Orbital Interception Research Articles

Delta-V analysis for impulsive orbital pursuit-evasion based on reachable domain coverage

This paper proposes a delta-V analysis method for the impulsive orbital interception of a non-cooperative maneuvering target from the perspective of reachable domain coverage. In the case of small impulse magnitude and short propagation time, the envelope of the impulsive reachable domain is approximately described by an ellipsoidal equation based on the linearized state transition matrix. Then, the minimum pursuit impulse magnitude under the reachable-domain coverage constraint is obtained by solving a two-dimensional nonlinear equation for given pursuit impulse time and given interception time. Two fuel optimization problems under the reachable-domain coverage constraint are constructed based on whether to optimize the first impulse of the chaser. For the first optimization problem, the optimization variables include the pursuit impulse time, the interception time, and the pursuit impulse magnitude; for the second optimization problem, two additional optimization variables are considered including the time and the aiming point of the first impulse. Numerical examples show that the proposed optimal delta-V approach for the chaser can cover the target's maneuvering reachable domain.

Fast calculation method for mission opportunities in orbital interception and rendezvous problems

This paper proposes a fast calculation method to solve all mission opportunities for orbital interception and orbital rendezvous under the impulse-magnitude constraint. Different from the existing search methods, the proposed method does not need to solve Lambert’s problem in the whole process. Three cases are considered for either departure time or transfer time being free, or both being free. For fixed departure time, the feasible windows of transfer time are obtained by solving a single-variable nonlinear equation only of terminal true anomaly. Similarly, for fixed interception (or rendezvous) time, the feasible windows of departure time are obtained. For free departure time and free transfer time, all mission opportunities are obtained by using a one-dimensional search strategy. The hyperbolic-transfer and the multiple-revolution cases are also analyzed. Numerical results show that the proposed method is superior to the typical pork-chop plot method and the two-dimensional launch window method in computational time.

Orbital Interception Pursuit Strategy for Random Evasion Using Deep Reinforcement Learning

Aiming at the interception problem of noncooperative evader spacecraft adopting random maneuver strategy in one-to-one orbital pursuit–evasion problem, an interception strategy with decision-making training mechanism for the pursuer based on deep reinforcement learning is proposed. Its core purpose is to improve the success rate of interception in the environment with high uncertainty. First of all, a multi-impulse orbit transfer model of pursuer and evader is established, and a modular deep reinforcement learning training method is built. Second, an effective reward mechanism is proposed to train the pursuer to choose the impulse direction and impulse interval of the orbit transfer and to learn the successful interception strategy with the optimal fuel and time. Finally, with the evader taking a random maneuver decision in each episode of training, the trained decision-making strategy is applied to the pursuer, the corresponding interception success rate of which is further analyzed. The results show that the pursuer trained can obtain universal and variable interception strategy. In each round of pursuit–evasion, with random maneuver strategy of the evader, the pursuer can adopt similar optimal decisions to deal with high-dimensional environments and thoroughly random state space, maintaining high interception success rate.

Covariance Analysis of the Optimal Orbital Interception With Navigation Errors

This paper derives the analytical linear covariances for the optimal single-impulse orbital interception problems with navigation errors. The initial position and velocity errors are considered for both the interceptor and the non-maneuvering target. Firstly, for free impulse time and free interception time, the necessary conditions for the minimum-fuel and the minimum-time interceptions are derived, and the optimal solutions are obtained by two-dimensional numerical search methods. Then, the linear covariance method is used to derive the error covariances for the minimum-fuel solution and the minimum-time solution, respectively. Finally, based on the first-order and second-order partial derivatives, the error covariances of the optimal impulse time, the optimal interception time, the required impulse vector and the interception position vector are analytically obtained. Numerical results indicate that the proposed analytical linear covariance method is accurate for both the minimum-fuel and the minimum-time interception problems.

