Vitaly Shaferman

Linear Quadratic Guidance Laws for Imposing a Terminal Intercept Angle

Linear quadratic guidance laws that explicitly enable imposing a predetermined intercept angle are presented. Two such guidance laws are derived, using optimal control and differential game theories, for arbitrary-order linear missile dynamics. The obtained guidance laws are dependent on the well-known zero-effort miss distance and on a new variable denoted zero-effort angle. It is shown that imposing the terminal angle constraint raises considerably the gains of the guidance laws. Theoretic conditions for the existence of a saddle-point solution in the differential game are also derived. These conditions show that imposing the terminal angle constraint requires a higher maneuverability advantage from the missile. The performance of the proposed guidance laws is investigated using a nonlinear two-dimensional simulation of the missiles lateral dynamics and relative kinematics, while assuming first-order dynamics for the targets evasive maneuvers. Using a Monte Carlo study, it is shown that, for the investigated problem, a target can be intercepted with a negligible miss distance and intercept angle error even when the target maneuvers and there are large initial heading errors.

Cooperative Multiple-Model Adaptive Guidance for an Aircraft Defending Missile

A cooperative guidance law, for a defender missile protecting an aerial target from an incoming homing missile, is presented. The filter used is a nonlinear adaptation of a multiple model adaptive estimator, in which each model represents a possible guidance law and guidance parameters of the incoming homing missile. Fusion of measurements from both the defender missile and protected aircraft is performed. A matched defender’s missile guidance law is optimized to the identified homing missile guidance law. It utilizes cooperation between the aerial target and the defender missile. The cooperation stems from the fact that the defender knows the future evasive maneuvers to be performed by the protected target and thus can anticipate the maneuvers it will induce on the incoming homing missile. Moreover, the target performs a maneuver that minimizes the control effort requirements from the defender. The estimator and guidance law are combined in a multiple model adaptive control configuration. Simulation results show that combining the estimations with the proposed optimal guidance law, that utilizes cooperation between the defending missile and protected target, yields hit-to-kill closed loop performance with very low control effort. This facilitates the use of relatively small defending missiles to protect aircrafts from homing missiles.

Cooperative Optimal Guidance Laws for Imposing a Relative Intercept Angle

Optimal control-based cooperative guidance laws, which enforce at intercept a relative geometry in between a group of missiles and a single maneuvering target, are presented. An example scenario of interest is that of intercepting a high-value target (such as a ballistic missile) by a team of cooperating interceptors arriving from different directions. The problem is posed in the linear quadratic framework, and closed-form analytic solutions are obtained for any team size with any linear missile dynamics. The performance of the cooperative guidance laws is investigated using a nonlinear two-dimensional simulation of the missiles’ lateral dynamics and relative kinematics. It is shown that cooperatively imposing a relative intercept angle between the missiles provides substantially better results than when each missile independently enforces, using a one-on-one strategy, a preselected intercept angle that satisfies the relative intercept requirement. It is also shown that the missiles’ acceleration requirem...

Cooperative Interception in a Multi-Missile Engagement

Two estimators are presented, that enable cooperative target tracking of several missiles intercepting a single maneuvering target. The flrst estimator is a nonlinear adaptation of an interacting multiple model fllter, whereas the second estimator is a multiple model particle fllter. The paper develops the fllters for the cooperative and non-cooperative estimation modes, and investigates their individual estimation performance, using a nonlinear two-dimensional simulation. An extensive Monte Carlo study is used to demonstrate the viability of the cooperative estimation concept, for both estimators. It is shown that the closed loop interception performance of two cooperating missiles, guided by an optimal guidance law, improves, when compared to that of non-cooperating missiles. The particle fllter based estimator demonstrates hit-to-kill closed loop interception performance in the cooperative mode, but requires higher computational load than the extended Kalman fllter based estimator, making the choice of estimator a tradeofi between performance and computational power.

