Yiyuan Zhao

Trajectory Synthesis for Air Traffic Automation

Trajectory synthesis algorithms that are key to the center ‐terminal radar approach control automation system (CTAS) developed at NASA Ames Research Center for air trafe c control automation are discussed. CTAS generates computer advisories based on synthesized trajectories that help controllers to produce a safe, efe cient, and expeditious e ow of trafe c over the extended terminal area. Trajectories are synthesized from initial aircraft positionsto ametering e x orrunway, depending on airspace.Thehorizontal pathisconstructed e rstfrom specie ed waypoints using straight lines and constant-radius turns. The vertical trajectory is divided into a series of e ight segments. Three types of e ight proe les are dee ned by connecting selected segments in a predetermined order: fast, nominal, and slow. Each proe lecan produce a certain rangeof arrivaltimes. A second-order Runge ‐Kutta scheme is used for integrating a set of simplie ed point-mass equations to generate vertical trajectories. Then, an iterative scheme is employed to determine the speed that meets a specie ed arrival time. Several special case trajectories are also explained. Two e ight scenarios are used to illustrate the use of trajectory synthesis algorithms.

SENSITIVITY OF TRAJECTORY PREDICTION IN AIR TRAFFIC MANAGEMENT

Trajectory prediction in air trafe c management computes the most likely or the most desirable aircraft trajectories by using models of aircraft performance and atmospheric conditions, as well as measurements of aircraft states. In comparison, actual trajectories are obtained using feedback control from a pilot or autopilot to track e ight objectives, while theaircrafte iesthrough an actual atmosphere. This paperintroduces the concept ofclosedloop sensitivities, which are dee ned as differences between actual and computed trajectories per unit of modeling errors, in thepresenceof pilot/autopilotfeedback controls.Modeling errorsareexpressed asuncertain parameters and/or uncertain functions. Pilot/autopilot control actions are approximated by nonlinear feedback control laws, designedwith themethod of feedback linearization. Both theaircraft equations of motion and the feedbackcontrol laws are linearized around computed reference trajectories, and these linearized equations are used to determine expressions for closed-loop terminal sensitivities. The proposed method is applied to the Center/Terminal Radar Approach Control (TRACON) Automation System as well as e ight management systems.

Trajectory Planning for Autonomous Aerospace Vehicles amid Known Obstacles and Conflicts

A discrete search strategy is presented for potential real-time generations of four-dimensional trajectories for a single autonomous aerospace vehicle amid known obstacles and conflicts. A model of autonomous operation isfirst developed. The problem of and requirements on real-time trajectory generations for autonomous aerospace vehicles are discussed. After an overview of various potential solution frameworks, a discrete search strategy is developed. In this strategy, a four-dimensional search space is defined and discretized. Potential obstacles and conflicts are represented by several basic geometric shapes and their combinations. Mathematical conditions are developed for a trajectory segment to be outside of an obstacle or conflict. Then, the A* search technique is used to obtain trajectory solutions, in which successor points are selected that avoid obstacles and conflicts and that satisfy dynamic motion constraints of the vehicle. A linear combination of flight distance and flight time is optimized in the trajectory generation process. A heuristic function that approximates this performance index is developed for the A * search procedure. Examples are provided that illustrate the application of the proposed method.

Deterministic resolution of two aircraft conflict in free flight

This paper studies strategies for resolving two aircraft conflicts in a free flight environment for air traffic management. In a free flight environment, pilots of individual aircraft can change flight paths in real time. As a result, resolving conflicts among aircraft becomes a key priority for controllers. In this paper, a pointmass level flight aircraft model is used. Resolution of a two-aircraft conflict is formulated as deterministic nonlinear optimal control problems. Performance indices are selected to minimize deviations of both aircraft from their originally-intended flight paths or to minimize banking angles, subject to a minimum separation requirement. In addition, terminal constraints are included that force each aircraft to return to its original path after conflict avoidance maneuvers. In an unrestricted region, it is assumed that aircraft are originally flying with a constant heading. In general, the two aircraft would turn the same way (left or right) by roughly the same amount to avoid a conflict. When the intersecting angle is small, however, one aircraft needs to take a path stretching to avoid the other aircraft. In the terminal region where aircraft converge to the same gate, one aircraft needs to stretch its flight paths to avoid the other aircraft. If the two aircraft have the same speed, either aircraft can perform the path stretching. If the two aircraft have different speeds, the slower aircraft should perform the path stretching.

Control of an aircraft in downbursts

Guidance schemes are designed to approximate the optimal survival and optimal performance paths through downbursts, which were determined in the previous paper. Specifically, climb-rate command following is used to achieve performance, and altitude command following is used to enhance survivability. Nonlinear simulations are conducted to investigate the effects of the climb-rate command and altitude command. Takeoff flight is considered and full thrust is assumed. In a mild to moderate downburst, an aircraft can follow a constant, smaller-than-nominal climb rate without stall. Better survival capability is achieved by climbing at a lower rate accompanied by lower altitude, and vice versa. In a severe downbursts, the aircraft must descend to avoid stall. The farther it descends, the higher the survival capability, but the poorer the performance. If the downburst is very severe, the best strategy is to descend immediately to the lowest safe altitude. Since the intensity of a downbursts is hard to evaluate prior to penetration, it is advisable to keep a high airspeed. Therefore, use of the survival strategy is recommended that employs maximum thrust and allows the aircraft to descend to a safe minimum altitude immediately upon entering a downburst on takeoff.

