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A new nonlinear guidance law for air-to-ground missile cooperation attacks is proposed in this paper. This guidance law enables missiles with different initial conditions to attack targets simultaneously, and it can also precisely satisfy the terminal impact angle conditions in both flight-path angle and heading angle. The guidance law is devised u...
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Citations
... Departing from controlling remaining flight time, the modified model predictive control (MPC) is adopted to make state variables converge over time, aiming for the simultaneous interception [11]. In a three-dimensional scenario, the model predictive static programming (MPSP) method is used to explore guidance laws incorporating remaining flight time and attack angle constraints [12]. Moreover, cooperative guidance laws incorporating both attack angle and line-of-sight constraints were separately focused, with limited-time convergence guidance laws proposed [13,14]. ...
This paper proposes a dynamic encircling cooperative guidance (DECG) law to enable multiple interceptors to cooperatively intercept a superior target, considering low velocity, limited overload, impact angle and simultaneous arrival constraints. First, the feasible escaping area of the target is analyzed and a dynamic encircling strategy for the target is established. This strategy efficiently provides virtual escaping points, allowing interceptors to dynamically encircle the target without excessive energy consumption, ultimately leading to a successful interception. Second, to enhance the physical feasibility of the kinematic equations governing the interaction between interceptors and target at the virtual escaping points, the independent variable is substituted and the kinematic equations are remodeled. Convex optimization is employed to address the multi-constraint optimal guidance problem for each interceptor, thereby facilitating simultaneous interception. Compared with the existing guidance laws, DECG has a more practical and feasible cooperative strategy, is able to handle more constraints including the interceptor’s own constraints and cooperative constraints, and does not rely on the precise calculation of explicit remaining flight time in the guidance law implementation. Lastly, the effectiveness, superiority and robustness of the DECG law are evaluated through a series of numerical simulations, and its performance is compared with that of the cooperative proportional navigation guidance law (CPNG).
... In recent years, the model predictive static programming (MPSP) paradigm has been extensively applied to the field of constrained vehicle guidance, yielding significant advancements. A novel nonlinear guidance law has been formulated utilizing MPSP, facilitating the simultaneous arrival of missiles with diverse initial conditions at their targets, while adhering to terminal impact angle constraints [18]. Building upon the variable time MPSP framework [19], a guidance law has been engineered for three-dimensional nonlinear guidance challenges, incorporating the expected attack time into the objective function to address constraints on both attack time and angle [20]. ...
This paper addresses the guidance of various flight vehicles under multiple constraints in three-dimensional space. A cooperative guidance strategy that satisfies both time and angle constraints is designed to reach a moving target. The strategy is organized into two parts: modeling and programming calculations. First, a nonlinear motion model for guidance is established and normalized, including both the vehicle and the target. Later, the arrival method is automatically determined according to the strategy and depending on the type of target. The cooperative terminal time is determined based on an augmented proportional navigation method. An improved model predictive static programming (MPSP) algorithm was designed as a means of adjusting the adaptive terminal time. Then, the algorithm was used to update the control quantity iteratively until the off-target quantity and the angle of constraints were satisfied. The simulation results showed that the strategy could enable multiple flight vehicles at different initial positions to reach the target accurately at the same time and with the ideal impact angle. The strategy boasts a high computational efficiency and is capable of being implemented in real time.
... Although the ITAC guidance problem has attracted great attention in recent years, there are only a few existing studies that can control both the impact time and angle in 3D space. In [32], the model predictive control was exploited to obtain a numerical 3D ITAC guidance law. Moreover, a two-stage 3D ITAC guidance law was developed in [33], in which the switching point between the two stages was selected via Newton iteration method to adjust the impact time. ...
... The accuracy of guidance laws may be degraded when the missile trajectory is highly curved. Instead of using time-to-go estimation, a variety of guidance laws were proposed by incorporating numerical iterative schemes into the guidance loop [14]- [16], [22], [23], [25]- [27], [29], [30], [32], [33]. Such derived guidance laws are effective for a highly nonlinear engagement model, but may result in intensive computational loads on the onboard flight computer. ...
... It is the smallest value that can be achieved physically. The second inequality in (32) implies the feasible region of the impact angle. The desired elevation LOS angle θ LF needs to be determined according to the initial launch conditions, i.e., θ L0 , and θ M 0 . ...
One major challenge for autonomous attitude takeover control for on-orbit servicing of spacecrafts is that an accurate dynamic motion model of the combined vehicles is highly nonlinear, complex and often costly to identify online, which makes traditional model-based control impractical for this task. To address this issue, a recursive online sparse Gaussian Process (GP)-based learning strategy for attitude takeover control of noncooperative targets with maneuverability is proposed, where the unknown dynamics are online compensated based on the learnt GP model in a semi-feedforward manner. The method enables the continuous use of on-orbit data to successively improve the learnt model during online operation and has reduced computational load compared to standard GP regression. Next to the GP-based feedforward, a feedback controller is proposed that varies its gains based on the predicted model confidence, ensuring robustness of the overall scheme. Moreover, rigorous theoretical proofs of Lyapunov stability and boundedness guarantees of the proposed method-driven closed-loop system are provided in the probabilistic sense. A simulation study based on a high-fidelity simulator is used to show the effectiveness of the proposed strategy and demonstrate its high performance.
