Guidance Law Design Research Articles

Cooperative guidance law design for multiple-vehicle under distributed event-triggered mechanism

Abstract To address the operational requirements of engaging important surface vessels with multiple anti-ship missiles, this paper proposes an attack time cooperative guidance law based on distributed event-triggered mechanism. This law enables multiple missiles to simultaneously engage the target with minimal communication. First, design a two-stage guidance law that includes a cooperative guidance stage and an independent guidance stage. In the cooperative guidance stage, the time-to-go estimates of each missile are synchronized through inter-missile communication to achieve consistency. In the independent guidance stage, the missiles can independently guide themselves towards the target without the need for further communication. The key to the implementation of this strategy is the time-to-go estimates can represent the real time-to-go after achieving consensus. Furthermore, an event-triggered mechanism is introduced during the cooperative stage to effectively reduce the frequency of communication required during the cluster coordination process. Finally, the stability of the proposed cooperative guidance law is proven using Lyapunov theory, ensuring the absence of Zeno behavior. Numerical simulation results validate the effectiveness of the algorithm and confirm the correctness of the stability analysis.

Missile Guidance Law Design Based on Free-Time Convergent Error Dynamics

Missile Guidance Law Design Based on Free-Time Convergent Error Dynamics

Design and Analysis of Terminal Guidance Law for Kinetic Interceptors based on Pulse Engine

A new terminal guidance law is proposed based on a solid propellant pulse engine and an improved proportional navigation method to address the terminal guidance issue for kinetic interceptors. On this basis, the start-stop curve of the pulse motor during the terminal guidance process is designed, along with its start-up logic. The effectiveness of the proposed guidance strategy is verified through simulation.

Two-stage spatiotemporal cooperative reentry guidance strategy using transformer and improved beluga whale optimization

This research addresses the challenge of insufficient control margin caused by the coupling of multiple constraints in the cooperative precise reentry guidance of hypersonic vehicles. Drawing inspiration from the concept of spatiotemporal decoupling control, a rapid guidance strategy is developed to ensure precise handling of all constraints, including attack time, attack angle, and trajectory constraints. Initially, during the early phase of gliding flight, the adjustment of the heading angle is conceptualized as a single variable root-solving problem, in relation to the entrance width of the lateral azimuth error corridor. Subsequently, a lateral azimuth error corridor with adaptively narrowing entrance width, coupled with a Transformer network-based bank angle predictor, is incorporated to achieve precise fine-tuning of the heading angle under the soft constraint of velocity. In the later phase of gliding flight, the design of a cooperative guidance law under complex multiple constraints is transformed into a nonlinear rapid optimization problem of control commands. An enhanced beluga whale optimization suited to this guidance task is proposed. Finally, numerical simulations are carried out to validate the effectiveness of the proposed strategy under both nominal and uncertain conditions.

Fixed-Time Distributed Event-Triggered Cooperative Guidance Methods for Multiple Vehicles with Limited Communications to Achieve Simultaneous Arrival

Aiming at the salvo-attack problem of multiple missiles, a distributed cooperative guidance law based on the event-triggered mechanism is proposed, which enables missiles with large differences in spatial location and velocity to achieve simultaneous attacks with only a few dozen information exchanges. It effectively reduces the generation of control commands and communication frequency, thereby reducing channel load and improving communication efficiency and reliability. Compared to traditional periodic sampling communication, the number of communications has been reduced by over 90%. The guidance process is divided into two stages. The first stage is the cooperative guidance stage, where missiles achieve consensus of the time-to-go estimates through information exchange. In this stage, each missile is designed with an event-triggered function based on its own state error, and the missile only updates and transmits its information in the communication network when the error meets the set threshold, effectively reducing the occupancy rate of missile-borne resources during the cooperation process. The second stage is the independent guidance stage, where missiles can hit the target simultaneously while keeping the communication network silent. This is achieved by ensuring that the time-to-go estimates of missiles can represent the real time-to-go after achieving consensus. By the design of the two-stage guidance law and the replacement of the event-triggered function, the cooperative guidance system can be ensured to remain stable in scenarios where the leader missile is present and destroyed, and this excludes Zeno behavior. The stability of the cooperative guidance law is rigorously proved by algebraic graph theory, matrix theory, and the Lyapunov method. Finally, the numerical simulation results demonstrate the validity of the algorithm and the correctness of the stability analysis.