Stochastic Cooperative Interception Using Information Sharing Based on Engagement Staggering

A novel cooperative tracking and interception strategy, which exploits information sharing and missile staggering, is presented. The key idea underlying the approach is to exploit the superior information collected by the leading missile to improve the interception performance of the trailing missiles. For tracking a maneuvering target, the paper derives a nonlinear adaptation of an interacting multiple model filter in cooperative and noncooperative estimation modes. The optimal staggering between the missiles is derived based on a linear model and a deterministic approximation of the stochastic estimation process. An extensive Monte Carlo study, in a nonlinear two-dimensional simulation of a ballistic missile defense scenario, is used to demonstrate the viability of the proposed strategy. It is shown that, for a two-on-one interception engagement, the trailing missile’s estimation performance, in the information-sharing mode, substantially improves, when compared to that of noncooperating missiles. Combi...

Cooperative UAV Tracking Under Urban Occlusions and Airspace Limitations

A centralized approach for multi UAV cooperative motion planning, for tracking a predictable ground moving target in urban environments with airspace limitations, using gimballed or body flxed sensors, is presented. Automating this task is motivated by the expected reduction in operators’ workload and performance improvement. To ensure ∞yable trajectories, adequate performance, and safety, the UAVs’ dynamics, occlusions and airspace constrains must all be incorporated into the problem’s formulation. The solution strategy involves determining visibility, sensor coverage, and restricted regions in the calculated horizon using either a priori or operator provided information on the urban terrain and target trajectory. The tracking task is then casted as a centralized optimization motion planning problem, in which the cost function is associated with the UAVs’ positions relative to the visibility and restricted regions, and the target’s position relative to the sensor coverage region. A computationally parsimonious stochastic search method (genetic algorithm) is proposed for solving the resulting optimization problem. The algorithm was implemented in a high fldelity simulation test-bed using a visual database of an actual city. The viability of using the algorithm is shown using a Monte Carlo study.

Co-Evolution Genetic Algorithm for UAV Distributed Tracking in Urban Environments

A distributed approach is proposed for planning a cooperative tracking task for a team of unmanned aerial vehicles (UAVs). In the scenario of interest UAVs are required to autonomously track, using their onboard sensors, a moving target in a known urban environment. The solution methodology involves finding visibility regions, from which a UAV can maintain a line of sight to the target during the scenario; and restricted regions, in which a UAV can not fly, due to the presence of buildings or other airspace limitations. A co-evolution genetic algorithm is derived for searching, in realtime, monotonically improving solutions. In the proposed distributed search method every UAV iteratively manipulates its own population of chromosomes, each encoding its control inputs in the calculated horizon. Team performance is attained by assigning fitness to each solution in the population based on the cooperative performance when using it together with preceding iteration tracking information obtained from teammates. Important attributes of the proposed solution approach are its scalability and robustness; and consequently it can be applied to large sized problems and adapt to the loss of UAV team members. The distributed nature of the algorithm also reduces the computation and communication loads. The performance of the algorithm is studied using a high fidelity simulation test-bed incorporating a visual database of the city of Tel-Aviv, Israel.© 2008 ASME

Cooperative Differential Games Guidance Laws for Imposing a Relative Intercept Angle

A cooperative guidance law for a team of interceptors trying to intercept, from multiple directions, an evading target is proposed. An example scenario of interest is that of intercepting an aerial target, such as a ballistic missile, from multiple directions. The engagement is analyzed in the framework of a linear quadratic zero-sum two-person differential game, where the team of interceptors constitutes one of the adversaries and the target the other. An arbitrary number of interceptors, each having linear dynamics, is considered. The obtained guidance law for the team of interceptors enables enforcement of a relative geometry in between the group of missiles and the target. Such an approach is superior (in the sense of the required control effort) to that where each interceptor independently enforces, using a one-on-one strategy, a preselected intercept angle that satisfies the relative intercept requirement. A nonlinear two-dimensional simulation is used to investigate the performance of the obtained ...