A design method of differential game guidance law based on Dubins path and neural network

Considering the missile autopilot as second-order dynamics with two zeros, a guidance law is designed using differential game theory. The autopilot dynamics are better to be described as a second-order system with two zeros because of the non-minimum phase property in practical. However, second-order dynamics with two zeros are so complicated that some guidance law design methods are difficult to be applied. The differential game guidance (DGG) law can be designed without the restriction of system equations. In this paper, the pursuer (missile) strategy is derived against the evader (target) strategy that is determined without knowledge about the pursuer autopilot dynamics in the linear-quadratic pursuit-evasion game. The optimal missile strategy improves the performance of the game-theoretic guidance law for homing missiles by taking into account the autopilot dynamics. Simulation results show that the proposed guidance law behaves better than the current guidance law not considering the missile autopilot dynamics.

In contrast, the differential game approach Air-to-air missile guidance laws are derived makes no assumption on future target maneuvers, using optimal control and differential game theory but instead takes into consideration the target's with final miss distance as the optimization cri- maneuver capabilities. The guidance law then terion. A perfect target airframe /autopilot re - guides the missile so as to minimize the potential sponse is assumed, while both perfect and first effects of the target's intelligent use of hie maorder missile responses are considered. With a neuver capabilities. first order missile response the target is always able to force a non zero final miss distance in the differential game formulation. For all other formulaticjns considered there are states from which the missile can force zero terminal miss. In these cases, an auxiliary performance index (e. g., control energy) can be used to specify unique controls. Two simulation scenarios were used to evaluate the guidance laws: one with missile launch near the inner launch boundary and the other near the outer launch boundary. The differential game guidance laws are less sensitive to errors i,: rstimates of current target acceleration than the optimal control laws. The laws based on a perfect missile response performed better for the outer launch boundary scenario, whereas for the inner launch boundary scenario the laws based on a first order missile response achieved srnaller miss distances. The purpose of this paper

To achieve the intelligent interception of different types of maneuvering evaders, based on deep reinforcement learning, a novel intelligent differential game guidance law is proposed in the continuous action domain. Different from traditional guidance laws, the proposed guidance law can avoid tedious manual settings and save cost efforts. First, the interception problem is transformed into the pursuit–evasion game problem, which is solved by zero-sum differential game theory. Next, the Nash equilibrium strategy is obtained through the Markov game process. To implement the proposed intelligent differential game guidance law, an actor–critic neural network based on deep deterministic policy gradient is constructed to calculate the saddle point of the differential game guidance problem. Then, a reward function is designed, which includes the tradeoffs among guidance accuracy, energy consumption, and interception time. Finally, compared with traditional methods, the interception accuracy of the proposed intelligent differential game guidance law is 99.2%, energy consumption is reduced by 47%, and simulation time is shortened by 1.58 s. All results reveal that the proposed intelligent differential game guidance law has better intelligent decision-making ability.

Guidance laws for intercept missiles are derived using zero-sum, perfect-information differential game theory and optimal control theory. The differential game laws are derived using both a linear constant coefficient missile model and a time varying linear model, which uses an open loop profile of the missile speed. The optimal control law is derived only using the variable velocity missile model. A series of six-degree-of-freedom simulations were used to compare missile performance for these three guidance laws. The results show that both differential game laws result in equivalent missile performance. The differential game laws, in turn, perform slightly better than the optimal control law. I. Introduction Intercept missile guidance laws derived using optimal control theory require an assumption on future action by the target in order to generate the optimal control for that specific projected target action. The feedback characteristic of missile guidance laws allows the missile to compensate for incorrect target action assumptions. In contrast, intercept missile guidance laws derived using zero-sum perfect information differential game theory do not require any assumptions on future target actions. Instead the controls are based on the lateral acceleration maneuver capabilities of the target relative to the missile.

For predicting missile’s interception point, the current guidance law based on neural networks avoids to model the strong nonlinear motion of a missile and simultaneously improve the anti-jamming ability of the guidance law. Although the advantages of solving the predicted intercept point problem based on neural networks are obvious, the difficulty in obtaining the target missile information still exists. In this work, we propose a dead-reckoning navigation guidance (DRNG) law. First, a neural network-based collaborative forecast scheme is proposed and utilize the advantages of different neural networks to greatly reduce the difficulty in acquiring the target information. Second, we construct an approximate realistic aerodynamic characteristics environment to simulate the motion parameters of missiles and targets. We also introduce real-time error correction for increasing the prediction accuracy of the network and improve the robustness of the proposed DRNG by using the model self-update algorithm. Finally, through a large number of simulation experiments, results show that the proposed DRNG completes the interception task in a noisy environment, when only the position parameters of a target missile are known. Moreover, it has a more optimized ballistic trajectory as compared with the traditional guidance law.

A new data-driven predictive discrete-time guidance law is presented for an interceptor pursuing a target which can perform arbitrary maneuver. The designed guidance law is driven by observed data of certain steps, which record previous positions of the target and make it feasible to estimate the behavior of the target and hence design the guidance command at each step by solving an time-dependent optimization problem, and this feature distinguishes the proposed guidance law from those traditional guidance laws which are usually described by an ordinary differential equations and use only the measurement at current time instant. To verify the performance of the new guidance law proposed, extensive simulations were carried out to compare it with some typical existing guidance laws like pursuit guidance (PG), beamer rider (BR) guidance, constant bearing (CB) guidance and proportional navigation (PN) law. The simulation studies show that the new predictive guidance law (abbreviated as LP) can provide comparative performance in all the cases studied, and it can even outperform other guidance laws when the target performs random maneuver, which show that the proposed guidance scheme exhibits certain robustness and adaptation.

