Interception Problem Research Articles

Optimal game theoretic solution of the pursuit‐evasion intercept problem using on‐policy reinforcement learning

AbstractThis article presents a rigorous formulation for the pursuit‐evasion (PE) game when velocity constraints are imposed on agents of the game or players. The game is formulated as an infinite‐horizon problem using a non‐quadratic functional, then sufficient conditions are derived to prove capture in a finite‐time. A novel tracking Hamilton–Jacobi–Isaacs (HJI) equation associated with the non‐quadratic value function is employed, which is solved for Nash equilibrium velocity policies for each agent with arbitrary nonlinear dynamics. In contrast to the existing remedies for proof of capture in PE game, the proposed method does not assume players are moving with their maximum velocities and considers the velocity constraints a priori. Attaining the optimal actions requires the solution of HJI equations online and in real‐time. We overcome this problem by presenting the on‐policy iteration of integral reinforcement learning (IRL) technique. The persistence of excitation for IRL to work is satisfied inherently until capture occurs, at which time the game ends. Furthermore, a nonlinear backstepping control method is proposed to track desired optimal velocity trajectories for players with generalized Newtonian dynamics. Simulation results are provided to show the validity of the proposed methods.

Pontryagin Neural Networks with Functional Interpolation for Optimal Intercept Problems

In this work, we introduce Pontryagin Neural Networks (PoNNs) and employ them to learn the optimal control actions for unconstrained and constrained optimal intercept problems. PoNNs represent a particular family of Physics-Informed Neural Networks (PINNs) specifically designed for tackling optimal control problems via the Pontryagin Minimum Principle (PMP) application (e.g., indirect method). The PMP provides first-order necessary optimality conditions, which result in a Two-Point Boundary Value Problem (TPBVP). More precisely, PoNNs learn the optimal control actions from the unknown solutions of the arising TPBVP, modeling them with Neural Networks (NNs). The characteristic feature of PoNNs is the use of PINNs combined with a functional interpolation technique, named the Theory of Functional Connections (TFC), which forms the so-called PINN-TFC based frameworks. According to these frameworks, the unknown solutions are modeled via the TFC’s constrained expressions using NNs as free functions. The results show that PoNNs can be successfully applied to learn optimal controls for the class of optimal intercept problems considered in this paper.

Time-optimal guidance for intercepting moving targets by Dubins vehicles

This paper is concerned with a Minimum-Time Intercept Problem (MTIP), for which a Dubins vehicle is guided from a position with a prescribed initial heading angle to intercept a moving target in minimum time. Some geometric properties for the solution of the MTIP are presented, showing that the solution paths must lie in a sufficient family of 4 candidates. Necessary and sufficient conditions for optimality of each candidate are established. By employing the geometric properties, it is found that the 4 candidates are determined by the zeros of some real-valued functions when the target’s velocity is constant. In order to compute all the 4 candidates, the derivatives of these real-valued functions are transformed to polynomials so that the extrema of those real-valued functions can be computed by standard polynomial solvers. This allows employing a simple bisection method to find all the 4 candidates. Since the MTIP with a constant target’s velocity is equivalent to the path planning problem of Dubins vehicle in a constant drift field, developing such an algorithm also enables efficiently finding the shortest Dubins path in a constant drift field. Finally, some numerical examples are presented, demonstrating and verifying the developments of the paper.

Interception time and uncertainty optimization for tangent-impulse orbit interception problem

The traditional tangent impulse interception problem does not consider the influence of actual deviation. However, by taking the actual state deviation of the interceptor into the orbit design process, an interception orbit that is more robust than the nominal orbit can be obtained. Therefore, we study the minimum time interception problem and the minimum terminal interception error problem under tangent impulse conditions and give an orbit optimization method that considers the interception time and the interception uncertainty. First, we express the interceptor's transfer time equation as a form of flight path angle, establish a global optimization model for solving the minimum time tangent impulse interception and give a hybrid optimization algorithm based on Augmented Lagrange Genetic Algorithm - Sequential Quadratic Programming (ALGA-SQP). Secondly, we use the universal time equation and Bootstrap resampling technology to calculate the interceptor's terminal error distribution and establish the relevant global optimization model by using the circumscribed cuboid volume of the interceptor's terminal position error ellipsoid as the optimization index. Finally, we combined the above two single-objective optimization models to establish a global multi-objective optimization model that considers interception time and interception uncertainty and gave a hybrid multi-objective optimization algorithm based on Non-dominated Sorting Genetic Algorithm II - Goal Achievement Method (NSGA2-GAM). The simulation example verifies the effectiveness of this method.

