This paper describes the derivation of a new set of nonlinear, 6{DOF equations of motion of a receiver aircraft undergoing an aerial refueling, including the efiect of timevarying mass and inertia properties associated with the fuel transfer and the tanker’s vortex induced wind efiect. Since the Center of Mass (CM) of the receiver is time{varying during the fuel transfer, the equations are written in a reference frame whose origin is at the CM of the receiver before fuel transfer begins and stays flxed at that position even though the CM is moving during the refueling. Due to the fact that aerial refueling simulation and control deal with the position and orientation of the receiver relative to the tanker, the equations of motion are derived in terms of the translational and rotational position and velocity with respect to the tanker. Further, the derivation of the equations takes into account the momentum transfer into the receiver due to the fuel transfer. The receiver aircraft before fuel transfer is treated as a rigid body made up of ‘n’ particles. The dynamic efiects due to fuel transfer are modeled by considering the mass change to be conflned to a flnite number of lumped masses, which would normally represent the fuel tanks on the receiver aircraft. Once the refueling begins, by using the design parameters such as the shape, size and location of the individual fuel tanks and the rate of fuel ∞owing into each of them, the mass and location of the individual lumped masses are calculated and fed into the equations of motion as exogenous inputs. The new receiver equations of motion are implemented in an integrated simulation environment with a feedback controller for receiver station-keeping as well as the full set of nonlinear, 6{DOF equations of motion of the tanker aircraft and a feedback controller to ∞y the tanker on a U-turn maneuver.

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Derivation of the Dynamics Equations of Receiver Aircraft in Aerial Refueling

This paper examines the application of differential geometry to the engagement of both nonmanoeuvring and manoeuvring targets. The kinematics of the engagement for both manoeuvring and nonmanoeuvring target are developed and expressed in differential geometric terms. Two-dimensional geometry is then used to determine the intercept conditions for a straight line target and a constant manoeuvre target. The intercept conditions for both targets are developed for the case when the interceptor missile guides onto a straight line interception. These two cases are shown to have a common set of core conditions such that it enables a unified guidance law to be developed. The guidance law is shown to be globally stable using Lyapunov theory, so that guidance capture is assured for any initial condition. The analysis and guidance law design does not rely on local linearisation and can be shown to produce guidance trajectories that mirror proportional navigation for the straight line interception of a nonmanoeuvring target for which proportional navigation was originally developed. The paper finishes with simulation in two dimensions, illustrating the convergence and solution properties of the approach.

Direct Intercept Guidance using Differential Geometry Concepts

This paper presents a novel approach to missile guidance using the differential geometry of curves and not relying on the line of sight information. The target’s trajectory is treated as a smooth curve of known curvature and the new algorithm is based on the involute of the target’s curve. The missile’s trajectory uses the concept of virtual target to generate the correct involute trace. It is shown that the missile is either on the trace immediately or may be able to reach it through an alignment procedure. In general, following the trace requires a three-dimensional maneuver in which the missile flies above the target’s tangent plane. The projection of the three-dimensional trajectory onto the tangent plane coincides with the involute trace, but is traversed in the time-to-go, thus resulting in the intercept. Two air-to-air scenarios of point masses are considered for a maneuvering target of the F-16 fighter class: 1) a two-dimensional engagement with target executing a constant g turn; 2) a three-dimensional engagement with target executing a barrel-roll maneuver. Perfect target information is assumed in simulations. In the first case, intercepts occur both for the involute law and proportional-navigation (PN) guidance; PN based intercepts occur quicker, but the involute-based trajectories are more difficult to evade and always result in a side impact. In the second case, PN fails to intercept the target, while the involute law is successful.

Differential Geometric Guidance Based on the Involute of the Target's Trajectory

The paper presents a near-optimal guidance law that has been developed using the direct method of calculus of variations. By the direct access to controlling the shape of the trajectory, this guidance law seeks to maximize the kinetic energy transfer upon interception from a surface launched medium range interceptor missile to a ballistic missile target during the boost phase of flight. Mathematical models of a two-stage liquid-fueled medium-range ballistic missile and a velocity-limited endoatmospheric interceptor missile with onboard active radar guidance are used to demonstrate the guidance law’s performance. This law will utilize the interceptor's onboard computer and active radar sensors to independently predict an intercept point, solve the two-point boundary-value problem, and determine the best feasible flight path to that point. While determining a truly optimal flight path would require significant computing power and therefore cannot be realized online, the proposed nearoptimal flight path can be calculated onboard the interceptor in fractions of a second and updated in multiple times during the intercept without significant technological advancements in the interceptor’s onboard hardware. That near-optimal guidance path is then converted into a set of command functions and fed back into the control system of the interceptor. By modifying just a few parameters affecting the higher-order derivatives at the intercept point, the optimization algorithm varies the shape of a three-dimensional trajectory over a wide range without compromising the constraints on controls or jeopardizing satisfaction of the final conditions. An example features the guidance solution for probably the most difficult scenario of maximizing kinetic energy upon impact by forcing it to occur at a right angle.

Trajectory-Shape-Varying Missile Guidance for Interception of Ballistic Missiles during the Boost Phase

The /spl kappa/-guidance dynamical equations, which are nonlinear and vary with respect to the independent parameter, range, are linearized and then the LQR method is used to solve the optimal control problem. The linearization is via a nonlinear coordinate transformation and nonlinear feedback. The cost function is approximated by a quadratic cost.

Linearized kappa guidance

The State of Dynamical Input)Output Systems as an Operator

In this paper, an intelligent autonomous deck landing system is designed for an Unmanned Air Vehicle (UAV) First, the design specifications and requirements are identified for the design of UAV flight control and landing systems Then the longitudinal models of the UAV are established for the design of an autonomous UAV landing system The system is designed using fuzzy logic, which is able to provide longitudinal stability and to improve the tracking performance Simulation results show that the developed landing control system has very good robustness against aerodynamic uncertainty, and good fault tolerance against actuator failures This indicates that the intelligent landing system has the ability to stabilize a damaged aircraft without knowledge of the types of fault or system parameters Wind disturbances are also investigated by using the turbulence model for the ship-landing environment The simulation results show that the designed landing system is robust against the wind disturbances Landing of a UAV on the deck of a ship is conducted Various automatic landing scenarios are simulated These scenarios consider the ship motion induced by environmental disturbances, the impact of the wind disturbances on the UAV, and aero variations Simulation results show that the designed intelligent automatic ship landing control system can land the UAV on the deck of an ocean-going ship automatically, accurately and safely The system is very robust against massive disturbances and uncertainties (ship heave motion, wind disturbances, and aero variations)

Demetrios Serakos

Papers

Linearized kappa guidance

Linearized kappa guidance

The State of Dynamical Input)Output Systems as an Operator

Autonomous Integrated Air Vehicle Control