Connectivity of Ad Hoc Networks for Advanced Air Traffic Management

This paper presents the concept and studies connectivities of wireless ad hoc networks among aircraft for enhanced situational awareness. Under this multi-hop broadcast concept, an aircraft would periodically broadcast not only its own state information, but also relay state information received from neighboring aircraft. In this paper, a basic architecture of such an airborne ad hoc network is established. The relationship between network connectivity and information reachability, which accounts for information latency and depends on transmission protocols, is discussed. Two general performance criteria are introduced that measure the connectivity performance of an airborne network subject to a specified maximum number of hops in the network. The first metric is the ratio of the total coverage area of a network cluster over that of a single aircraft. The second metric is the number of aircraft each individual aircraft can connect to within the network cluster. Three representative types of traffic scenarios are considered: a one-dimensional flight stream, two streams merging into one, and randomly distributed traffic over a horizontal region. In all cases, aircraft positions are checked against their conflict-free requirements. For the onedimensional traffic and merging traffic scenarios, the best, the worst, and the average values of the connectivity performance criteria are obtained via numerical simulations. For the two-dimensional random traffic scenario, random simulations are repeated, and both average connectivity performances and their standard deviations are calculated. Simulation results indicate that the connectivity of the proposed airborne ad hoc network is always better than that of the non-relay scheme. Overall, the proposed concept offers great flexibilities through the use of different transmission protocols and maximizes the benefits of a given digital data link.

Optimal vertical takeoff and landing helicopter operation in one engine failure

This article presents optimal vertical takeoff and landing (VTOL) trajectories of a multiengine helicopter in the event of a single engine failure. A point-mass model of the UH-60A helicopter is used. Time derivatives of thrust coefficients are treated as control variables. A first-order response dynamics is assumed for the contingency power available after an engine failure. Ground effect is included in the study of landing trajectories. A linear backup procedure is assumed for normal takeoff and a straight-in procedure for normal landing. Nonlinear optimal control problems are formulated for flights of rejected takeoff, continued takeoff, continued landing, and balked landing after one engine failure. Constraints on rotor speed and thrust vector are included. In rejected takeoff and continued landing, the cost functional minimizes the distance between the touchdown point and the original takeoff point, subject to impact speed limits at touchdown. In continued takeoff and balked landing, two cost functionals are used subject to specified final speed components required for a steady climb. One minimizes the horizontal distance required to achieve the steady climb, whereas the other maximizes the minimum altitude during the transitional flight from engine failure to the steady climb. Extensive numerical solutions are obtained. In all optimal trajectories, the helicopter adjusts its power requirement to accommodate the contingency power available. The helicopter gross weight capability hi VTOL operation is limited by safe rejected takeoff or continued landing. A concept of balanced-weight takeoff and landing decision point is proposed from which the maximum gross weight hi emergency landing and in flying-out maneuver is the same.

Extracting Energy from Downdraft to Enhance Endurance of Uninhabited Aerial Vehicles

The ability of uninhabited aerial vehicles to perform drastic maneuvers enables them to benefit from wind profiles that may be unfavorable to inhabited aircraft. This paper examines optimal uninhabited aerial vehicle flights that can extract energy from downdrafts for enhancing endurance. Uninhabited aerial vehicle motions are described by a point-mass dynamic model. A downdraft wind field is modeled by a pair of three-dimensional vortex rings placed symmetrically with respect to the ground. Fundamental dimensionless parameters that affect uninhabited aerial vehicle behaviors in a downdraft are identified through the normalization of the equations and wind expressions. Uninhabited aerial vehicle flight through a downdraft is formulated as a nonlinear optimal control problem that minimizes the average thrust or power per unit time. Vehicle performance and operational limits are enforced through boundary conditions and path constraints. These optimal control problems are converted into parameter optimization problems with a collocation method and solved numerically using the sparse parameter optimization software SNOPT. Numerical solutions systematically obtained for a range of dimensionless parameters reveal four basic patterns of optimal uninhabited aerial vehicle flights through a downdraft in the vertical plane. Results demonstrate that traditional definitions of favorable winds may need to be revised for uninhabited aerial vehicles.

Optimal Short Takeoff of Tiltrotor Aircraft in One Engine Failure

Optimal tiltrotor flight paths in the event of a single engine failure during short takeoff operations are investigated. A vertical plane rigid-body model is used that has as state variables aircraft position, body components of aircraft velocity, pitch angle and rate, and rotor angular speed. The control variables are the thrust coefficient of one rotor, the pilots longitudinal stick displacement, and the nacelle angle. The model uses both parameters and aerodynamic data of the XV-15 research aircraft. The tabular aerodynamic data are interpolated with smooth functions. Tiltrotor flights after engine failure are formulated as nonlinear optimal control problems. Both continued takeoff and rejected takeoff flight after an engine failure are studied. Performance indices are selected to minimize runway length, subject to various constraints from safety considerations and tiltrotor performance limitations. These optimal control problems are parameterized via collocation into parameter optimizations for numerical solutions. Extensive numerical solutions are obtained, and sensitivity analyses are conducted to examine effects of model uncertainties

Capture Conditions for Merging Trajectory Segments to Model Realistic Aircraft Descents

A typical commercial aircraft trajectory consists of a series of flight segments. An aircraft switches from one segment to another when certain specified variables reach their desired values. Trajectory synthesis for air traffic control automation must be consistent with practical pilot procedures. We examine capture conditions for merging trajectory segments to model commercial aircraft descent in trajectory synthesis. These conditions translate into bounds on measurements of atmospheric wind, pressure, and temperature. They also define ranges of thrust and drag feasible for a descent trajectory. Capture conditions are derived for the Center-TRACON Automation System developed at NASA Ames Research Center for automated air traffic control. Various uses of capture conditions are discussed. A Boeing 727-200 aircraft is used to provide numerical examples of capture conditions.