Autonomous Navigation of a Team of Unmanned Surface Vehicles for Intercepting Intruders on a Region Boundary.

We study problems of intercepting single and multiple invasive intruders on a boundary of a planar region by employing a team of autonomous unmanned surface vehicles. First, the problem of intercepting a single intruder has been studied and then the proposed strategy has been applied to intercepting multiple intruders on the region boundary. Based on the proposed decentralised motion control algorithm and decision making strategy, each autonomous vehicle intercepts any intruder, which tends to leave the region by detecting the most vulnerable point of the boundary. An efficient and simple mathematical rules based control algorithm for navigating the autonomous vehicles on the boundary of the see region is developed. The proposed algorithm is computationally simple and easily implementable in real life intruder interception applications. In this paper, we obtain necessary and sufficient conditions for the existence of a real-time solution to the considered problem of intruder interception. The effectiveness of the proposed method is confirmed by computer simulations with both single and multiple intruders.

Robust Head-Pursuit Guidance Accounting for Hit-to-Kill and Angle Constraints

In this paper, the hit-to-kill strategy is introduced to solve the three-dimensional (3D) robust head-pursuit (HP) interception problem considering the line-of-sight (LOS) angle constraints. Firstly, a target based relative dynamic model is proposed to be the nominal model for designing the robust HP guidance laws, where the HP interception problem is formulated as a target passively chases after the interceptor missile. Secondly, the 3D retro-proportional navigation (RPN) guidance law is reinterpreted from the point of control theory, which forces the corresponding guidance system asymptotically stable. Meanwhile, the concept of nullifying the LOS angular rates is successfully introduced to solve the 3D robust HP guidance problem via the sliding mode control. Thirdly, the LOS angles constrained robust HP guidance law is proposed based on the nonsingular terminal sliding mode control. The stabilities of the presented guidance laws are analyzed via the Lyapunov approach. The simulation results are in agreement with the theoretical statements.

Disturbance and Time Constant Estimation for Compensating Dynamics of Guidance Systems in Intercept Problems

Disturbance and Time Constant Estimation for Compensating Dynamics of Guidance Systems in Intercept Problems

Cooperative Intercepting Guidance Law for Large Maneuvering Target with Impact Angle Constraint

A distributed multi-missile cooperative guidance law based on the finite time theory is proposed to solve the terminal guidance problem of three-dimensional multi-missiles cooperative interception of large maneuvering target. According to the finite time consistency theory, an adaptive guidance law based on the integral sliding mode is designed to ensure that all missiles can reach the target at the same time in the terminal guidance process. The longitudinal and lateral acceleration of the line of sight are based on the guidance law of the fast terminal sliding mode surface. The terminal attack angle is constrained, so that the terminal attack Angle can reach the expected value in finite time. The simulation results show that the designed guidance law can achieve the cooperative attack on the maneuvering targets.

Harbour protection: moving invasion target interception for multi-AUV based on prediction planning interception method

In recent years, harbour security protection has received extensive attention. For the moving invasion target interception problem in the underwater environment with ocean current, a new interception algorithm with multiple autonomous underwater vehicles (multi-AUV) called prediction planning interception (PPI) method is proposed in this paper. First, the interception position is determined quickly and simply through the movement tracking of target, and then the intercept path of each AUV in the environment is planned by the artificial potential field method. When the target is intercepted by any AUV, it is considered a successful interception. The AUV can rapidly intercept the moving target whose trajectory is dynamically changing along relatively short path in the changeable and complicated underwater environment by PPI method. The simulation results show that the interception efficiency of the prediction planning interception method is greatly improved compared with the traditional tracking interception method under different conditions.

