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NASA NTRS2015

An Overview of a Trajectory-Based Solution for En Route and Terminal Area Self-Spacing: Sixth Revision

This paper presents an overview of the sixth revision to an algorithm specifically designed to support NASA's Airborne Precision Spacing concept. This algorithm is referred to as the Airborne Spacing for Terminal Arrival Routes version 13 (ASTAR13). This airborne self-spacing concept contains both trajectory-based and state-based mechanisms for calculating the speeds required to achieve or maintain a precise spacing interval. The trajectory-based capability allows for spacing operations prior to the aircraft being on a common path. This algorithm was also designed specifically to support a standalone, non-integrated implementation in the spacing aircraft. This current revision to the algorithm adds the state-based capability in support of evolving industry standards relating to airborne self-spacing.

Abbott, Terence S.↗
NASA NTRS2015

A New Architecture for Extending the Capabilities of the Copernicus Trajectory Optimization Program

This paper describes a new plugin architecture developed for the Copernicus spacecraft trajectory optimization program. Details of the software architecture design and development are described, as well as examples of how the capability can be used to extend the tool in order to expand the type of trajectory optimization problems that can be solved. The inclusion of plugins is a significant update to Copernicus, allowing user-created algorithms to be incorporated into the tool for the first time. The initial version of the new capability was released to the Copernicus user community with version 4.1 in March 2015, and additional refinements and improvements were included in the recent 4.2 release. It is proving quite useful, enabling Copernicus to solve problems that it was not able to solve before.

Williams, Jacob↗
NASA NTRS2015

Combining Simulation Tools for End-to-End Trajectory Optimization

Trajectory simulations with advanced optimization algorithms are invaluable tools in the process of designing spacecraft. Due to the need for complex models, simulations are often highly tailored to the needs of the particular program or mission. NASA's Orion and SLS programs are no exception. While independent analyses are valuable to assess individual spacecraft capabilities, a complete end-to-end trajectory from launch to splashdown maximizes potential performance and ensures a continuous solution. In order to obtain end-to-end capability, Orion's in-space tool (Copernicus) was made to interface directly with the SLS's ascent tool (POST2) and a new tool to optimize the full problem by operating both simulations simultaneously was born.

Whitley, Ryan↗
NASA NTRS2015

An Overview of a Trajectory-Based Solution for En Route and Terminal Area Self-Spacing: Seventh Revision

This paper presents an overview of the seventh revision to an algorithm specifically designed to support NASA's Airborne Precision Spacing concept. This paper supersedes the previous documentation and presents a modification to the algorithm referred to as the Airborne Spacing for Terminal Arrival Routes version 13 (ASTAR13). This airborne self-spacing concept contains both trajectory-based and state-based mechanisms for calculating the speeds required to achieve or maintain a precise spacing interval. The trajectory-based capability allows for spacing operations prior to the aircraft being on a common path. This algorithm was also designed specifically to support a standalone, non-integrated implementation in the spacing aircraft. This current revision to the algorithm adds the state-based capability in support of evolving industry standards relating to airborne self-spacing.

Abbott, Terence S.↗
NASA NTRS2015

Rapid Generation of Optimal Asteroid Powered Descent Trajectories Via Convex Optimization

This paper investigates a convex optimization based method that can rapidly generate the fuel optimal asteroid powered descent trajectory. The ultimate goal is to autonomously design the optimal powered descent trajectory on-board the spacecraft immediately prior to the descent burn. Compared to a planetary powered landing problem, the major difficulty is the complex gravity field near the surface of an asteroid that cannot be approximated by a constant gravity field. This paper uses relaxation techniques and a successive solution process that seeks the solution to the original nonlinear, nonconvex problem through the solutions to a sequence of convex optimal control problems.

Pinson, Robin↗
NASA NTRS2015

Mars Hybrid Propulsion System Trajectory Analysis: Cargo Missions - Part II

NASA's Human Spaceflight Architecture Team is developing a reusable hybrid transportation architecture in which both chemical and electric propulsion systems are used to send crew and cargo to Mars destinations such as Phobos, Deimos, the surface of Mars, and other orbits around Mars. By combining chemical and electrical propulsion into a single spaceship and applying each where it is more effective, the hybrid architecture enables a series of Mars trajectories that are more fuel-efficient than an all chemical architecture without significant increases in flight times. This paper shows the feasibility of the hybrid transportation architecture to pre-deploy cargo to Mars and Phobos in support of the Evolvable Mars Campaign crew missions. The analysis shows that the hybrid propulsion stage is able to deliver all of the current manifested payload to Phobos and Mars through the first three crew missions. The conjunction class trajectory also allows the hybrid propulsion stage to return to Earth in a timely fashion so it can be reused for additional cargo deployment. The 1,100 days total trip time allows the hybrid propulsion stage to deliver cargo to Mars every other Earth-Mars transit opportunity. For the first two Mars surface mission in the Evolvable Mars Campaign, the short trip time allows the hybrid propulsion stage to be reused for three round-trip journeys to Mars, which matches the hybrid propulsion stage's designed lifetime for three round-trip crew missions to the Martian sphere of influence.

Chai, Patrick R.↗
NASA NTRS2015

Mars Hybrid Propulsion System Trajectory Analysis: Crew Missions - Part I

NASAs Human spaceflight Architecture team is developing a reusable hybrid transportation architecture in which both chemical and electric propulsion systems are used to send crew and cargo to Mars destinations such as Phobos, Deimos, the surface of Mars, and other orbits around Mars. By combining chemical and electrical propulsion into a single space- ship and applying each where it is more effective, the hybrid architecture enables a series of Mars trajectories that are more fuel-efficient than an all chemical architecture without significant increases in flight times. This paper provides the analysis of the interplanetary segments of the three Evolvable Mars Campaign crew missions to Mars using the hybrid transportation architecture. The trajectory analysis provides departure and arrival dates and propellant needs for the three crew missions that are used by the campaign analysis team for campaign build-up and logistics aggregation analysis. Sensitivity analyses were performed to investigate the impact of mass growth, departure window, and propulsion system performance on the hybrid transportation architecture. The results and system analysis from this paper contribute to analyses of the other human spaceflight architecture team tasks and feed into the definition of the Evolvable Mars Campaign.