... Although the ITAC guidance problem has attracted great attention in recent years, there are only a few existing studies that can control both the impact time and angle in 3D space. In [32], the model predictive control was exploited to obtain a numerical 3D ITAC guidance law. Moreover, a two-stage 3D ITAC guidance law was developed in [33], in which the switching point between the two stages was selected via Newton iteration method to adjust the impact time. ...
... The accuracy of guidance laws may be degraded when the missile trajectory is highly curved. Instead of using time-to-go estimation, a variety of guidance laws were proposed by incorporating numerical iterative schemes into the guidance loop [14]- [16], [22], [23], [25]- [27], [29], [30], [32], [33]. Such derived guidance laws are effective for a highly nonlinear engagement model, but may result in intensive computational loads on the onboard flight computer. ...
... It is the smallest value that can be achieved physically. The second inequality in (32) implies the feasible region of the impact angle. The desired elevation LOS angle θ LF needs to be determined according to the initial launch conditions, i.e., θ L0 , and θ M 0 . ...
This paper presents a nonlinear three-dimensional (3D) guidance law for homing missiles with field-of-view (FOV) constraint to achieve impact time and angle control against a stationary target. Specifically, a guidance error vector and its nonlinear error dynamics are first developed. The desired impact time and angle can be satisfied as long as the guidance error converges to zero before the interception. The proposed nonlinear error dynamics is then enhanced with an auxiliary function to address the FOV constraint, and the prescribed-time control technique is employed to obtain a feedback guidance law. The guidance framework in this paper is rigorously derived under the original 3D missile-target kinematics model, without decoupling the engagement geometry into two mutually orthogonal planes. Furthermore, different from existing similar studies, the proposed guidance law does not require explicit time-to-go estimation and numerical iterations, which avoids estimation error and allows for convenient implementation.
... Unlike the above scenarios, some researchers have focused on the research of cooperatively intercepting maneuvering target with multimissiles in recent years [2,3]. As is known to all, a missile can intercept a low maneuvering target (such as early warning aircraft) easily [12][13][14][15], but it is difficult for a missile to intercept a target with highly maneuverability (such as unmanned aerial vehicle). Thus, it is necessary to develop cooperative guidance law for multiple missiles against the highly maneuvering target. ...
In this paper, a new dynamic surrounding attack cooperative guidance law against highly maneuvering target based on decoupled model is proposed. First, a new dynamic surrounding guidance strategy is proposed, and virtual targets are introduced to establish the cooperative guidance model for dynamic surrounding attack. Second, a dynamic inverse method is used to decouple the cooperative guidance model, and extended state observers (ESOs) are introduced to estimate the disturbances caused by target maneuver. Then, the impact time and dynamic surrounding guidance (ITDSG) law against highly maneuvering target is designed based on a prescribed-time stable method and the decoupled model. Finally, numerical simulations are performed to illustrate the superiority and effectiveness of the proposed ITDSG.
... For example, the antitank missile uses a rocket engine as the propulsion to fly at high speed, and its main speed schemes include the following three types: boost + glide flight, boost + acceleration cruising + glide flight, and acceleration boost + constant velocity (boost + cruising flight). A propulsion map and speed of typical high-speed kinetic energy antitank missile are shown in Figure 3, and in general, while designing the guidance algorithms ,it will be assumed that the flight speed is constant, especially at the terminal guidance phase [16][17][18], or the flight speed is time varying passively affected by gravity, propulsion, and aerodynamic forces [12,[19][20][21]. At the same time, the research topic of speed is mainly focused on the cruise flight process [22,23] or is considered as a terminal constraint at some special flight mission, for example, a rendezvous mission to a tanker [24]. ...
The loitering munitions are advanced new ammunitions, which reflect both the characteristics of UAV and missile and have their own novel characteristics. This paper analysed the characteristics of the attack process of a small loitering munition and proposed a speed scheme suitable for precise strike of loitering munitions based on the concept of traditional ammunition’s speed-thrust schemes. Then, the boundary conditions and the existence of the solution have been discussed. Finally, flight test results showed that the scheme was effective.
1. Introduction
A loitering munition (LM), as a new member of the precision-guided munitions [1–5], fits in the niche between cruise missiles and unmanned combat aerial vehicles (UCAVs) sharing characteristics with both. In the cruise section, the LM mainly conducts flight and mission target search in the form of a UAV, but in the launch section and the final guidance-attacking section, the LM works as a missile [5–7]. After launch, the original folded wings are unfolded, and the aircraft is converted from projectile form to drone form, and the configuration of the loitering munitions does not change again after the conversion of the machine finished [1, 8–10]. Therefore, it is a challenge for a LM to adapt to the control requirements of different mission phases under the same aerodynamic shape. The typical working process for a loitering munition includes pneumatic launch, loitering and gathering intelligence, locking on target, aborting mission, or precise attack. Some mature products of small LM are shown in Figure 1, and the working process diagram for a LM can be seen in Figure 2 [11].