Synchronous intercept strategies for a robotic defense-intrusion game with two defenders

We study the defense-intrusion game, in which a single attacker robot tries to reach a stationary target that is protected by two defender robots. We focus on the “synchronous intercept problem”, where both robots have to reach the attacker robot synchronously to intercept it. Assume that the attacker robot has the control policy which is based on attraction to the target and repulsion from the defenders, two kinds of synchronous intercept strategies are proposed for the defense-intrusion game, introduced here as Attacker-oriented and Neutral-position-oriented. Theoretical analysis and simulation results show that: (1) the two strategies are able to generate different synchronous intercept patterns: contact intercept pattern and stable non-contact intercept pattern, respectively. (2) The contact intercept pattern allows the defender robots to intercept the attacker robot in finite time, while the stable non-contact intercept pattern generates a periodic attractor that prevents the attack robot from reaching the target for infinite time. There is potential to apply the insights obtained into defense-intrusion in real systems, including aircraft escort and the defense of military targets or territorial boundaries.

Optimal two-impulse space interception with multiple constraints

We consider optimal two-impulse space interception problems with multiple constraints. The multiple constraints are imposed on the terminal position of a space interceptor, impulse and impact instants, and the component-wise magnitudes of velocity impulses. These optimization problems are formulated as multi-point boundary value problems and solved by the calculus of variations. Slackness variable methods are used to convert all inequality constraints into equality constraints so that the Lagrange multiplier method can be used. A new dynamic slackness variable method is presented. As a result, an indirect optimization method is developed. Subsequently, our method is used to solve the two-impulse space interception problems of free-flight ballistic missiles. A number of conclusions for local optimal solutions have been drawn based on highly accurate numerical solutions. Specifically, by numerical examples, we show that when time and velocity impulse constraints are imposed, optimal two-impulse solutions may occur; if two-impulse instants are free, then a two-impulse space interception problem with velocity impulse constraints may degenerate to a one-impulse case.

An impact angle constraint integral sliding mode guidance law for maneuvering targets interception

An integral sliding mode guidance law (ISMGL) combined with the advantages of the integral sliding mode control (SMC) method is designed to address maneuvering target interception problems with impact angle constraints. The relative motion equation of the missile and the target considering the impact angle constraint is established in the longitudinal plane, and an integral sliding mode surface is constructed. The proposed guidance law resolves the existence of a steady-state error problem in the traditional SMC. Such a guidance law ensures that the missile hits the target with an ideal impact angle in finite time and the missile is kept highly robust throughout the interception process. By adopting the dynamic surface control method, the ISMGL is designed considering the impact angle constraints and the autopilot dynamic characteristics. According to the Lyapunov stability theorem, all states of the closed-loop system are finally proven to be uniformly bounded. Simulation results are compared with the general sliding mode guidance law and the trajectory shaping guidance law, and the findings verify the effectiveness and superiority of the ISMGL.

Compound robust flight time and heading angle constrained guidance law

Abstract This work studies accurate interception problem for salvo-attack missions and proposes a robust guidance law in the presence of impact time and angle constraints. First, the dynamic model for planar homing endgame guidance is built. Different with conventional guidance dynamic model, this work takes the derivative with respect to range, rather than time. Next, the trajectory of desired line-of-sight is formed and a time-to-go prediction method is introduced. On this basis, according to sliding mode methodology, a sliding manifold consisting the knowledge of time-to-go and line-of-sight angle is built and an integrated Lyapunov control method based guidance law is deduced to force this sliding manifold converge to a small region around zero in finite time, so that the missile will intercept target with a desired flight time and a heading angle. Detailed theoretical analysis and numerical simulations verified above properties.

Adaptive Sliding Mode Guidance With Impact Time and Angle Constraints

Based on adaptive sliding mode control method, this paper considers the interception problem to deal with both impact time and angle constraints. The stability and convergence characteristic of proposed guidance law are analyzed. The requirements of the terminal constraints and minimum miss distance can be satisfied. An adaptive law is put forward to adjust the guidance gain. The simulation results indicate that the missile with proposed guidance law can intercept the target successfully with not only desired impact time but also expected impact angle. The interception task can be fulfilled in a satisfactory manner.

