Closed-loop Guidance System Research Articles

Appointed-time-control-based three-dimensional parallel approaching guidance for intercepting maneuvering target

This study presents an improved guidance method consisting of the parallel approaching guidance (PAG) and the appointed-time-control-based guidance for addressing the challenge of the three-dimensional guidance with maneuvering target. The relative kinematic equations of the guidance system are divided into the line-of-sight (LOS) angle subsystem and the relative velocity subsystem. For the LOS angle subsystem, the nonsingular finite-time backstepping control (NFTBC) based guidance method is proposed to converge the LOS angles to achieve the PAG. To solve the issue of the singularity and ensure the continuity of the guidance law, a segmented function is designed to obtain the virtual control and further derive the NFTBC. For the relative velocity subsystem, the appointed-time-control-based guidance method is applied with the utilization of the time-to-go to achieve the successful interception at an appointed time for the missile against the target. Besides, the finite-time nonlinear disturbance observer is developed to estimate the target maneuvers. Furthermore, the Lyapunov stability theory is utilized to demonstrate the stability of the closed-loop guidance system. Finally, the simulations of the three-dimensional guidance system are implemented to verify the effectiveness of the proposed method.

Event-Triggered-Backstepping-Based Parallel Approaching Guidance Method for Maneuvering Target Interception

In order to achieve a straight ballistic trajectory of missile and reduce the update frequency of the missile normal acceleration for the interception of maneuvering target, a backstepping-based parallel approaching guidance method is designed with nonlinear disturbance observer (NDO) technique and event-triggered (ET) mechanism in this paper. In order to suppress the adverse effect of target maneuver, the NDO is designed to estimate the target maneuvering acceleration. Then, the NDO-based backstepping method is used to obtain the normal acceleration of missile and realize the parallel approaching guidance. In order to reduce the update frequency of missile normal acceleration, the ET mechanism is employed in the parallel approaching guidance method. If the missile trajectory is relatively straight, the normal acceleration of missile remains unchanged. On the contrary, if the missile trajectory is not straight, the normal acceleration of missile is updated to make the missile trajectory straight. In this way, the ET-based parallel approaching guidance can be obtained. Furthermore, a determined method for the initial missile flight-path angle is proposed to keep the normal acceleration of missile at zero in the initial stage of interception. Besides, Lyapunov stability analysis method is used to prove that all signals in the closed-loop guidance system are uniformly ultimately bounded. Finally, simulation results show the effectiveness of the proposed guidance method.

Three-dimensional adaptive fixed-time guidance law against maneuvering targets with impact angle constraints and control input saturation

This paper presents an adaptive fixed-time guidance law for the three-dimensional interception guidance problem with impact angle constraints and control input saturation against a maneuvering target. First, a coupled guidance model formulated by the relative motion equation is established. On this basis, a fixed-time disturbance observer is employed to estimate the lumped disturbances. With the help of this estimation technique, the adaptive fixed-time sliding mode guidance law is designed to accomplish accurate interception. The stability of the closed-loop guidance system is proven by the Lyapunov method. Simulation results of different scenarios are executed to validate the effectiveness and superiority of the proposed guidance law.

New Integrated Guidance and Control of Homing Missiles with an Impact Angle against a Ground Target

A new integrated guidance and control (IGC) law is investigated for a homing missile with an impact angle against a ground target. Firstly, a control-oriented model with impact angle error of the IGC system in the pitch plane is formulated by linear coordinate transformation according to the motion kinematics and missile dynamics model. Secondly, an IGC law is proposed to satisfy the impact angle constraint and to improve the rapidity of the guidance and control system by combining the sliding mode control method and nonlinear extended disturbance observer technique. Thirdly, stability of the closed-loop guidance and control system is proven based on the Lyapunov stability theory, and the relationship between the accuracy of the impact angle and the estimate errors of nonlinear disturbances is derived from stability of the sliding mode. Finally, simulation results confirm that the proposed IGC law can improve the performance of the missile guidance and control system against a ground target.

Robust finite-time guidance against maneuverable targets with unpredictable evasive strategies

This paper presents a robust finite-time guidance (RFTG) law to a short-range interception problem. The main challenge is that the evasive strategy of the target is unpredictable because it is determined not only by the states of both the interceptor and the target, but also by external un-modeled factors. By robustly stabilizing a line-of-sight rate, this paper proposes an integrated continuous finite-time disturbance observer/bounded continuous finite-time stabilizer strategy. The design of this integrated strategy has two points: 1) effect of a target maneuver is modeled as disturbance and then is estimated by the second-order homogeneous observer; 2) the finite-time stabilizer is actively coupled with the observer. Based on homogeneity technique, the local finite-time input-to-state stability is established for the closed-loop guidance system, thus implying the proposed RFTG law can quickly render the LOS rate within a bounded error throughout intercept. Moreover, convergence properties of the LOS rate in the presence of control saturation are discussed. Numerical comparison studies demonstrate the guidance performance.

