Atilla Dogan

Modeling of Aerodynamic Coupling Between Aircraft in Close Proximity

A method is developed for modeling the aerodynamic coupling between aircraft Hying in close proximity. Velocities induced on a trailing aircraft by vortices from an aircraft upstream are written as a function of the relative separation and relative orientation between the two aircraft. The nonuniform vortex-induced wind and wind gradients acting on the trail aircraft are approximated as effective uniform wind and wind gradients. In a dynamic simulation, the effective wind can be used directly in the equations of motion, whereas the wind gradient can be used in the standard buildup equations for the aerodynamic moments. This removes necessity to explicitly compute the induced forces and moments. Various vortex models for estimating induced velocities and averaging schemes for computing effective wind components and gradients are assessed

Derivation of the dynamics equations of receiver aircraft in aerial refueling

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.

Flight Control and Simulation for Aerial Refueling

This paper addresses the problem of controlling the receiver aircraft to achieve a successful aerial refueling. For the performance veriflcation of the controller, a new set of nonlinear, 6-DOF, rigid body equations of motion for the receiver aircraft has been derived. The equations are developed using the reference frame as one that is attached to, translates and rotates with the tanker aircraft. Furthermore, the nonlinear equations contain the wind efiect terms and their time derivatives to represent the aerodynamic coupling involved between the two aircraft. These wind terms are obtained using an averaging technique that computes the efiective induced wind components and wind gradients in the receiver aircraft’s body frame. Dynamics of the engine and the actuators are also included in the study. A linear position-tracking controller has been designed using a combination of integral control and optimal LQR design. The controller does not use the information of the tanker’s vortex induced wind efiects acting on the receiver aircraft as well as the mass change that occurs during refueling. The performance of the controller is evaluated in the high fldelity simulation environment employing the new sets of equations of motion. The simulation and control design are applied to a tailless flghter aircraft with innovative control efiectors and thrust vectoring capability. Various allocation schemes for redundant control variables are analyzed in a realistic approach maneuver to the refueling contact position behind the tanker aircraft. In this paper, the performance evaluation is presented only during the initial phase of aerial refueling maneuver when the receiver aircraft maneuvers to reach the refueling contact position.

Nonlinear Control for Reconfiguration of Unmanned-Aerial-Vehicle Formation

The design of a nonlinear controller to reconfigure a formation of a group of unmanned aerial vehicles (UAVs) is described. Reconfiguration of the formation might be needed to maintain the efficiency of the formation. Nonlinear six-degree-of-freedom, rigid-body, equations of motion developed in the virtual leader (VL)’s frame are used to model the UAVs in the formation. The formulation of the formation flight in VL frame enables the formationkeeping and formation reconfiguration to be treated in the same framework. The nonlinear equations of motion contain the wind effect terms and their time derivatives to represent the aerodynamic coupling involved in close formation flight. These wind terms are obtained by using an averaging technique that computes the effective induced wind components and wind gradients in the UAV’s body frame. Dynamics of the engine and the actuators are also included in the study. An algorithm that generates a safe and feasible trajectory, given the current position and the position to go to, has been developed. A combination of integral control, optimal LQR design, and nonlinear state feedback linearization is used in the design of the position-tracking controller. Simulation results demonstrate that the controller is capable of producing a smooth reconfiguration without using the information of the vortex-induced wind effects on the follower UAV.

