Terminal Angle Constraint Research Articles

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.

Intelligent diving guidance with terminal angle and velocity constraints via deep reinforcement learning

An adaptive guidance strategy that integrates optimal guidance and deep reinforcement learning to address a highly dynamic terminal guidance problem that entails meeting terminal position, angle, and velocity constraints. The proposed strategy leverages optimal guidance commands to accomplish position and angle control while introducing a deep reinforcement learning-based bias for the velocity constraint. In the training process, a dual-velocity state space is constructed to enhance the adaptability of the strategy to different guidance tasks, while training is optimized using the prediction-correction and expert knowledge to improve the training efficiency and optimality of the strategy. Simulations demonstrate that the proposed guidance strategy can achieve simultaneous control of terminal position, angle and velocity, and adapt to different guidance tasks.

Multi-UAV DMPC Cooperative Guidance with Constraints of Terminal Angle and Obstacle Avoidance

This paper studies the salvo attack problem for multiple unmanned aerial vehicles (UAVs) against a maneuvering target, and a guidance scheme based on distributed model predictive control (DMPC) is presented to achieve cooperative interception with constraints of terminal impact angle and no-fly zone (or obstacle) avoidance. Firstly, for guaranteeing the synchronization of UAVs in calculating their acceleration commands, the assumed predictive trajectories are introduced, whose deviation from the actual state trajectories is limited by the designed compatibility constraints. Secondly, based on the velocity-obstacle model, the obstacle avoidance constraints are presented, and for guaranteeing the convergence of impact time and impact angles, the auxiliary controller and terminal ingredients are developed, which complete the design of DMPC cooperative guidance scheme. Subsequently, the rigorous proof for the convergence of the proposed guidance scheme is provided. Based on the above design, a complete implementation process of the guidance scheme is presented, in which each UAV uses the particle swarm optimization algorithm to solve the preprocessed local optimization problem, and only the shared information among neighbors is utilized for calculation. Finally, the numerical simulations are conducted under diverse cases, which demonstrate the effectiveness of the proposed guidance scheme when solving cooperative interception problems with terminal angle and obstacle avoidance constraints.

Three-dimensional terminal angle constraint guidance law with class [formula omitted] function-based adaptive sliding mode control

This paper investigates the three-dimensional (3-D) interception guidance problem, where the missile is required to intercept the maneuvering target with the desired terminal angles. For the nonlinear relative kinematic model, a class K∞ function-based adaptive sliding mode guidance law is proposed, which ensures that the errors of terminal Line-of-Sight (LOS) angles converge to the small neighborhoods of origin at the time of interception, without relying on information about the target's acceleration. To overcome the challenges of large initial control input and chattering in existing sliding mode guidance laws, two improved control schemes are introduced. The first scheme is to directly impose saturation constraints into the adaptive gain. However, it is important to ensure that the unknown disturbance remains within the prescribed saturation bound. To avoid the limitation, another approach involves introducing auxiliary dynamics to eliminate the reaching phase and slow down the convergence of LOS angles by presetting the convergence time of the sliding mode variables, which helps mitigate excessive initial control inputs. Numerical simulations are conducted using a realistic missile model and considering a 3-DOF point-mass aircraft as the target to evaluate three different guidance laws. The results indicate that the proposed guidance law ensures interception accuracy while substantially reducing the control gain.

Prescribed-Time Chattering-Free Sliding Mode Guidance Law with Terminal Angle Constraint Based on Periodic Delayed Feedback

Prescribed-Time Chattering-Free Sliding Mode Guidance Law with Terminal Angle Constraint Based on Periodic Delayed Feedback

Distributed adaptive cooperative guidance against maneuvering targets with time-varying terminal angle constraint and overload saturation

Distributed adaptive cooperative guidance problem for multiple missiles intercepting a maneuvering target with time-varying terminal angle constraint and overload saturation is investigated in this paper. First of all, an extended state observer (ESO) is designed for each missile which can estimate the line-of-sight (LOS) rate and unknown external disturbances simultaneously. Secondly, a sliding manifold is proposed for each missile which consists of states of the ESO and neighbor terminal angle formation error. Then, a distributed cooperative guidance law is presented which can achieve the terminal angle constrained cooperative guidance. Furthermore, in order to deal with overload saturation, an auxiliary state is designed for the stability of the whole guidance system. Thirdly, the design process of cooperative guidance law is summarized as a guidance algorithm and the stability of the guidance error dynamics is proved via Lyapunov theories. Finally, the validity of the presented cooperative guidance algorithm is demonstrated by a numerical example.