Three-dimensional adaptive dynamic surface guidance law for missile with terminal angle and field-of-view constraints

In this paper, an adaptive dynamic surface (DSC) guidance law for missile is designed to intercept the maneuvering target with field-of-view (FOV) and terminal angle constraints in three-dimensional(3D) space, and the missile autopilot dynamics is considered. Firstly, the time-varying transformation function related to line of sight (LOS) is used to replace the FOV constraints, transforming the process-constrained control problem into the output-constrained control problem. Meanwhile, the 3D coupled relative kinematics model considering missile autopilot dynamics and maneuvering target acceleration is established. Secondly, a novel time-varying asymmetric barrier Lyapunov function (TABLF) with dead-zone characteristics is introduced to the adaptive dynamic surface guidance law design process to improve the robustness of parameter debugging. Thirdly, with the help of a nonlinear adaptive filter, the ‘explosion of complexity’ problem can be avoided effectively, which is caused by analytic computation of virtual signal derivatives. Furthermore, aiming at the problem of autopilot dynamic errors, target acceleration disturbances, and unmeasurable parameters in the model, a novel adaptive law is used to evaluate online. Then, the stability of the closed-loop system is rigorously proven using Lyapunov criteria. Ultimately, Numerical simulations with various constraints and comparison studies have been considered to show the feasibility and effectiveness of the proposed missile guidance law.

Design of air-breathing supersonic vehicle guidance law for intercepting the high maneuvering target with impact angle constraint

Abstract To achieve interception vehicles that can intercept high maneuvering targets with impact angle constraint, and improve the strike effectiveness of the vehicle, based on the two-dimensional planar motion model of the vehicle and the target, this article proposes a sliding mode control vehicle guidance law. The stability of the guidance law is verified through the Lyapunov function, and an extended state observer is set to check for disturbances. After simulation verification, the guidance law can intercept the target with predetermined terminal angle constraints and has good tracking performance.

Three-dimensional piecewise cooperative guidance with smooth switching topology

To investigate the issue of large-scale multi-missile cooperative attacks on a same target, this paper presents a three-dimensional piecewise cooperative guidance law based on smooth switching topology, realizing time consensus and impact angle constraints. Firstly, to implement the piecewise cooperative guidance law design, we establish the attack surface of the arc profile according to the expected LOS angle and the communication switching point, and obtain the virtual impact point (VIP). Secondly, a switching function is designed to ensure the smooth transition of the communication topology, mitigating the chattering issue in existing communication topology switching, while a time consensus protocol control input is implemented to facilitate the time cooperative attack of the missile in the LOS direction. Meanwhile, a fixed-time terminal sliding mode guidance law is established to guarantee the satisfaction of the impact angle constraint at the VIP. Additionally, an adaptive three-dimensional proportional navigation guidance (PNG) law is designed to guarantee zero miss distance at the real impact point (RIP). Finally, simulations involving four missiles attacking stationary targets simultaneously validate the effectiveness and superiority of the piecewise cooperative guidance law.

Predefined-time prescribed performance guidance law design against maneuvering target under input saturation

A novel SMC-based prescribed performance guidance law combined with a base generator (TBG) is proposed. A TBG-based modified Lyapunov function is first proposed, which ensures that the LOS tracking error converges into zero within a predefined time. A novel sliding manifold with adjusting convergent time property is proposed, which brings about a smaller control magnitude and predefined time convergent rate. To ensure a satisfied transit and steady performance, some converted variables are defined based on which a novel prescribed performance guidance law is constructed. The input saturation problem is properly solved by designing a novel TBG-based one-order auxiliary system. Extensive simulation results have verified the effectiveness of the proposed method.

A novel impact angle control guidance law design via predefined time convergence theory

A predefined time guidance law with impact angle control is proposed for intercepting the stationary target. With such a guidance law, the convergence time of the impact angle error for the missile is independent of the initial conditions, and it can be selected at the will of the designer. First, a heading error shaping method based on the Lyapunov asymptotic stability theory will be introduced, which ensures the missile hits the target. Then, a bias term will be designed and introduced into this method, which can make sure the impact angle error converges to zero in the predefined time. The Lyapunov stability analysis is discussed in detail for the resulting predefined-time convergent guidance system. Finally, simulation examples are carried out to illustrate the effectiveness of the proposed guidance law.