(a)
... Therefore, it has high computational efficiency in comparison with the conventional numerical methods and dynamic programming approach. Also, this method has been successfully applied to formulate several optimal guidance laws with terminal angle constraint [6], [19]- [21]. However, to ensure the Euler integration within a desired precision limitation, a large number of discrete points should be selected for MPSP. ...
This paper aims at proposing a nonlinear suboptimal impact-angle-constrained guidance law for an interceptor engaging against an incoming high-speed ballistic missile in three dimensions. The method is based on an improved Linear Pseudospectral Model Predictive Control (LPMPC), in which the control variable is parameterized as a sum of general standard basis functions with few undetermined coefficients. Although the final solution is suboptimal, a series of analytical improved formulas can be also successively derived to eliminate the final predictive errors, which remains the character that few points will achieve high accuracy. Furthermore, the number of improved variables will significantly decrease, which will further improve the computational efficiency and provide smoother control history. Several numerical simulations are carried out to evaluate the performance of the proposed method. Results show that it performs well in achieving desired impact angles and the near-zero miss distance with high accuracy. In comparison with other typical methods, the proposed method has superior performance in computational efficiency. Therefore, it has the potential to be applied in the framework of guidance.
... The solution of this algorithm is very close to the optimal solution, and the computational efficiency is high. At present, MPSP has been successfully applied to some aerospace engineering problems [30][31][32]. However, this algorithm needs a lot of computing nodes. ...
This paper aims at proposing a pseudospectral collocation conjugate gradient method (PCCG) for solving the nonlinear optimal control problems with terminal constraints and to apply it to rocket landing guidance. Firstly, the projection technique and conjugate gradient method are combined to obtain the control that can satisfy the terminal constraints. In addition, a new step-size adjustment strategy is applied to make the algorithm converge faster. Secondly, to improve the computational efficiency, the nonlinear adjoint and auxiliary differential equations are transformed into a set of linear algebraic equations by using the Gauss pseudospectral collocation scheme. Therefore, the values of adjoint and auxiliary functions at LG nodes can be obtained by solving the system of linear equations, and the special integrals needed in the control update process can be solved more effectively by using the Gauss quadrature method. Finally, PCCG algorithm is applied to the rocket landing guidance problem. A comparison with conjugate gradient method and GPOPS-II is also provided. Simulation results show that the algorithm has high convergence speed and computational efficiency, and the solution is optimal.
... Unfortunately, due to parasitic echoes generated on the radio locator screen, the limitations of algorithms related to processing the signals coming from different sensors [1], the position of the targets can be determined with approximation. The values measured can enhance multiple variable features and may be constrained by different initial conditions depending on the flight angle [2] and on the position of the target towards the radar [3]. ...
Radio-electronic means, including equipment for transmissions, radio-location, broadcasting, and navigation, allow the execution of various research missions and combat forces management. Determining the target coordinates and directing the armament towards them, obtaining and processing data about enemies, ensuring the navigation of ships, planes and outer atmospheric means, transmitting orders, decisions, reports and other necessary information for the armed forces; these are only some of the possibilities of radio-electronic technology. Fuzzy logic allows the linguistic description of the laws of command, operation and control of a system. When working with complex and nonlinear systems, it can often be observed that, as their complexity increases, there is a decrease in the significance of the details in describing the global behavior of the system. Even though such an approach may seem inadequate, it is often superior and less laborious than a rigorous mathematical approach. The main argument in favor of fuzzy set theory is to excel in operating with imprecise, vague notions. This article demonstrates the superiority of a fuzzy tracking system over the standard Kalman filter tracking system under the conditions of uneven accelerations and sudden change of direction of the targets, as well as in the case of failure to observe the target during successive scans. A cascading Kalman filtering algorithm was used to solve the speed ambiguity and to reduce the measurement error in real-time radar processing. The cascade filters are extended Kalman filters with controlled gain using fuzzy logic for tracking targets using radar equipment under difficult tracking conditions.
This paper presents a generalized Newton iteration based MPSP algorithm for the terminal constrained guidance problems. In the proposed approach, the Chebyshev polynomial is used to approximate the dynamics and constraint equations, by which the continuous-time guidance problem is transcribed into a discrete root-finding problem, and then it is solved by the Newton method. A significant improvement to the previous methods lies in the fact that both the state and control are treated as the variables to be determined and simultaneously iteratively solved on the principle of the Newton method, which greatly reduces the computational complexity as well as improves the convergence robustness. The simulation case with a scenario of intercepting a high-speed target with both impact-angle and impact-time constraint in the midcourse phase was conducted to illustrate the effectiveness of the proposed method. The results show that the proposed guidance is superior to model predictive static programming and other state-of the-art Newton-type methods in terms of computational efficiency and convergence robustness
