Modeling relationships using graph state variables
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position trajectory time↗
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Modeling relationships using graph state variables
This paper shows example GSV representations for spacecraft orientation, location, trajectories, dynamics, and kinematics.
graph MDS relationships dependency topology state ↗
Trajectory Specification Language for Air Traffic Control
Trajectory Specification is a method of specifying aircraft trajectories with tolerances such that the position at any instant in time is constrained to a precisely defined bounding space. The bounding space at any instant in time is defined by tolerances relative to a reference trajectory that specifies position as a function of time. The tolerances are dynamic and are based on the aircraft navigation capabilities and the traffic situation. This paper proposes a standard Trajectory Specification Language (TSL) based on the Extensible Markup Language (XML) to represent these specifications and to communicate them by datalink. The language can be used to downlink trajectory requests from air to ground and to uplink trajectory assignments from ground to air. The XML format can be converted to binary for operational use, if necessary, using Efficient XML Interchange (EXI) or Abstract Syntax Notation (ASN.1).
XM↗
Trajectory Specification Applied to Terminal Airspace
Despite major efforts to automate air traffic control (ATC), it is still performed by humans today. The complexity and safety-criticality of ATC makes it very difficult to safely automate, but it must be automated to increase airspace capacity (the density of traffic that can be safely managed) and airport throughput (the number of arrivals and departures that an airport can safely handle in a given period of time) beyond what is possible with human controllers. This paper presents the Trajectory Specification (TS) concept, which can help to safely automate ATC. TS is a method of specifying aircraft trajectories such that the position at any given time in flight is restricted to a precisely defined bounding space, removing all ambiguity as to where the flight is allowed to be. The bounding space or volume is determined by tolerances relative to a reference trajectory (position as a function of time). The tolerances are dynamic and are based on the aircraft navigation capabilities and the traffic situation. The tolerances can be a piecewise linear function of time or distance along the route, allowing the tolerances to vary as needed, typically increasing with time for departures and decreasing for arrivals. A Trajectory Specification Language (TSL) is proposed for communicating trajectories from aircraft to ATC as requests and from ATC to aircraft as assignments. The TS concept requires a new generation of airborne Flight Management Systems (FMS) that understand the TSL and can fly the assigned trajectories, but this paper focuses on the ATC functions and the prototype ATC algorithms and software that were developed to test the TS concept. Assuming conformance, TS can guarantee safe separation for an arbitrary length of time even in the event of an ATC system or communication outage. It can help to achieve the high level of safety and reliability needed for ATC automation, and it can also reduce the reliance on ATC backup systems for tactical conflict detection and resolution during normal operation. TS can be applied to any controlled airspace, including enroute, terminal, and urban airspace, but this paper presents algorithms and software for arrival spacing and conflict detection and resolution in the terminal airspace serving a major airport. In a fast-time simulation of a full day of traffic in a major terminal airspace, all conflicts were resolved in near real time, demonstrating the computational feasibility and the preliminary operational feasibility of the TS concept. This paper is a compilation of previous papers, and it adds significant information that was omitted from those papers due to length limitations. It also updates some of the results of those earlier papers due to algorithm refinements and corrections of minor software errors.
air traffic control, trajectory↗
Time controlled descent guidance algorithm for simulation of advanced ATC systems
Concepts and computer algorithms for generating time controlled four dimensional descent trajectories are described. The algorithms were implemented in the air traffic control simulator and used by experienced controllers in studies of advanced air traffic flow management procedures. A time controlled descent trajectory comprises a vector function of time, including position, altitude, and heading, that starts at the initial position of the aircraft and ends at touchdown. The trajectory provides a four dimensional reference path which will cause an aircraft tracking it to touchdown at a predetermined time with a minimum of fuel consumption. The problem of constructing such trajectories is divided into three subproblems involving synthesis of horizontal, vertical, and speed profiles. The horizontal profile is constructed as a sequence of turns and straight lines passing through a specified set of waypoints. The vertical profile consists of a sequence of level flight and constant descent angle segments defined by altitude waypoints. The speed profile is synthesized as a sequence of constant Mach number, constant indicated airspeed, and acceleration/deceleration legs. It is generated by integrating point mass differential equations of motion, which include the thrust and drag models of the aircraft.