Guidance laws for attacking defended target

As the maneuverability of targets has been further increased in recent years, it is highly desirable to improve the performance of an interceptor’s guidance law. The ‘‘hit-to-kill’’ scenarios of a kinetic kill vehicle (KKV) require a centimeter-level miss distance, and control of impact angle can considerably increase the KKV’s lethality. Two forms of linear quadratic differential game (LQDG) guidance laws for the KKV are proposed in this paper. The first can achieve only zero terminal miss distance, and the second can achieve a specified impact angle as well as zero terminal miss distance. The LQDG guidance laws are obtained by solving a two-sided linear quadratic optimization problem. In game theory, the adversaries are considered as two independent controlled objects. A major advantage is that the LQDG guidance laws make no assumption of the target’s future maneuver strategy. Simulation results show that the two guidance laws can meet the requirements of the KKV and that the centimeter-level miss distance does not lead to a large guidance command near the terminal time.

Air-to-air missile guidance laws are derived using optimal control and differential game theory with final miss distance as the optimization criterion. A perfect target airframe/autopilot response is assumed, while both perfect and first-order missile responses are considered. With a first-order missile response the target is always able to force a nonzero final miss distance in the differential game formulation. For all other formulations considered there are states from which the missile can force zero terminal miss. In these cases, an auxiliary performance index (e.g., control energy) can be used to specify unique controls. Two simulation scenarios were used to evaluate the guidance laws: one with missile launch near the inner launch boundary and the other near the outer launch boundary. The differential game guidance laws are less sensitive to errors in estimates of current target acceleration than the optimal control laws. The laws based on a perfect missile response performed better for the outer launch boundary scenario; whereas for the inner launch boundary scenario the laws based on a first-order missile response achieved smaller miss distances.

To deal with the task assignment problem of multi-AUV systems under kinematic constraints, which means steering capability constraints for underactuated AUVs or other vehicles likely, an improved task assignment algorithm is proposed combining the Dubins Path algorithm with improved SOM neural network algorithm. At first, the aimed tasks are assigned to the AUVs by the improved SOM neural network method based on workload balance and neighborhood function. When there exists kinematic constraints or obstacles which may cause failure of trajectory planning, task re-assignment will be implemented by changing the weights of SOM neurals, until the AUVs can have paths to reach all the targets. Then, the Dubins paths are generated in several limited cases. The AUV's yaw angle is limited, which results in new assignments to the targets. Computation flow is designed so that the algorithm in MATLAB and Python can realize the path planning to multiple targets. Finally, simulation results prove that the proposed algorithm can effectively accomplish the task assignment task for a multi-AUV system.

Canonical dual solutions to nonconvex radial basis neural network optimization problem

This paper presents a mission planning method for multiple unmanned aircraft vehicles (UAVs) attacking multiple ground targets. The mission planning method includes mission allocation based on ant colony optimization (ACO) and path planning based on improved Dubins path. First, the multiple targets attacking problem is transformed to an optimization problem. Second, to make the method more applicative for real battlefield, several common constraints are considered in the optimization problem. The constraints of mission allocation mainly include the UAVs' executive ability, flight range, targets' threat degree and attack profit, etc. The constraints of path planning mainly include the minimum turning radius and length of path. To meet the goal of optimization of multiple performance indexes, comprehensive performance index is designed. Moreover, the Dubins path is adopted to generate flight paths for every UAV. And some improvement of Dubins path is made to fit the path planning problem. The improved Dubins path is easier to be calculated and shorter than the original Dubins path. Finally, an example of multiple UAVs attacking multiple ground targets is carried out to verify the feasibility of strategies for mission planning. Results of MATLAB simulations indicate that the strategy is feasible to the problems of mission planning.

In this paper, we study the differential game cooperative guidance law for multiple missiles to combat single intelligent targets in future air warfare. First, we derive the differential game guidance law between the single missile and the single target through optimal control theory. On the basis of this, we design the cooperative guidance law using the leader-followers framework, in which the differential game guidance law is applied to the leader. We design the cooperative guidance law of followers by using a kind of second-order nonlinear system. Finally, simulation result are shown to assert the potency of the designed guidance law.KeywordsDifferential gameCooperative guidance lawOptimal control theory

The missile confrontment technology was taken as the background. The mid-course evasive maneuver guidance strategy was studied based on the differential game theory. The ballistic missile used differential game guidance law as the evasive strategy, while the terminal guidance of Exo-atmospheric Kinetic Vehicle (EKV) was the proportional guidance law. Firstly, taking the miss-distance and the energy of both sides as the performance index, the optimal guidance law was deduced with its analytic expression came only with the starting time of maneuvering, the initial position and the velocity of both sides. Then the penetration effect of the ballistic missile is verified through missile confrontment simulation. The results of the simulation show that with the limited acceleration, selecting the properly and timely maneuvering can greatly reduce the interception effect of EKV.

ABSTRACTTrajectory planning of formation rendezvous of multiple unmanned aerial vehicles (UAVs) is formulated as a mixed-integer optimal control problem, and an efficient hierarchical planning approach based on the Dubins path and sequential convex programming is proposed. The proposed method includes the assignment of rendezvous points (high level) and generation of cooperative trajectories (low level). At the high level, the assignment of rendezvous points to UAVs is optimized to minimize the total length of Dubins-path-based approximate trajectories. The assignment results determine the geometric relations between the UAVs’ goals, which are used as equality constraints for generating trajectories. At the low level, trajectory generation is treated as a non-convex optimal control problem, which is transformed to a non-convex parameter optimization and then solved via sequentially performing convex optimization. Numerical experiments demonstrate that the proposed method can generate feasible trajectories and can outperform a typical nonlinear programming method in terms of efficiency.