reliability of the improved and original guidance algorithms which show the superiority of the improved guidance law in preventing collision to the surface over the original one.

On-line optimal autonomous reentry guidance based on improved Gauss pseudospectral method

The on-line optimal autonomous reentry guidance of the hypersonic vehicle is proposed based on the improved Gauss pseudospectral method (IGPM). The autonomous reentry guidance requires the hypersonic vehicle can generate the optimal trajectory for the latest flight mission on line and track the new trajectory well under the uncertainty. These two problems are simplified into a nonlinear optimal control problem with nonlinear constraints. The IGPM is introduced to solve the above two problems. The trajectory has to change according to the flight mission and therefore the new optimal trajectory can be obtained by IGPM within about 10 s. The optimal feedback guidance law is used to track the reference trajectory to handle the uncertainty. In order to deal with the CPU time delay, which comes from optimizing the new trajectory, the new on-line optimal autonomous reentry guidance is depicted. Finally, the numerical simulation shows that the proposed autonomous guidance can generate optimal trajectory for the new flight mission and have a high tracking accuracy.

Optimal Feedback Guidance of a Small Aerial Vehicle in a Stochastic Wind

The navigation of a small unmanned aerial vehicle is challenging due to a large influence of wind to its kinematics. When the kinematic model is reduced to two dimensions, it has the form of the Dubins kinematic vehicle model. Consequently, this paper addresses the problem of minimizing the expected time required to drive a Dubins vehicle to a prescribed target set in the presence of a stochastically varying wind. First, two analytically-derived control laws are presented. One control law does not consider the presence of the wind, whereas the other assumes that the wind is constant and known a priori. In the latter case it is assumed that the prevailing wind is equal to its mean value; no information about the variations of the wind speed and direction is available. Next, by employing numerical techniques from stochastic optimal control, feedback control strategies are computed. These anticipate the stochastic variation of the wind and drive the vehicle to its target set while minimizing the expected time of arrival. The analysis and numerical simulations show that the analytically-derived deterministic optimal control for this problem captures, in many cases, the salient features of the optimal feedback control for the stochastic wind model, providing support for the use of the former in the presence of light winds. On the other hand, the controllers anticipating the stochastic wind variation lead to more robust and more predictable trajectories than the ones obtained using feedback controllers for deterministic wind models.

Spacecraft Guidance Algorithms for Asteroid Intercept and Rendezvous Missions

This paper presents a comprehensive review of spacecraft guidance algorithms for asteroid intercept and rendezvous missions. Classical proportional navigation (PN) guidance is reviewed first, followed by pulsed PN guidance, augmented PN guidance, predictive feedback guidance, Lambert guidance, and other guidance laws based on orbit perturbation theory. Optimal feedback guidance laws satisfying various terminal constraints are also discussed. Finally, the zero-effort-velocity (ZEV) error, analogous to the well-known zero-effort-miss (ZEM) distance, is introduced, leading to a generalized ZEM/ZEV guidance law. These various feedback guidance laws can be easily applied to real asteroid intercept and rendezvous missions. However, differing mission requirements and spacecraft capabilities will require continued research on terminal-phase guidance laws.

Robust Nonlinear Optimal Solution to the Lunar Landing Guidance by Using Neighboring Optimal Control

A closed-loop time-optimal control strategy for the highly nonlinear problem of the lunar landing mission by using the perturbation technique is developed in this study. The first part of the study considers analytical solution for an optimal control policy of variable mass spacecraft, while it descents on the surface of the moon in the variable gravitational field of it. To validate the accuracy of perturbation solution, a numerical approach based on steepest descent method is employed. The second part considers analytical derivation of an optimal feedback guidance solution by employing the neighboring optimal control (NOC) law when effects of imperfection in the dynamic model or disturbing noises have been taken into account. The technique of NOC produces time-varying feedback gains that minimize the performance index to the second order for perturbations from a nominal optimal path. The robustness of the designed NOC law is examined with applying sinusoidal noises. From the study of the simulation results, it may be concluded that the developed optimal guidance laws may be used in real world spacecraft applications.