Lee, H. Q.↗
Trajectory Specification for Terminal Air Traffic: Pairwise Conflict Detection and Resolution
Trajectory Specification is the explicit bounding and control of aircraft trajectories such that the position at any point in time is constrained to a precisely defined volume of space. The bounding space is defined by cross-track, along-track, and vertical tolerances relative to a reference trajectory that specifies position as a function of time. The tolerances are dynamic and will be based on the aircraft navigation capabilities and the current traffic situation. Assuming conformance, Trajectory Specification can guarantee safe separation for an arbitrary period of time even in the event of an air traffic control (ATC) system or datalink failure; hence it can help to achieve the high level of safety and reliability needed for ATC automation. It can also reduce the reliance on tactical backup systems during normal operation. This paper applies it to the terminal area around a major airport and presents algorithms and software for detecting and resolving conflicts. A representative set of pairwise conflicts was generated, and a fast-time simulation was run on them. All conflicts were successfully resolved in real time, demonstrating the computational feasibility of the concept.
terminal area↗
Trajectory Specification for Terminal Air Traffic: Pairwise Conflict Detection and Resolution
Trajectory specification is the explicit bounding and control of aircraft trajectories such that the position at each point in time is constrained to a precisely defined volume of space. The bounding space is defined by cross-track, along-track, and vertical tolerances relative to a reference trajectory that specifies position as a function of time. The tolerances are dynamic and will be based on the aircraft navigation capabilities and the current traffic situation. A standard language will be developed to represent these specifications and to communicate them by datalink. Assuming conformance, trajectory specification can guarantee safe separation for an arbitrary period of time even in the event of an air traffic control (ATC) system or datalink failure, hence it can help to achieve the high level of safety and reliability needed for ATC automation. As a more proactive form of ATC, it can also maximize airspace capacity and reduce the reliance on tactical backup systems during normal operation. It applies to both enroute airspace and the terminal area around airports, but this paper focuses on the terminal area and presents algorithms and software for spacing arrivals and deconflicting both arrivals and departures.
air traffic control↗
Dynamic Forms: Application to Aircraft Guidance - Part 2
The paper describes a method for guiding a dynamic system through a given set of points. The paradigm is a fully automatic aircraft subject to air traffic control (ATC). The ATC provides a sequence of waypoints through which the aircraft trajectory must pass. The waypoints typically specify time, position, and velocity. The guidance problem is to synthesize a system state trajectory that satisfies both the ATC and aircraft constraints. Complications arise because the controlled process is multidimensional, multiaxis, nonlinear, highly coupled, and the state space is not flat. In addition, there is a multitude of operating modes, which may number in the hundreds. Each such mode defines a distinct state space model of the process by specifying the state space coordinatization, the partition of the controls into active controls and configuration controls, and the output map. Furthermore, mode transitions are required to be smooth. The proposed guidance algorithm is based on the inversion of the pure feedback approximation, followed by correction for the effects of zero dynamics. The paper describes the structure and major modules of the algorithm, and the performance is illustrated by several example aircraft maneuvers.
Meyer, George↗
Determination of Comet Halley gas emission characteristics from mass loading of the solar wind
The velocity profile of the solar wind during Giotto's approach to Comet Halley is fitted with the mass loading produced by a simple model of the neutral particle distribution. The model is used to calculate the implanted ion flux at Giotto for any given time and position along the spacecraft trajectory. Comparing the added flux with Giotto's solar wind proton data from the inbound leg outside the bow shock, the ratio of the total mass-loaded ion flux to the solar wind flux at the spacecraft is computed. Hence, using equations given by Galeev et al. (1985) values of the solar wind velocity, u-infinity, far upstream from the comet are inferred. Imposing the condition that u-infinity should be as nearly as possible constant in time, values of gas production rate and the ratio between radial expansion velocity and ionization rate required to fit the model to data are derived. The values obtained are consistent with those derived by more direct methods.