Control and Simulation of Relative Motion for Aerial Refueling in Racetrack Maneuvers

T HIS paper focuses on the development of an integrated simulation environment and control algorithms for a receiver aircraft in boom–receptacle refueling (BRR) operation while the tanker flies in a racetrack maneuver. A racetrack maneuver is the standard pattern flown by tanker aircraft, with straight legs and bank turns [1]. This paper applies the earlier work by the authors on mathematical modeling of relative motion [2,3] and aerodynamic coupling [4] to the simulation of aerial refueling, and it develops control laws for the motion of the receiver relative to the tanker that flies in racetrack maneuvers. An integrated simulation environment is developed to take into account tanker maneuvers, motion of the receiver relative to the tanker, and the aerodynamic coupling due to the trailingwake vortex of the tanker. The separate dynamicmodel of the tanker, including its own controller, allows the simulation of the standard racetrack maneuvers of the tanker in aerial refueling operations. The mathematical model of the receiver expressed in terms of the relative position and orientation with respect to the tanker’s body frame facilitates the formulation, in a single framework, of maneuver and stationkeeping of the receiver behind the tanker. For the racetrack maneuvers of the tanker, a linear quadratic regulator (LQR)-based multi-input/multi-output (MIMO) state feedback and integral control technique is developed to track commanded speed, altitude, and yaw rate. Similarly, for the relative motion of the receiver, an LQR-based MIMO state feedback and integral control technique is designed to track the commanded trajectory expressed in the body frame of the tanker. Both controllers schedule their corresponding feedback and integral gains based on the commanded speed and yaw rate of the tanker. The tanker aircraft model represents KC-135R, and the receiver aircraft model is a tailless fighter aircraft with innovative control effectors (ICE) and thrust-vectoring capability. Because the receiver has redundant control variables, various control allocation schemes are investigated for trajectory tracking and stationkeeping while the tanker flies in various racetrack maneuvers with different commanded turn rates.

Unmanned aerial vehicle dynamic-target pursuit by using probabilistic threat exposure map

A strategy is presented for an unmanned aerial vehicle (UAV) to follow a moving target in an area the probabilistic threat exposure map of which is assumed to be known based on a priori data. A probabilistic threat exposure map is defined to be the risk of exposure to multiple sources of threat as a function of position. The strategy generates speed and heading angle commands within the dynamic constraints of the UAV. There are three main objectives in order of priority: 1) All of the restricted areas are avoided. 2) The UAV stays within the proximity of the target by a prespecified distance. 3) The total threat exposure level is minimized. During the pursuit, the heading and speed of the target and their time variations are not directly measured but are estimated from the measurements of the target positions. If, for any reason, the sensor can no longer measure the current position of the target, the strategy starts using the predicted target states based on the past measurements to guide the UAV toward the proximity of the target until the UAV detects the target again. I. Introduction I N this paper, a target following strategy is introduced for an unmanned aerial vehicle (UAV) flying through an area of multiple sources of threat that are modeled as a probabilistic threat exposure map (PTEM). The PTEM is a map that indicates the threat level of an area due to different types of static threat sources using probability density functions. Recently, there has been an increasing interest in probabilistic approaches in mission planning for the UAVs. This is because the probabilistic approaches are inherently very suitable to handle the uncertainty in the information, such as the locations of the threats. There are several papers in the literature using various probabilistic approaches to deal with the path-planning problem of the UAV applications based on the probabilistic map of the area of operation. 1,2 In Refs. 1 and 2, various path-planning strategies are proposed to minimize the level of threat exposure while flying to a stationary target through an area of multiple threats. This risk of exposure to a source of threat is a function of position, defined to be the probability of becoming disabled by the source of threat at a given position. The probability is assumed to have a Gaussian distribution over the area of operation. The probabilistic threat exposure map is constructed from the probability distribution functions of all of the sources of threat in the area. In Ref. 3, a graph-based probabilistic approach is developed to use the probabilistic map of the area. Unlike the Voronoi graph-based approaches, the nodes and links of the graph are based directly on the probabilistic map. The region of operation is divided into cells whose occupancy value is determined based on the sensor readings. By the application of the conditional probability of occupancy using Bayes rule and the Bellman‐Ford algorithm, the shortest path is found. Because the path-planning strategies rely on probabilistic maps, the construction and online update of the maps are very crucial. In Ref. 4, a probabilistic map of an area with multiple distinguishable moving obstacles is built by using Bayesian estimation, and