Hybrid Ground-Space Target Visit Problem With a Coplanar Impulse

The hybrid ground–space target visit problem is solved by applying a single coplanar impulse. Considering the linear <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$J_{2}$</tex-math></inline-formula> perturbation, the ground target visit problem is transformed into the ground track adjustment problem, and it is expressed as a time constraint equation. The space target visit problem is viewed as the orbit interception (or flyby) problem, and it is expressed as time and radius constraint equations. Then, based on Gauss’s variational equations, the hybrid ground–space target visit problem is simplified into solving a single-variable equation only of maneuver position. Finally, the exact solution under the high-precision dynamic model is obtained by the differential correction method. Several numerical examples are presented to validate the efficiency of this approach, and the results show that there are a series of discrete solutions to this problem.

Near-optimal interception strategy for orbital pursuit-evasion using deep reinforcement learning

Two participants with competing objectives are considered in one-to-one orbital pursuit-evasion problem, one of which attempts to satisfy some certain terminal conditions with a minimum cost through its own control while the other player attempts to maximize the specified payoff and avoids entering this terminal range. This paper treats the problem of minimax time to a given final distance, within which the interception between pursuer and evader is defined to occur. To achieve the successful interception with an evader that adopts any unknown maneuvers, a near-optimal interception strategy for the orbital pursuit-evasion is presented in this paper. The pursuit-evasion problem is formulated as a differential game first, and a closed-form barrier solution is provided next. A near-optimal guidance law using deep learning is proposed to intercept the evader inside the capture zone. For the games that start outside the barrier, a learning algorithm for the capture zone embedding strategy is presented based on deep reinforcement learning to help the game state cross the barrier surfaces. The simulation cases of intercepting the evaders that adopt different maneuvering strategies are provided, and the results demonstrate the effectiveness and onboard feasibility of the proposed strategy in solving the orbital interception problem.

A guidance method for coplanar orbital interception based on reinforcement learning

This paper investigates the guidance method based on reinforcement learning (RL) for the coplanar orbital interception in a continuous low-thrust scenario. The problem is formulated into a Markov decision process (MDP) model, then a well-designed RL algorithm, experience based deep deterministic policy gradient (EBDDPG), is proposed to solve it. By taking the advantage of prior information generated through the optimal control model, the proposed algorithm not only resolves the convergence problem of the common RL algorithm, but also successfully trains an efficient deep neural network (DNN) controller for the chaser spacecraft to generate the control sequence. Numerical simulation results show that the proposed algorithm is feasible and the trained DNN controller significantly improves the efficiency over traditional optimization methods by roughly two orders of magnitude.

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.

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.

On the possibility of using small asteroids for deflecting near-Earth asteroids

This paper presents the trajectory design and analysis of the near-Earth asteroid (NEA) deflection mission enabled by a kinetic impact of an intermediate asteroid. The sequential transfer trajectory is designed by solving two Lambert’s problems that yield a chain collision between a spacecraft and an intermediate asteroid, followed by a collision between the intermediate asteroid and an NEA. The characteristics of the low-cost trajectories are then identified with respect to the optimal collision point. We show that the feasibility of the mission depends on the existence of an intermediate asteroid with small minimum orbit interception distance (MOID) with the NEA. Moreover the selection strategy of an intermediate asteroid that makes the mission feasible is discussed. We show that several asteroids exist that allow a 10ton spacecraft with limited ΔV to be launched and impact the NEA 99442 Apophis allowing a deflection given several years warning time.

A Method of Determining Multiple-Targets Interception Based on Traversing Points

Space attack-defense confrontation is the commanding height in modern warfare. This paper takes space platform as research object and tries to solve problems such as space non-coplanar, large energy consumption of multiple-targets orbit interception and long interception time. Firstly, a design energy-optimal method of orbit interception based on Traversing Points is proposed. Secondly, the optimal design model of orbital interception is established. Finally, we take space platform interception of three targets in low earth orbit as an example and STK simulations analysis is carried out to verify the effectiveness of the proposed method. The research provides a theoretical basis for analysing non-coplanar and multi-targets interception strategy.