Huddleston, D. E.↗
Guidance of Nonlinear Systems
The paper describes a method for guiding a dynamic system through a given set of points. The paradigm is a fully automatic aircraft subject to air traffic control (ATC). The ATC provides a sequence of way points through which the aircraft trajectory must pass. The way points typically specify time, position, and velocity. The guidance problem is to synthesize a system state trajectory which satisfies both the ATC and aircraft constraints. Complications arise because the controlled process is multi-dimensional, multi-axis, nonlinear, highly coupled, and the state space is not flat. In addition, there is a multitude of possible operating modes, which may number in the hundreds. Each such mode defines a distinct state space model of the process by specifying the state space coordination, the partition of the controls into active controls and configuration controls, and the output map. Furthermore, mode transitions must be smooth. The guidance algorithm is based on the inversion of the pure feedback approximations, which is followed by iterative corrections for the effects of zero dynamics. The paper describes the structure and modules of the algorithm, and the performance is illustrated by several example aircraft maneuvers.
Meyer, George↗
Guidance of Nonlinear Systems
The paper describes a method for guiding a dynamic system through a given set of points. The paradigm is a fully automatic aircraft subject to air traffic control (ATC). The ATC provides a sequence of way points through which the aircraft trajectory must pass. The way points typically specify time, position, and velocity. The guidance problem is to synthesize a system state trajectory which satisfies both the ATC and aircraft constraints. Complications arise because the controlled process is multi-dimensional, multi-axis, nonlinear, highly coupled, and the state space is not flat. In addition, there is a multitude of possible operating modes, which may number in the hundreds. Each such mode defines a distinct state space model of the process by specifying the state space coordinatization, the partition of the controls into active controls and configuration controls, and the output map. Furthermore, mode transitions must be smooth. The guidance algorithm is based on the inversion of the pure feedback approximations, which is followed by iterative corrections for the effects of zero dynamics. The paper describes the structure and modules of the algorithm, and the performance is illustrated by several example aircraft maneuvers.
Meyer, George↗
The eivaN: A forward-looking interactive orbital trajectory plotting tool for use with proximity operations (PROX OPS) and other maneuvers: Description and user's manual
The results of vehicle burns on-orbit are very difficult to anticipate because of nonlinearities in the equations of motion governing orbiting bodies. This confusion was noticed firsthand in prior experimentation. Out of plane motion is relatively simple as it is uncoupled from the other two degrees of freedom. However, in plane thrusts are more complex because the motions resulting from these inputs are coupled. An interactive planning device, eivaN, was developed to plot resulting trajectories, to provide a better comprehension of orbital mechanics effects, and to help the user to develop heuristics for on-orbit mission planning. The eivaN runs with Microsoft Excel on a Macintosh computer. It provides a forward looking display: burn parameters in the three orthogonal axes in addition to time inputted, and the resultant trajectory is then plotted. Position and velocity components for any burn at any user specified time are readily available. A new area of research related to the human factors of real time, on-orbit mission planning was identified and is currently being investigated.
Brody, Adam R.↗
Unsteady surface pressure measurements on a slender delta wing undergoing limit cycle wing rock
An experimental investigation of slender wing limit cycle motion known as wing rock was investigated using two unique experimental systems. Dynamic roll moment measurements and visualization data on the leading edge vortices were obtained using a free to roll apparatus that incorporates an airbearing spindle. In addition, both static and unsteady surface pressure data was measured on the top and bottom surfaces of the model. To obtain the unsteady surface pressure data a new computer controller drive system was developed to accurately reproduce the free to roll time history motions. The data from these experiments include, roll angle time histories, vortex trajectory data on the position of the vortices relative to the model's surface, and surface pressure measurements as a function of roll angle when the model is stationary or undergoing a wing rock motion. The roll time history data was numerically differentiated to determine the dynamic roll moment coefficient. An analysis of these data revealed that the primary mechanism for the limit cycle behavior was a time lag in the position of the vortices normal to the wing surface.