Three-Dimensional Diving Guidance for Hypersonic Gliding Vehicle via Integrated Design of FTNDO and AMSTSMC

The three-dimensional multiple constrained guidance problem for a hypersonic gliding vehicle (HGV) against a stationary ground target in dive phase is investigated. A coupled nonlinear dynamic model is established on account of the bank-to-turn control scheme adopted by the HGV, which formulates the relation between line-of-sight angles and trajectory control variables. On this basis, a finite-time nonlinear disturbance observer is introduced to estimate the lumped uncertainty. Utilizing the estimation as feedforward compensation, a guidance law based on the adaptive multivariable super-twisting sliding mode control is designed to realize precise strike with designated impact angles. The finite-time stability of closed-loop guidance system is proven through the Lyapunov technique. Numerical simulations are executed to validate the mission adaptiveness and the robustness of the presented guidance scheme.

Designing a closed-loop guidance system to increase the accuracy of satellite-carrier boosters' landing point

A novel closed loop guidance method is provided in this paper to increase the accuracy of satellite-carrier boosters' landing point. The proposed method can be used in the first stage of flight vehicles that fly in atmosphere. In this case, solid motor propelled boosters would be able to more accurately land on the desired point. Moreover, in sub-optimal technique, the closed-loop guidance system would produce commands after booster separation, which guide second stage of satellite-carrier from initial conditions to the desired condition of orbit injection. In this method, sub-optimal integrated solution of control and guidance in closed-loop is developed. This sub-optimal technique named as Model Predictive Static Programming (MPSP) that is based on nonlinear optimal control theory and derived from combined philosophies of Model Predictive Control and Approximate Dynamic Programming; solves a class of finite horizon optimal control problems with terminal constraints. Furthermore because sensitivity matrices that are necessary for obtaining this solution can be computed recursively, this technique is computationally efficient and is appropriate for online implementation. In this paper, the dynamic equations of system are modeled in the presence of aerodynamic loading and the servo-mechanism dynamic. Moreover, by considering integrated guidance and control loops, a solution of the guidance and control system is proposed by three-degree of freedom spherical earth simulation model in atmosphere. Result show that proposed closed-loop guidance not only is able to remove aerodynamic and thrust modeling errors in first stage by flight data update that caused to more accurate of boosters' landing point, but also would still be able to guide second stage of satellite-carrier to the desired condition of placement in the orbit.

Super-twisting integral-sliding-mode guidance law considering autopilot dynamics

A new guidance law considering missile autopilot dynamics is established via integrating a smooth super-twisting algorithm with nonlinear integral sliding mode. In this guidance law, a finite-time disturbance observer is introduced to estimate mismatched and matched disturbances resulting from target maneuvers. Based on Lyapunov stability theory, the finite-time stability of the closed-loop guidance system under this law is analyzed using a finite-time bounded function. The super-twisting algorithm guarantees that the proposed guidance law is chattering-free and the disturbance observer does not depend on the prior knowledge of target acceleration. So the proposed guidance law is easy to be implemented in practice. The finite-time convergence and robustness of the proposed guidance law are demonstrated via numerical simulations accounting for missile autopilot dynamics.

Comparative investigations of nonlinear and linear observers for a highly manoeuvrable target in sliding mode guidance

Abstract Target manoeuvre is one of the key factors affecting guidance accuracy. To intercept highly maneuverable targets, a second-order sliding-mode guidance law, which is based on the super-twisting algorithm, is designed without depending on any information about the target motion. In the designed guidance system, the target estimator plays an essential role. Besides the existing higher-order sliding-mode observer (HOSMO), a first-order linear observer (FOLO) is also proposed to estimate the target manoeuvre, and this is the major contribution of this paper. The closed-loop guidance system can be guaranteed to be uniformly ultimately bounded (UUB) in the presence of the FOLO. The comparative simulations are carried out to investigate the overall performance resulting from these two categories of observers. The results show that the guidance law with the proposed linear observer can achieve better comprehensive criteria for the amplitude of normalised acceleration and elevator deflection requirements. The reasons for the different levels of performance of these two observer-based methods are thoroughly investigated.