Ballistic Missile Trajectory Design Considering Impact Angle Constraint

The current paper investigates the problem of guiding ballistic re-entry vehicles to the terminal point under the additional terminal constraint of final flight path angle. In this regard, the classical Lambert’s Problem is reformulated to include the final flight path angle constraint. The proposed solution of the modified Lambert’s problem consists of a minimum of two different trajectories starting from the same initial location and intersecting each other at a location, which is determined by applying the desired time of flight and terminal flight path angle constraints. The modified Lambert strategy strategy is shown to satisfy terminal flight path angle constraint along with the time of flight, initial and final location constraints. This scheme requires the ballistic vehicle to perform an additional stage burn during descent in-order to switch from an initial trajectory, using Lambert strategy, to a final trajectory which satisfies the final flight path angle constraint. An additional stage burn is provided such that the position and velocity of the vehicle traveling in the initial trajectory is matched with that required for it to be on the final trajectory. It is also found that the amount of propellant required for the trajectory transfer, is dependent on the total time of flight and the altitude at which the additional stage burn occurs. The optimal values of these two parameters are found using interior-point optimization technique.

A new three-dimensional adaptive sliding mode guidance law for maneuvering target with actuator fault and terminal angle constraints

In this paper, an adaptive terminal sliding mode guidance law is designed to intercept the maneuvering target with terminal line of sight angle constraints in three-dimensional space, and the actuator failure is considered. First, the relative kinematics model of three-dimensional space missile target considering fault is established. Then, the guidance law is designed by using the nonsingular fast terminal sliding mode method, which makes the tracking error and rate converge in finite time; Aiming at the problem of uncertain disturbance and fault in the model, the adaptive method is used to evaluate online. Finally, the Lyapunov stability theorem is used to prove that the missile target system is closed-loop stable under the proposed guidance law. Simulation results verify the performance of the proposed guidance law.

Differentiator-Based Incremental Three-Dimensional Terminal Angle Guidance With Enhanced Robustness

In this article, an incremental guidancelaw with terminal angle constraint is proposed against maneuvering targets in the 3-D space. First, a sliding surface is constructed such that its first-order dynamics excludes the relative range and line-of-sight angles in the perturbation. This manipulation avoids unboundedperturbations induced by target maneuvers near collision. Then, a benchmark guidance law is derived via the nonlinear dynamic inversion (NDI) based sliding mode control (NDI-SMC). To further enhance guidance system robustness, an incremental nonlinear dynamic inversion (INDI) based SMC (INDI-SMC) 3-D guidance law is developed. The INDI-SMC guidance law exploits the first-order derivative of the sliding variable and guidance command output at the latest step, which leads to reduced perturbation and thus requires smaller gains than the NDI-SMC guidance law. A multivariable continuous differentiator is employed to estimate the sliding variable's first-order derivative for guidance law implementation. Moreover, the stability of the differentiator is analyzed and the guidance robustness under uncertainties is compared. Extensive numerical simulations and a Monte Carlo test are conducted to verify effectiveness and robustness of the proposed method.