Arena, Andrew S., Jr.↗
Measurement of CPAS Main Parachute Rate of Descent
The Crew Exploration Vehicle Parachute Assembly System (CPAS) is being designed to land the Orion Crew Module (CM) at a safe rate of descent at splashdown. Flight test performance must be measured to a high degree of accuracy to ensure this requirement is met with the most efficient design possible. Although the design includes three CPAS Main parachutes, the requirement is that the system must not exceed 33 ft/s under two Main parachutes, should one of the Main parachutes fail. Therefore, several tests were conducted with clusters of two Mains. All of the steady-state rate of descent data are normalized to standard sea level conditions and checked against the limit. As the Orion design gains weight, the system is approaching this limit to within measurement precision. Parachute "breathing," cluster interactions, and atmospheric anomalies can cause the rate of descent to vary widely and lead to challenges in characterizing parachute terminal performance. An early test had contradictory rate of descent results from optical trajectory and Differential Global Positioning Systems (DGPS). A thorough analysis of the data sources and error propagation was conducted to determine the uncertainty in the trajectory. It was discovered that the Time Space Position Information (TSPI) from the optical tracking provided accurate position data. However, the velocity from TPSI must be computed via numerical differentiation, which is prone to large error. DGPS obtains position through pseudo-range calculations from multiple satellites and velocity through Doppler shift of the carrier frequency. Because the velocity from DGPS is a direct measurement, it is more accurate than TSPI velocity. To remedy the situation, a commercial off-the-shelf product that combines GPS and an Inertial Measurement Unit (IMU) was purchased to significantly improve rate of descent measurements. This had the added benefit of solving GPS dropouts during aircraft extraction. Statistical probability distributions for CPAS Main parachute rate of descent and drag coefficient were computed and plotted. Using test data, a terminal rate of descent at splashdown can be estimated as a function of canopy loading.
Ray, Eric S.↗
Evolution of Space Shuttle Range Safety (RS) Ascent Flight Envelope Design
Ascent flight envelopes are trajectories that define the normal operating region of a space vehicle s position from liftoff until the end of powered flight. They fulfill part of the RS data requirements imposed by the Air Force s 45th Space Wing (45SW) on space vehicles launching from the Eastern Range (ER) in Florida. The 45SW is chartered to protect the public by minimizing risks associated with the inherent hazards of launching a vehicle into space. NASA s Space Shuttle program has launched 130+ manned missions over a 30 year period from the ER. Ascent envelopes were delivered for each of those missions. The 45SW envelope requirements have remained largely unchanged during this time. However, the methodology and design processes used to generate the envelopes have evolved over the years to support mission changes, maintain high data quality, and reduce costs. The evolution of the Shuttle envelope design has yielded lessons learned that can be applied to future endevours. There have been numerous Shuttle ascent design enhancements over the years that have caused the envelope methodology to evolve. One of these Shuttle improvements was the introduction of onboard flight software changes implemented to improve launch probability. This change impacted the preflight nominal ascent trajectory, which is a key element in the RS envelope design. While the early Shuttle nominal trajectories were designed preflight using a representative monthly mean wind, the new software changes involved designing a nominal ascent trajectory on launch day using real-time winds. Because the actual nominal trajectory position was not known until launch day, the envelope analysis had to be customized to account for this nominal trajectory variation in addition to the other envelope components.