IDVD-based trajectory generator for autonomous underwater docking operations

This paper investigates capability and efficiency of utilizing the inverse dynamics in the virtual domain (IDVD) method to provide the real-time updates of feasible trajectory for an autonomous underwater vehicle (AUV) during underwater docking operations. The applicability of the IDVD method is examined for two scenarios. For the first scenario, referred to as an offline scenario, a nominal trajectory may be generated ahead of time based on a priori knowledge about the docking station (DS) pose (position and orientation). The second scenario, referred to as an online scenario, assumes some uncertainty in the DS pose; hence, the reference trajectory needs to be constantly recomputed in real time based on the updates about the DS pose. The offline scenario solution serves as a benchmark solution to check feasibility and optimality of generated trajectory subject to constraints on the states and controls. In particular, the offline solution can assist in making informed trade-off decisions between optimality of solution and computational efficiency. For the relatively simple offline scenario, the IDVD-method solution is compared with the Legendre–Gauss–Lobatto pseudo-spectral (LGLPS) method solution. The software-in-the-loop simulations and Monte Carlo trials are run for robustness assessment. Finally, the potential for the IDVD method to work online, in a closed-loop guidance system, is explored using a realistic cluttered operational simulation environment. Simulation results show that the IDVD-method based guidance system guarantees a reliable and efficient docking process by generating computationally efficient, feasible and ready to be tracked trajectories.

Prox-1 University-Class Mission to Demonstrate Automated Proximity Operations

The Georgia Institute of Technology Prox-1 mission will demonstrate automated trajectory control in low Earth orbit relative to the deployed LightSail 2 CubeSat for an on-orbit inspection application. Passive thermal imaging provides the basis for a relative navigation system used to provide state estimation and optical tracking of LightSail 2. Automated maneuver planning and execution uses a guidance algorithm based upon relative orbital elements, with persistent collision avoidance using an artificial potential function. Simulation of the closed-loop guidance, navigation, and control system shows that the system is capable of performing automated station-keeping and relative orbit transfers for close-proximity operations. Funded by the U.S. Air Force Office of Scientific Research/U.S. Air Force Research Laboratory through the University Nanosatellite Program-7, Prox-1 is scheduled to launch in September 2016 as a secondary payload on the Space Test Program-2 launch.

Three-Dimensional Impact Angle Guidance Laws Based on Model Predictive Control and Sliding Mode Disturbance Observer

This paper presents a suboptimal three-dimensional guidance law to intercept unknown maneuvering targets with terminal angle constraint using multivariable control design. The presented guidance law is essentially a composite control method, which is constructed through a combination of standard continuous model predictive control (MPC) and adaptive multivariable sliding mode disturbance observer (SMDO). More specifically, the MPC method is utilized to obtain optimal line-of-sight (LOS) angle tracking performance for nonmaneuvering targets, while the SMDO technique is used to estimate and compensate for the unknown target maneuver online. By virtue of the adaptive nature, the proposed guidance law does not require any information on the bounds of target maneuver and its gradient except for their existence. The stability of the closed-loop guidance system is also analyzed by using Lyapunov function method. Simulation results clearly confirm the effectiveness of the proposed formulation against a maneuvering target.

Sliding mode based impact angle guidance law considering actuator fault

In this paper, a new continuous impact angle constraint guidance law in the presence of actuator fault is presented based on sliding mode control theory. The robustness and finite-time convergence of the basic guidance law is established using Lyapunov stability theory. For actuator compensation, an additional term is augmented in the original guidance law to guarantee finite-time stability of the closed-loop guidance system. Theoretical analysis and simulation results demonstrate the effectiveness of the proposed method.

Composite guidance laws using higher order sliding mode differentiator and disturbance observer

This paper has proposed a new composite robust guidance law to intercept maneuvering targets without line-of-sight (LOS) angular rate information. The presented guidance law is constructed through a combination of second-order sliding mode, higher-order sliding mode (HOSM) differentiator, and finite-time convergent disturbance observer (FTDOB). More specifically, the HOSM differentiator is used to extract the LOS angular rate information from LOS angle measurement, while the FTDOB is used to estimate and compensate the unknown target maneuvers. The finite-time stability of the closed-loop guidance system is established using finite-time bounded function and Lyapunov function methods. Next, the proposed guidance law is applied to three-dimensional homing engagement, where the FTDOB is used to estimate the target maneuver as well as the cross-coupling terms between the elevation and the azimuth motions. Numerical simulations with some comparisons are carried out to demonstrate the superiority of the proposed method.

Impact time control guidance law with large impact angle constraint

The problem of impact time control with large impact angle constraint is addressed. The dynamics of impact time error under the biased proportional navigation based impact angle control guidance law is first derived for the case of large impact angle constraint. Based on the impact time error dynamics, an additional control term is designed to drive the impact time error to converge in finite time. The resultant impact time and impact angle control guidance law comprises the biased proportional navigation based impact angle control guidance law and an additional term. The first term is used to achieve zero miss distance with the designated impact angle, and the second term is used to control the impact time. Compared with the existing impact time and impact angle control guidance law, which is shown to be only applicable for the case of small impact angle constraint, its application is not limited by the magnitude of the designated impact angle. Finite time convergence of the closed-loop guidance system under the proposed impact time and impact angle control guidance law is proved. Numerical simulations are performed to verify the effectiveness of the proposed impact time and impact angle control guidance law, especially for case of large impact angle constraint.