Design of Integral Sliding Mode Guidance Law Based on Disturbance Observer

Design of Integral Sliding Mode Guidance Law Based on Disturbance Observer

Design of Convergent and Accurate Guidance Law with Finite Time in Complex Adversarial Scenarios

The target can deceive the flight vehicle by releasing an infrared decoy to make the line-of-sight (LOS) angle rate deflect greatly, thus causing the flight vehicle to miss the target. Therefore, in order to accurately strike the target in complex adversarial scenarios, this paper proposes a finite-time convergence guidance law (FTCG) combined with a finite-time disturbance observer (FTDO). The complex adversarial scenario is established by combining the relative motion model between the flight vehicle and the target and the motion model of the infrared decoy. Based on this, considering the dynamic characteristic of the flight vehicle’s autopilot, a guidance model is obtained. Utilizing sliding mode control theory and finite-time control theory, an FTCG of the LOS angle rate is designed. Then, the finite-time convergence of the guidance law is proved and the total convergence time is derived. Finally, for the target maneuvering that is difficult to measure in the guidance law, an FTDO is used to estimate and compensate for the target maneuvering in the guidance law. Simulation results show that the FTCG can make the LOS angle rate quickly converge and accurately strike the target in different scenarios, with a good guidance accuracy and robustness. Compared with the sliding mode guidance law (SMGL) and the adaptive sliding mode guidance law (ASMGL) based on an extended state observer (ESO), the advantages of the designed guidance law are illustrated. Finally, FTCG is extended to be three dimensional and compared with the proportional navigation guidance law (PNG) to further illustrate its effectiveness in a three-dimensional coordinate system.

Integrated guidance and control with impact angle and general field-of-view constraints

This paper investigates the problem of integrated guidance and control (IGC) law design with impact angle and general field-of-view (FOV) constraints. Firstly, the IGC model for intercepting non-maneuvering moving target is parameterized by state-dependent coefficient matrices. The nominal IGC law for intercepting the target with the desired impact angle is obtained by solving the state-dependent Riccati equation. Secondly, since the relative degrees of the general FOV constraints with respect to the IGC model exceed one, the high-order control barrier functions are constructed. The satisfaction of the FOV constraints is equivalent to ensuring that the superlevel sets defined by the barrier functions are forward invariant, which is converted into affine constraints on the control input. The nominal IGC law is modified in a minimally invasive way by quadratic programming. Then, the proposed method is extended to the case of intercepting maneuvering target by leveraging a relative coordinate frame. Finally, numerical simulations are conducted to verify the effectiveness of the proposed method.

A Sliding Mode Control-Based Guidance Law for a Two-Dimensional Orbit Transfer with Bounded Disturbances

The aim of this paper is to analyze the performance of a state-feedback guidance law, which is obtained through a classical sliding mode control approach, in a two-dimensional circle-to-circle orbit transfer of a spacecraft equipped with a continuous-thrust propulsion system. The paper shows that such an inherently robust control technique can be effectively used to obtain possible transfer trajectories even when the spacecraft equations of motion are affected by perturbations. The problem of the guidance law design is first addressed in the simplified case of an unperturbed system, where it is shown how the state-feedback control may be effectively used to obtain simple mathematical relationships and graphs that allow the designer to determine possible transfer trajectories that depend on a few control parameters. It is also shown that a suitable combination of the controller parameters may be exploited to obtain trade-off solutions between the flight time and the transfer velocity change. The simplified control strategy is then used to investigate a typical heliocentric orbit raising/lowering in the presence of bounded disturbances and measurement errors.

Optimal guidance law design for three-dimensional trajectory tracking of missiles based on fixed-gain disturbance observer

To address the trajectory tracking problem of missiles, an optimal disturbance rejection guidance law (ODRGL) in three dimensions is proposed under the premise of uncontrollable speed. Error models of the actual and the reference trajectory are built in channels of pitch and yaw, respectively. In the yaw channel, a modeling error is introduced as the model cannot be built directly. According to the separation theorem, the controller and the observer are designed respectively. A fixed-gain disturbance observer (FGDO) is proposed to estimate the disturbance such as wind disturbances and modeling errors, and the disturbance is compensated for feed-forward. The nominal error models of pitch and yaw channels are linearized by the differential geometric linearization theory, and then linear quadratic regulator (LQR) controllers are designed for the linearized models. The simulation results show that in the presence of wind disturbances and modeling errors, the optimal guidance law proposed in this paper can stabilize the original nonlinear system and ensure energy optimization.

Design of an Optimal Cooperative Guidance Law Confronting Evaders with High Maneuver

Design of an Optimal Cooperative Guidance Law Confronting Evaders with High Maneuver

Distributed observer‐based fixed‐time cooperative guidance law against maneuvering target