Terminal angle constraint finite-time guidance law with input saturation and autopilot dynamics

This paper proposes a finite-time command filtered backstepping guidance law (FCFBGL) with the terminal angle constraint while accounting for the input saturation and the autopilot dynamics. To eliminate the adverse effect induced by the filtering errors and the acceleration saturation, a new finite-time error compensation mechanism is integrated in the guidance law design. The proposed FCFBGL not only guarantees the the line-of-sight (LOS) angle error to converge to a small neighborhood of the origin in finite time but also achieves the continuity of the input signal. in finite time. Moreover, with the aid of the fractional power extended state observer (FPESO), the proposed FCFBGL requires no information on the target acceleration and the acceleration derivative of the missile, which is preferable in the practical application. The finite-time stability of the proposed guidance law is derived with the Lyapunov methodology. Simulation results illustrate the effectiveness and superiority of the proposed guidance law.

Adaptive improved super-twisting integral sliding mode guidance law against maneuvering target with terminal angle constraint

This paper investigates the maneuvering target interception problem considering terminal angle constraint, the input saturation and the second-order autopilot lag with the unavailable missile's acceleration. The considering problem is formulated as an output feedback control problem of a four-order nonlinear uncertain weakly observable system, which is challenging to address by general composite methods directly. Hence, the liner normal equivalent control model of the original guidance system is firstly derived to facilitate the extended state observer (ESO) based method design. Then, a nonlinear ESO is introduced to estimate the unmeasured system states and modeled disturbances as well as compensate for control saturation. Thereafter, the ESO-based guidance scheme is developed by integrating a novel four-order integral sliding mode manifold and an adaptive improved super-twisting algorithm. The main novelty is that a novel integral sliding mode manifold is proposed to replace the linear sliding mode manifold of super-twisting sliding mode to further reduce the convergent time of closed-loop system states. Besides, the conventional super-twisting algorithm is improved by modifying the reaching law and designing the adaptive gains to guarantee the continuity of guidance command and suppress the large constant gains and parameter uncertainties. Notably, only the output relative information is utilized in its design process. Numerical simulations validate the previous analyses and show the superiorities in reducing the energy consumption in high maneuvering target interception and achieving robustness to a certain margin under various uncertainties.

Nonlinear Guidance Laws for Maneuvering Target Interception With Virtual Look Angle Constraint

For the problem of intercepting a maneuvering target with a desired terminal impact angle, we propose a guidance law in this article based on a nonlinear relative virtual guidance model in which the origin is attached to the target. In this way, the original maneuvering target is transformed to a stationary one. We introduce the idea of polynomial guidance in the range domain into the relative virtual guidance model, then the acceleration command is obtained considering the terminal line-of-sight angle constraint and the terminal virtual look angle constraint. After linearization, the proposed law turns to a similar structure with the trajectory shaping guidance law, which is the optimal guidance law in the linear system. Finally, the performance of the proposed guidance law is demonstrated through numerous nonlinear simulations <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">.</b>

Virtual target approach-based optimal guidance law with both impact time and terminal angle constraints

Virtual target approach-based optimal guidance law with both impact time and terminal angle constraints

A new three-dimensional fixed time sliding mode guidance with terminal angle constraints

In this paper, a continuous fixed-time guidance law with terminal angle constraints considering coupled dynamics is proposed for intercepting maneuvering targets in three-dimensional space. First, a fast fixed-time nonsingular sliding manifold is designed to guarantee the line-of-sight angle tracking errors and angular rates to zero in a fixed time. Next, a novel sliding mode reaching law is proposed to weaken the chattering phenomenon and guarantee guidance system states converge to sliding mode manifold in a fixed time. Finally, numerical simulations are conducted to validate the effectiveness and superiority of the proposed guidance law.

Sensor-Based Robust Incremental Three-Dimensional Guidance Law with Terminal Angle Constraint