Modeling of bow wave effect in aerial refueling

This paper develops a simple method of modeling the bow wave e ect in aerial refueling. Inviscid ow modeling around solid bodies based on the stream function de ned with various types of singularities are used. The ow eld induced by the presence of aircraft bodies is superimposed on the ow eld generated by horseshoe vortices. The induced total nonuniform ow eld is approximated by e ective uniform translational and rotational ow velocity components. The approximations are used in build-up equations for lift, drag and pitching moment coe cients of both tanker and receiver aircraft. The variations of the aerodynamic coe cients are calculated as the receiver aircraft position is varied (i) longitudinally from two and a half wing spans behind the contact position to half a wing span ahead of the contact position, and (ii) laterally from about one wing span left of the contact position to one wing span right. Comparisons with CFD results show that the vortex-based approaches alone are inadequate for modeling the bow wave e ects. The combination of the vortex-induced and the volume induced ow eld as implemented in this research results in much better agreement with the CFD results.

Probabilistic trajectory planning for UAVs in dynamic environments

In this paper, we will introduce a probabilistic solution to the problem of trajectory planning for a UAV ying in a dynamic environment. By dynamic environment we mean that the probabilistic map is time-variant i.e the probability of becoming disabled at a given location might be changing over time. Probabilistic map is dened as the risk exposure to the sources of threat as a function of time and position. This might be the case when the likelihood of threat sources and/or obstacles changing their position is a priori known. The objective in the trajectory planning is to arrive at a given target position while maximizing the safety of the UAV in a feasible trajectory. By feasible we mean that the turning rate constraints and velocity constraints of the UAV are not violated along the trajectory. A locally minimizing strategy will be used in single as well as multiple-target implementations. The strategy uses the local information of the probabilistic map and the information about the location of the target. It is parameterized to change the weighting on nding a shorter path or nding a path with smaller probability of getting disabled. Since the probabilistic map is changing with time, the probability of getting disabled at a given location will be constantly changing. Thus, the paths generated by the strategy will be functions of time as well as position. This will tell the UAV not only what path to follow but also how to adjust its speed on the path while satisfying the given velocity constraints.

Escaping Microburst with Turbulence: Altitude, Dive, and Pitch Guidance Strategies

Three escape strategies are compared for microburst encounters during e nal landing approach: altitude guidance, dive guidance, and pitch guidance. The main difference between pitch guidance and the other two strategies is that pitch guidance immediately attempts to increase altitude at the expense of airspeed, whereas dive and altitude guidances initially trade altitude for airspeed. We use a full, six-degree-of-freedom, nonlinear, rigid-body aircraft model, including the effects of windshear and wind vorticity, and a model of microburst with turbulence. We also model the effect of stall prevention on the escape path. Two different approaches are used for comparison: 1) In a sample analysis approach, typical samples of the time histories of various variables are analyzed. 2 ) In a statistical approach, the probability distribution of the minimum altitude is estimated by the Monte Carlo method when the statistical properties of the microburst parameters are known. In the sample analysis and statistical approaches, the simulations take into account turbulence in addition to windshear. Both approaches suggest that, within the modeling assumptions presented, and in the absence of human factors, altitude and dive guidance with low commanded altitude may provide better safety than pitch guidance.

DYNAMIC TARGET PURSUIT BY UAVs IN PROBABILISTIC THREAT EXPOSURE MAP

In this paper, we present a strategy to follow a moving target in an area whose probabilistic threat exposure map is assumed to be known based on a priori data. Probabilistic threat exposure map is dened to be the risk of exposure to multiple sources of threat as a function of position. During the pursuit, the heading and speed of the target and their time variations are not directly measured but estimated from the measurements of the target positions. In order for the commanded trajectory generated by the strategy to be realizable by the pursuer UAV, turning rate constraints and velocity constraints of the UAV are also taken into consideration. The UAV is considered to be following the target if its distance to the target remains smaller than a prespecied length during the