Brewer, Joan D.↗
Rapid Calculation of Spacecraft Trajectories Using Efficient Taylor Series Integration
A variable-order, variable-step Taylor series integration algorithm was implemented in NASA Glenn's SNAP (Spacecraft N-body Analysis Program) code. SNAP is a high-fidelity trajectory propagation program that can propagate the trajectory of a spacecraft about virtually any body in the solar system. The Taylor series algorithm's very high order accuracy and excellent stability properties lead to large reductions in computer time relative to the code's existing 8th order Runge-Kutta scheme. Head-to-head comparison on near-Earth, lunar, Mars, and Europa missions showed that Taylor series integration is 15.8 times faster than Runge- Kutta on average, and is more accurate. These speedups were obtained for calculations involving central body, other body, thrust, and drag forces. Similar speedups have been obtained for calculations that include J2 spherical harmonic for central body gravitation. The algorithm includes a step size selection method that directly calculates the step size and never requires a repeat step. High-order Taylor series integration algorithms have been shown to provide major reductions in computer time over conventional integration methods in numerous scientific applications. The objective here was to directly implement Taylor series integration in an existing trajectory analysis code and demonstrate that large reductions in computer time (order of magnitude) could be achieved while simultaneously maintaining high accuracy. This software greatly accelerates the calculation of spacecraft trajectories. At each time level, the spacecraft position, velocity, and mass are expanded in a high-order Taylor series whose coefficients are obtained through efficient differentiation arithmetic. This makes it possible to take very large time steps at minimal cost, resulting in large savings in computer time. The Taylor series algorithm is implemented primarily through three subroutines: (1) a driver routine that automatically introduces auxiliary variables and sets up initial conditions and integrates; (2) a routine that calculates system reduced derivatives using recurrence relations for quotients and products; and (3) a routine that determines the step size and sums the series. The order of accuracy used in a trajectory calculation is arbitrary and can be set by the user. The algorithm directly calculates the motion of other planetary bodies and does not require ephemeris files (except to start the calculation). The code also runs with Taylor series and Runge-Kutta used interchangeably for different phases of a mission.
Scott, James R.↗
Distributed Spatiotemporal Motion Planning for Spacecraft Swarms in Cluttered Environments
This paper focuses on trajectory planning for spacecraft swarms in cluttered environments, like debris fields or the asteroid belt. Our objective is to reconfigure the spacecraft swarm to a desired formation in a distributed manner while minimizing fuel and avoiding collisions among themselves and with obstacles. In our prior work we proposed a novel distributed guidance algorithm for spacecraft swarms in static environments. In this paper, we present the Multi-Agent Moving-Obstacles Spherical Expansion and Sequential Convex Programming (MAMO SE-SCP) algorithm that extends our prior work to include spatiotemporal constraints such as time-varying, moving obstacles and desired time-varying terminal positions. In the MAMO SE-SCP algorithm, each agent uses a spherical-expansion-based sampling algorithm to cooperatively explore the time-varying environment, a distributed assignment algorithm to agree on the terminal position for each agent, and a sequential-convex-programming-based optimization step to compute the locally-optimal trajectories from the current location to the assigned time-varying terminal position while avoiding collision with other agents and moving obstacles. Simulation results demonstrate that the proposed distributed algorithm can be used by a spacecraft swarm to achieve a time-varying, desired formation around an object of interest in a dynamic environment with many moving and tumbling obstacles.
Bandyopadhyay, Saptarshi↗
Distributed Spatiotemporal Motion Planning for Spacecraft Swarms in Cluttered Environments
This paper focuses on trajectory planning for spacecraft swarms in cluttered environments, like debris fields or the asteroid belt. Our objective is to reconfigure the spacecraft swarm to a desired formation in a distributed manner while minimizing fuel and avoiding collisions among themselves and with the obstacles. In our prior work we proposed a novel distributed guidance algorithm for spacecraft swarms in static environments.1 In this paper, we present the Multi-Agent Moving-Obstacles Spherical Expansion and Sequential Convex Programming (MAMO SE–SCP) algorithm that extends our prior work to include spatiotemporal constraints such as time-varying, moving obstacles and desired time-varying terminal positions. In the MAMO SE–SCP algorithm, each agent uses a spherical-expansion-based sampling algorithm to cooperatively explore the time-varying environment, a distributed assignment algorithm to agree on the terminal position for each agent, and a sequential-convex-programming-based optimization step to compute the locally-optimal trajectories from the current location to the assigned time-varying terminal position while avoiding collision with other agent and the moving obstacles. Simulations results demonstrate that the proposed distributed algorithm can be used by a spacecraft swarm to achieve a time-varying, desired formation around an object of interest in a dynamic environment with many moving and tumbling obstacles.
Hadaegh, Fred Y.↗