Synthesis of optimal feedback guidance law for homing missiles using neural networks

Most existing missiles are guided by proportional navigation guidance (PNG) law, but PNG is a particular case for LQ guidance rule with two main assumptions of small line-of-sight angles and negligible acceleration along the line-of-sight. However, most missile engagements exceed these limits because of high tangential and normal accelerations. Unfortunately, it is not possible to determine the feedback guidance law for non-linear systems such as homing missiles in real-time. We use artificial neural networks to synthesize feedback laws for homing missiles with non-linear state equations. We first obtain an open-loop optimal numerical solution for non-linear state equations and then use these data to train a feed-forward multilayer neural network in an off-line session. The network is then used effectively in a real-time for feedback guidance method. Simulation results show that this neural networks guidance method can efficiently produce an optimal feedback law in spite of relatively simple network architecture. Copyright © 2000 John Wiley & Sons, Ltd.

Synthesis of optimal feedback guidance law for homing missiles using neural networks

Synthesis of optimal feedback guidance law for homing missiles using neural networks

Predictive Control-Based Optimal Nonliear Reentry Guidance Law.

This Paper discusses a new nominal riding reentry guidance low design based on a nonlinear optimal predictive control approach. In this method, the error between the actual trajectory and the nominal trajectory is predicted, and a quadratic cost function of these predicted errors is minimised, resulting in an optimal feedback guidance law design. The guidance low thus obtained does not require linearisation of the equations of motion. A nominal trajectory is selected which Satisfies the vehicle constraints and mission objectives. This nominal data is used with actual data to evaluate the guidance low. simulations have been carried out for a planar trajectory for a variety of initial condition errors and also for off nominal conditions and the results are presented.

Optimality and guidance for planar multiple-burn orbit transfers

An analysis of the second variation for extremal orbital transfers is presented, as well as a discussion of a multipleburn guidance scheme that may be implemented for such transfers. The second variation analysis includes the examination of the conditions for free final time transfers. A continuous burn transfer is shown to have neighboring extremals through these conditions. An implicit guidance scheme is explored, which implements a neighboring optimal feedback guidance strategy to calculate thrust direction and thrust off-times. A new time-to-go formulation is introduced, which has improved performance for this transfer. This continuous burn guidance scheme is adapted to multiple-burn transfers. A two-burn guidance problem is simulated. , C a d(-) e eT f go H

OPTIMAL FEEDBACK GUIDANCE FOR LOW‐THRUST ORBIT INSERTION

SUMMARYAn optimal feedback guidance scheme is developed for the terminal orbit insertion phase of a low‐thrust planar transfer to geosynchronous orbit. The minimum fuel trajectory between specified energy levels is utilized as a reference trajectory and the guidance law is derived using linear quadratic regulator optimization. The feedback guidance scheme responds effectively to a wide range of initial conditions and results in very precise terminal orbit conditions with near‐optimal performance. The guidance scheme also successfully handles propulsion system uncertainties and extremely large initial state deviations. Numerical results are presented for a variety of orbit insertion manoeuvres.

Optimal guidance for acceleration constrained missile and maneuvering target

Explicit formulas of optimal guidance laws for an acceleration-constrained, arbitrary-order missile and maneuvering target are derived. These formulas are given in terms of the transfer function and acceleration constraint of the missile and the transfer function/shaping filter of the target. Optimal full-state feedback guidance law is synthesized against a target performing a barrel roll maneuver, and compared with the performance of proportional navigation (PN) for minimum and nonminimum phase missile. Simulation of a third-order missile shows the relative gain from using the full-order guidance law. >

Stochastic pursuit-evasion differential games in 3D

A stochastic version of Isaacs's homicidal chauffeur game in the (x, y, z)-space is considered. This is used to solve a pursuit-evasion problem in the (x, y, z)-space in which the pursuer has incomplete information on the evader motion. Optimal feedback strategies for the game, and optimal feedback guidance laws for the pursuer, which uses only the measurements available to the pursuer, are computed. A simple suboptimal guidance law for the pursuer is suggested.

Real-Time Optimal Guidance for Orbital Maneuvering

A new formulation for soft-constraint trajectory optimization is presented as a real-time optimal feedback guidance method for multiburn orbital maneuvers. Control is always chosen to minimize burn time plus a quadratic penalty for end condition errors, weighted so that early in the mission (when controllability is greatest) terminal errors are held negligible. Eventually, as controllability diminishes, the method partially relaxes but effectively still compensates perturbations in whatever subspace remains controllable. Although the soft-constraint concept is well-known in optimal control, the present formulation is novel in addressing the loss of controllability inherent in multiple burn orbital maneuvers. Moreover the necessary conditions usually obtained from a Bolza formulation are modified in this case so that the fully hard constraint formulation is a numerically well behaved subcase. As a result convergence properties have been greatly improved.