In this work, a robust incremental three-dimensional (3D) guidance law is proposed considering terminal angle constraint against maneuvering targets. As a stepping stone, the line-of-sight (LOS) tracking error dynamics is employed for the 3D guidance law design. A sliding variable is constructed such that its first-order derivative excludes the relative range in the perturbation, which avoids the unboundedness of system perturbation induced by target maneuvers near collision. A time-varying version of the sliding variable is designed to accelerate convergence of the LOS tracking errors and avoid large initial sliding variables. Then, two guidance laws are derived as a benchmark via the nonlinear dynamic inversion (NDI)-based sliding mode control (NDI-SMC) and NDI-based time-varying sliding mode control (NDI-TVSMC), respectively. To further improve guidance robustness with reduced system perturbation, the sensor-based incremental nonlinear dynamic inversion (INDI) control is used to design the INDI-SMC-based and INDI-TVSMC-based guidance laws. The sensor-based guidance laws exploit the LOS angular acceleration and guidance command output at the latest step, which result in smaller guidance gains to reject the perturbation than the NDI guidance laws. Numerical simulations in various cases and comparison studies are conducted to verify the effectiveness and robustness of the proposed method.

Three-dimensional time-varying sliding mode guidance law against maneuvering targets with terminal angle constraint

This paper deals with the problem of intercepting maneuvering targets with terminal angle constraints for missiles subjected to three-dimensional non-decoupling engagement geometry. To achieve the finite-time interception and satisfactory overload characteristics, a time varying sliding mode control methodology is developed based on a time base generator function. The main feature of the proposed guidance law guarantees the Line-of-Sight (LOS) angles to converge to small neighborhoods of the desired values at the interception time. First, a fractional power extended state observer is used to estimate the unknown target acceleration, which can significantly reduce the adaptive switching gain. The fractional power extended state observer enjoys the advantage of better noise tolerance. Then, a newly designed sliding mode surface is constructed by introducing a time base generator function and the time-varying sliding mode guidance law is developed based on this time-varying sliding surface. The proposed guidance law significantly reduces the overload magnitudes. Numerical simulations are carried out to verify the performance of the proposed guidance law.

Three-dimensional terminal angle constraint finite-time dual-layer guidance law with autopilot dynamics

Considering the problem of intercepting a target at desired terminal angles in the three-dimensional (3D) space, this paper proposes a finite-time dual-layer guidance law with consideration of the second-order autopilot dynamics. The proposed guidance law owns a cascaded structure, which is divided into an outer system and an inner system. To achieve the finite-time convergence, the outer and inner controllers are developed based on the nonsingular terminal sliding mode control. With the aid of the command filter, which can compute the first and the second derivatives of the virtual signal simultaneously, the design procedure of the fourth-order guidance system is simplified into two steps. Moreover, extended state observers are used to estimate the unknown target maneuver and the acceleration derivative of the missile, which facilitates the real implementation. Simulation results verify the performance of the proposed guidance law.

A Practical Optimal Guidance Scheme Under Impact Angle and Terminal Acceleration Constraints

This paper proposes a practical optimal guidance law that can handle terminal angle and acceleration constraints while providing robustness against uncertainty in autopilot dynamics. Building upon a well-established linear-quadratic optimal guidance framework, we first derive an energy-minimizing guidance scheme that nullifies terminal acceleration called optimal guidance law with impact angle and terminal acceleration constraints (OGL–IATA). Then, a practical modification to OGL–IATA is proposed to deal with the stability degradation of OGL–IATA due to unmodeled high-order autopilot dynamics. The modification primarily features feedback of pseudo-acceleration that is computed by passing the true acceleration signal through approximate missile dynamics; this simple modification is demonstrated to improve the stability margin of the guidance loop. Numerical examples of nonlinear engagement kinematics demonstrate the performance and the robustness characteristics of the proposed practical guidance scheme.

Optimal Guidance Law for Intercepting the Active Defense Aircraft with Terminal Angle Constraint

For the scenario where the target can actively defend against the attacking missile, an optimal guidance law for the attacking missile that can simultaneously evade the defending missile and intercept the target is proposed. To increase lethality of the attacking missile, the terminal angle constraint is considered. Assuming that the defending missile and the target is using a known control strategy, the guidance law design problem for the attacking missile is formulated as an optimal control problem with inequality constraint. General solution of the problem is derived for arbitrary order dynamics of the adversaries. Then first-order dynamics of the three players are considered and an analytic solution is presented. Numerical simulations are carried out to demonstrate the high performance of the proposed guidance law.