Fixed Speed-increment Interception Orbit Calculation Based on QPSO Algorithm

Aiming at the problem of orbit interception under fixed speed increment condition, a method based on quantum-behaved particle swarm optimization (QPSO) algorithm for interception orbit parameters is proposed. This method quickly finds the rendezvous time that can achieve the target interception through the QPSO algorithm based on swarm intelligence, and avoids the problem of large computation and low efficiency caused by the enumeration method. The practical application of the orbit interception problem under an initial condition shows that the method can quickly determine the interception orbit parameters.

Flocking and Target Interception Control for Formations of Nonholonomic Kinematic Agents

In this brief, we present solutions to the flocking and target interception problems of multiple nonholonomic unicycle-type robots using the distance-based framework. The control laws are designed at the kinematic level and are based on the rigidity properties of the graph modeling the sensing/communication interactions among the robots. An input transformation is used to facilitate the control design by converting the nonholonomic model into the single-integrator-like equation. We assume only a subset of the robots knows the desired, time-varying flocking velocity, or the target's motion. The resulting control schemes include distributed, variable structure observers to estimate the unknown signals. Our stability analyses prove convergence to the desired formation while tracking the flocking velocity or the target motion. The results are supported by experiments.

Optimal Midcourse Guidance Algorithm for Exoatmospheric Interception Using Analytical Gradients

This paper is aimed at providing a semianalytical method to solve the optimal exoatmospheric interception problem with the minimum fuel consumption. A nonlinear programming (NLP) problem with the minimum velocity increment, which involves Lambert’s problem with unspecified time-of-flight, is firstly formulated. Then, a set of Karush-Kuhn-Tucker conditions and the Jacobian matrix corresponding to those conditions are derived in an analytical manner, even though the derivatives are mathematically complicated and computationally onerous. Therefore, the Newton-Raphson method can be used to efficiently solve this problem. To further decrease computational cost, a near-optimal initialization method reducing the dimension of the search space is presented to provide a better initial guess. The performance of the proposed method is assessed by numerical experiments and comparison with other methods. The results show that this method is not only of high computational efficiency and accuracy but also applicable to onboard guidance.

Research on Minimum Time Interception Problem with a Tangent Impulse under Relative Motion Models

The minimum time interception problem with a tangent impulse whose direction is the same as the satellite’s velocity direction is studied based on the relative motion equations of elliptical orbits by the combination of analytical, numerical, and optimization methods. Firstly, the feasible domain of the true anomaly of the target under the fixed impulse point is given, and the interception solution is transformed into a univariate function only with respect to the target true anomaly by using the relative motion equation. On the basis of the above, the numerical solution of the function is obtained by the combination of incremental search and the false position method. Secondly, considering the initial drift when the impulse point is freely selected, the genetic algorithm-sequential quadratic programming (GA-SQP) combination optimization method is used to obtain the minimum time interception solution under the tangent impulse in a target motion cycle. Thirdly, under the high-precision orbit prediction (HPOP) model, the Nelder-Mead simplex method is used to optimize the impulse velocity and transfer time to obtain the accurate interception solution. Lastly, the effectiveness of the proposed method is verified by simulation examples.

Adaptive Integral Sliding Mode Guidance Law with Impact Angle Constraint Considering Autopilot Lag

For the interception problem of maneuvering targets, considering impact angle constraint and first-order autopilot lag, an adaptive integral sliding mode guidance law is designed. A new nonsingular finite-time integral sliding mode surface is constructed, which consists of LOS angle, LOS angular rate and LOS angular acceleration, and ensures that the states of the guidance system converge to zero on the sliding mode surface in a finite time. Moreover, an adaptive law is designed to estimate the upper bound of the target’s unknown acceleration. The Lyapunov stability theory proves that the guidance system can converge to zero strictly in a finite time with the proposed guidance law. Finally, the simulation results verify the effectiveness of the designed guidance law.

Intercept problem in dynamic flow field

Intercept problem in dynamic flow field