SummaryThis paper presents a fixed‐time cooperative guidance law for leader‐following missiles, comprising one leader missile with the target seeker and several seeker‐less follower missiles. The aim is to achieve a simultaneous attack on a maneuvering target at desired impact angles. First, a guidance law with impact angle control for the leader missile against a maneuvering target is proposed based on nonsingular fast terminal sliding mode (NFTSM) control algorithm. Then, the design of cooperative guidance law for the follower missiles is composed of two parts: along the follower‐to‐leader line of sight (LOS) direction, the guidance command derived from bi‐homogeneous property is designed to ensure that the follower‐leader ranges keep proportional consensus with the range‐to‐go of the leader missile, thus avoiding the estimation of time‐to‐go (); in the normal follower‐to‐leader LOS direction, considering the relative impact angle constraints which is determined by the leader LOS angle, the guidance command is proposed based on predefined‐time sliding mode control method. What's more, a distributed fixed‐time observer is designed for the follower missiles to compensate for unobtainable leader missile information. The fixed‐time stability of the proposed methods is demonstrated using the Lyapunov theory and bi‐homogeneous property. Finally, simulation results confirm the effectiveness and superiority of the proposed fixed‐time cooperative guidance law with leader‐following strategy.

Integrated Design of Multi-Constrained Snake Maneuver Surge Guidance Control for Hypersonic Vehicles in the Dive Segment

Focusing on the large maneuver penetration of the hypersonic glide vehicle with multiple constraints and uncertain disturbance, a robust integrated guidance and control law, which can achieve the snake-shape maneuver, is designed. A snake-shape maneuver acceleration command, in the framework of sine function, determined by the altitude, target declination of the line of sight and the missile-target distance, is discussed. The integrated guidance and control law includes the terminal guidance law with multiple constraints, attitude control law and angular velocity control law. In the terminal guidance law design, the sliding mode control is adopted while the adaptive technique is applied to estimate the disturbance. The selected sliding mode surface has variable gain determined by the estimated time-to-go. With the designed terminal guidance law, using the snake-shape maneuver acceleration command as the bias item, the angular rate of the line of sight will converge to zero and the line of sight angle will converge to the expected value, simultaneously. The attitude control law and angular velocity control law are designed to track the expected attack and bank angles. The stability of the whole system is proved with the application of the Lyapunov theorem. The effectiveness and robustness of the proposed integrated guidance and control law is verified by simulation.

Cooperative game penetration guidance for multiple hypersonic vehicles under safety critical framework

The rapid development of the anti-missile weapon technology brings new challenges to the cooperative penetration strategy solution and the guidance law design for Hypersonic Vehicles (HVs). This paper studies the coordinated game penetration guidance problem for multiple hypersonic vehicles faced with space threat areas. A scheme for seeking cooperative game penetration guidance strategy under safety critical control framework is presented. In this scheme, a multi-HV cooperative game model is proposed in a minimum optimization form which can simplify the solving process and accelerate the computing speed. Then, a second-order control barrier function is developed to transform the implicit nonlinear constraints of the proposed model into linear ones. In order to obtain better performance of guidance strategy, a composite guidance law under the safety critical control framework is presented to allocate guidance strategies appropriately in the whole process. It is shown that the proposed scheme can guarantee successful penetration while avoiding threat areas. Finally, a comparative simulation with a two-on-three game is conducted to verify the effectiveness of the proposed method.

Formation flying orbits and GNC design in binary asteroid systems

Formation flying represents a promising opportunity for next space missions, due to its benefits in cost saving, redundancy and fault tolerance given by multiple small and cheap space segments exploitation, with comparable performance of a single, large monolithic spacecraft. That is even more relevant in asteroid exploration, as the harsh environment poses great risks to the probes survival. The low, irregular gravity field, the poor knowledge of shape and composition, and the possible presence of floating particles in the surroundings suggest adopting a low-risk strategy for the exploration of these bodies, delegating proximity operations to multiple nanosatellites, while keeping the main spacecraft at safe distance. As a downside, multiple cooperating spacecraft imply advanced capabilities in accurately reconstructing the relative positions and displacements and in fixing reconfiguration manoeuvres. Moreover, whenever relative distance is very close, agents’ guidance and control shall be autonomously computed by the spacecraft, as promptness of commands is not ensured relying on ground segment only. The partially unknown environment exacerbates this issue, demanding navigation and control schemes capable of withstanding potentially large uncertainties in the dynamics. If a binary system is considered, the multiple gravitational sources complicate even more the setup of the formation, requiring an accurate search and selection of operative orbits. This study will be thus defined by three different steps. First the search and development of suitable trajectories to host a reconfigurable satellite formation is carried out. Then the design of a Model Predictive on-board guidance and control law is performed to assess the capability of the spacecraft to execute successful reconfiguration transfers relying on a simplified dynamical model (namely the Circular Restricted Three-Body Problem). At the end the navigation error requirements are derived, in order to ensure the feasibility of the guidance and control scheme. Inspired by the Hera mission, this study explores the aforementioned aspects of the design of a formation for the exploration of the Didymos binary asteroid system, which comprises many complications but also challenges for many other future missions to fly in unexplored environments.