Impact time control guidance law with field of view constraint

The problem of Impact Time Control Guidance (ITCG) with field-of-view (FOV) constraint is investigated. The proposed ITCG law is a combination of the well-known Proportional Navigation Guidance (PNG) law and an additional biased term of impact time error, which is defined as the difference between the impact time by PNG and the prescribed one. A rule of the cosine of weighted leading angle in the biased term is used to guarantee that the FOV constraint is not violated during the engagement. Stability of the closed-loop guidance system is proved strictly. Numerical simulation results are presented to demonstrate the effectiveness of the proposed guidance law.

Cooperative Guidance Law for Multiple Near Space Interceptors with Impact Time Control

We propose a novel cooperative guidance law design method based on the finite time disturbance observer (FTDO) for multiple near space interceptors (NSIs) with impact time control. Initially, we construct a cooperative guidance model with head pursuit, and employ the FTDO to estimate the system disturbance caused by target maneuvering. We subsequently separate the cooperative guidance process into two stages, and develop the normal acceleration command based on the super-twisting algorithm (STA) and disturbance estimated value, to ensure the convergence of the relative distance. Then, we also design the acceleration command along the line-of-sight (LOS), based on the nonsingular fast terminal sliding mode (NFTSM) control, to ensure that all the NSIs simultaneously hit the target. Furthermore, we prove the stability of the closed-loop guidance system, based on the Lyapunov theory. Finally, our simulation results of a three-to-one interception scenario show that the proposed cooperative guidance scheme makes all the NSIs hit the target at the same time.

Guidance Law for Near Space Interceptor based on Block Backstepping Sliding Mode and Extended State Observer

This paper proposes a novel guidance law based on the block backstepping sliding mode control and extended state observer (ESO), which also takes into account the autopilot dynamic characteristics of the near space interceptor (NSI), and the impact angle constraint of attacking the maneuvering target. Based on the backstepping control approach, the target maneuvers and the parameter uncertainties of the autopilot are regarded as disturbances of the outer loop and inner loop, respectively. Then, the ESO is constructed to estimate the target acceleration and the inner loop disturbance, and the block backstepping sliding model guidance law is employed, based on the estimated disturbance value. Furthermore, in order to avoid the "explosion of complexity" problem, first-order low-pass filters are also introduced, to obtain differentiations of the virtual control variables. The stability of the closed-loop guidance system is also proven, based on the Lyapunov theory. Finally, simulation results demonstrate that the proposed guidance law can not only overcome the influence of the autopilot dynamic delay and target maneuvers, but also obtain a small miss distance.

Optimal guidance law in quantum mechanics

Following de Broglie’s idea of a pilot wave, this paper treats quantum mechanics as a problem of stochastic optimal guidance law design. The guidance scenario considered in the quantum world is that an electron is the flight vehicle to be guided and its accompanying pilot wave is the guidance law to be designed so as to guide the electron to a random target driven by the Wiener process, while minimizing a cost-to-go function. After solving the stochastic optimal guidance problem by differential dynamic programming, we point out that the optimal pilot wave guiding the particle’s motion is just the wavefunction Ψ(t,x), a solution to the Schrödinger equation; meanwhile, the closed-loop guidance system forms a complex state–space dynamics for Ψ(t,x), from which quantum operators emerge naturally. Quantum trajectories under the action of the optimal guidance law are solved and their statistical distribution is shown to coincide with the prediction of the probability density function Ψ∗Ψ.

Linear Covariance Techniques for Orbital Rendezvous Analysis and Autonomous Onboard Mission Planning

A novel trajectory control and navigation analysis software approach is developed. The program quickly determines trajectory dispersions, navigation errors, and required maneuver Δv at selected key points along a nominal trajectory. It can be used for mission design and planning activities or in autonomous flight systems to help determine the best trajectories, the best maneuver locations, and the best navigation update times to ensure mission success. These features are illustrated with two simple examples. The software works by applying linear covariance analysis techniques to a closed-loop guidance, navigation, and control (GN&C) system. The nonlinear dynamics and flight software models of a closed-loop six-degree-of-freedom Monte Carlo simulation are linearized. Then, linear covariance techniques are used to produce a program that will accurately predict 3-σ trajectory dispersions, navigation errors, and Av variations. Although the application presented is orbital rendezvous, the tools, techniques, and mathematical formulations are applicable to a variety of other space missions and GN&C problems including atmospheric entry, low-thrust electric propulsion missions, translunar injection and lunar orbit insertion, lunar ascent/descent, and formation-flying missions.