Indirect Optimization for Finite-Thrust Orbital Interception Problem

The nonlinear programming method is used to study the finite-thrust minimum-time orbital interception problem. Considering the spacecraft with fixed impulse, the Modified Equinoctial Elements are used to describe the movement of the spacecraft in the attached coordinate, and the model of the orbital interception problem is established. Then the trajectory optimization problem is solved by the nonlinear programming method. The simulations demonstrate that the minimum time orbital interception mission is well accomplished, and the spacecraft fly around the earth with maximum thrust magnitude at whole time history.

Semi-Analytical Solution for the Optimal Low-Thrust Deflection of Near-Earth Objects

This paper presents a semi-analytical solution of the asteroid deviation problem when a low-thrust action, inversely proportional to the square of the distance from the sun, is applied to the asteroid. The displacement of the asteroid at the minimum orbit interception distance from the Earth's orbit is computed through proximal motion equations as a function of the variation of the orbital elements. A set of semi-analytical formulas is then derived to compute the variation of the elements: Gauss planetary equations are averaged over one orbital revolution to give the secular variation of the elements, and their periodic components are approximated through a trigonometric expansion. Two formulations of the semi-analytical formulas, latitude and time formulation, are presented along with their accuracy against a full numerical integration of Gauss equations. It is shown that the semi-analytical approach provides a significant savings in computational time while maintaining a good accuracy. Finally, some examples of deviation missions are presented as an application of the proposed semi-analytical theory. In particular, the semi-analytical formulas are used in conjunction with a multi-objective optimization algorithm to find the set of Pareto-optimal mission options that minimizes the asteroid warning time and the spacecraft mass while maximizing the orbital deviation.

Head Pursuit Guidance

DOI: 10.2514/1.27737 Aguidancelawforintercepting high-speedtargetsinanovelheadpursuitengagementispresented.Theguidance law imposes a geometric relation in which the interceptor missile is positioned ahead of the target so that both fl yi n the same direction. The missile speed is planned to be lower than that of the target, and therefore the target closes in on the interceptor missile and it is intercepted from its front end. The guidance law also enables enforcing a predeterminedinterceptionanglerelativetothetarget’s flightdirection.Analyticconditionsenablinginterceptionin this novel engagement are provided. The guidance law is implemented using the sliding mode approach, and simulation results confirm its viability in several representative engagements against maneuvering high-speed targets. NTERCEPTION of high-speed targets, such as reentering ballistic missiles, is a formidable challenge. The interception in these scenarios is typically head-on, with a very high closing speed. This imposes severe requirements on the interceptor systems such as precise detection of the target from a large distance by the onboard seekers, and very fast response time of the missile subsystems. To overcome these difficulties, a different approach was suggested in [1],inwhichtheinterceptorvelocityismatchedwiththatofthetarget by a preliminary maneuver. If the target path is predictable, as in the case of ballistic missiles, the maneuver can be designed such that the interceptor missile is positioned ahead of the target on its predicted flight path, flying in the same direction but at a slightly lower speed. This way the target closes in on the interceptor that is conducting the necessary lateral maneuvers to achieve interception. The interceptor speed along the target’s predicted path can be selected to achieve a desired closingrate. Asimilar lowclosingspeedcanbe obtainedina tail-chase scenario. However, tail chase requires that the interceptor will be faster than the target, and therefore more energy is needed during the preliminary maneuver to reach the desired closing speed. Various guidance methods have been examined for implementation in the different stages of high-speed exo- or endo-atmospheric interception scenarios of ballistic missiles. Some of these methods are described next. In [2] a modified version of proportional navigation (PN) guidance law [3] was proposed for implementation in the coast phase. A variable bias was applied to the actual line of sight (LOS) to account for engine burn. The terminal guidance in a hyper-velocity exo-atmospheric orbital interception was studied in [4]. The control energy expenditure is reduced by constraining the expected final state to a function of the estimation error. An optimal guidance algorithm was proposed in [5] for the interception of a nonmaneuvering target decelerated by atmospheric drag. Its implementation requires knowledge on many scenario states, obtained from a nonlinear state estimator. In a recent paper [6] a differential game guidance law was proposed against targets having knownspeedandlateralaccelerationlimitprofiles.Itwasshownthat in a ballistic missile interception scenario such a guidance law provides a significant improvement in the homing accuracy