Chai, Patrick R.↗
NASA NTRS2016

End-to-End Trajectory for Conjunction Class Mars Missions Using Hybrid Solar-Electric/Chemical Transportation System

NASA's Human Spaceflight Architecture Team is developing a reusable hybrid transportation architecture in which both chemical and solar-electric propulsion systems are used to deliver crew and cargo to exploration destinations. By combining chemical and solar-electric propulsion into a single spacecraft and applying each where it is most effective, the hybrid architecture enables a series of Mars trajectories that are more fuel efficient than an all chemical propulsion architecture without significant increases to trip time. The architecture calls for the aggregation of exploration assets in cislunar space prior to departure for Mars and utilizes high energy lunar-distant high Earth orbits for the final staging prior to departure. This paper presents the detailed analysis of various cislunar operations for the EMC Hybrid architecture as well as the result of the higher fidelity end-to-end trajectory analysis to understand the implications of the design choices on the Mars exploration campaign.

Chai, Patrick R.↗
NASA NTRS2014

Updating the Reference Trajectory for the Cassini Solstice Mission

The Cassini-Huygens deep-space probe has successfully completed a four-year prime tour and a two-year extended tour of the Saturnian system. Now in a second extended phase called the Solstice Mission, the Cassini spacecraft will continue to gather data as directed by the reference trajectory until 2017. This paper will describe the process of how a reference trajectory update is prepared and delivered to the project by the navigation team during Solstice Mission flight operations. This paper will also document the timeline of products released and utilized, as well as the study to include an Enceladus occultation observation that occurs in 2016.

navigation operations↗
NASA NTRS2016

Comparing Eyewitness-Derived Trajectories of Bright Meteors to Ground Truth Data

The NASA Meteoroid Environment Office is a US government agency tasked with analyzing meteors of public interest. When queried about a meteor observed over the United States, the MEO must respond with a characterization of the trajectory, orbit, and size within a few hours. If the event is outside meteor network coverage and there is no imagery recorded by the public, a timely assessment can be difficult if not impossible. In this situation, visual reports made by eyewitnesses may be the only resource available. This has led to the development of a tool to quickly calculate crude meteor trajectories from eyewitness reports made to the American Meteor Society. A description of the tool, example case studies, and a comparison to ground truth data observed by the NASA All Sky Fireball Network are presented.

Moser, D. E.↗
NASA NTRS2016

Comparing Eyewitness-Derived Trajectories of Bright Meteors to Ground Truth Data

The NASA Meteoroid Environment Office (MEO) is the only US government agency tasked with analyzing meteors of public interest. When queried about a meteor observed over the United States, the MEO must respond with a characterization of the trajectory, orbit, and size within a few hours. Using observations from meteor networks like the NASA All Sky Fireball Network or the Southern Ontario Meteor Network, such a characterization is often easy. If found, casual recordings from the public and stationary web cameras can be used to roughly analyze a meteor if the camera's location can be identified and its imagery calibrated. This technique was used with great success in the analysis of the Chelyabinsk meteorite fall. But if the event is outside meteor network coverage, if an insufficient number of videos are found, or if the imagery cannot be geolocated or calibrated, a timely assessment can be difficult if not impossible. In this situation, visual reports made by eyewitnesses may be the only resource available. This has led to the development of a tool to quickly calculate crude meteor trajectories from eyewitness reports made to the American Meteor Society. The output is illustrated in Figure 1. A description of the tool, example case studies, and a comparison to ground truth data observed by the NASA All Sky Fireball Network will be presented.

Moser, D. E.↗
NASA NTRS2016

Spline Trajectory Algorithm Development: Bezier Curve Control Point Generation for UAVs

A greater need for sophisticated autonomous piloting systems has risen in direct correlation with the ubiquity of Unmanned Aerial Vehicle (UAV) technology. Whether surveying unknown or unexplored areas of the world, collecting scientific data from regions in which humans are typically incapable of entering, locating lost or wanted persons, or delivering emergency supplies, an unmanned vehicle moving in close proximity to people and other vehicles, should fly smoothly and predictably. The mathematical application of spline interpolation can play an important role in autopilots' on-board trajectory planning. Spline interpolation allows for the connection of Three-Dimensional Euclidean Space coordinates through a continuous set of smooth curves. This paper explores the motivation, application, and methodology used to compute the spline control points, which shape the curves in such a way that the autopilot trajectory is able to meet vehicle-dynamics limitations. The spline algorithms developed used to generate these curves supply autopilots with the information necessary to compute vehicle paths through a set of coordinate waypoints.

Howell, Lauren R.↗
NASA NTRS2016

Conflict Resolution for Wind-Optimal Aircraft Trajectories in North Atlantic Oceanic Airspace with Wind Uncertainties

Air traffic in the North Atlantic oceanic airspace (NAT) experiences very strong winds caused by jet streams. Flying wind-optimal trajectories increases individual flight efficiency, which is advantageous when operating in the NAT. However, as the NAT is highly congested during peak hours, a large number of potential conflicts between flights are detected for the sets of wind-optimal trajectories. Conflict resolution performed at the strategic level of flight planning can significantly reduce the airspace congestion. However, being completed far in advance, strategic planning can only use predicted environmental conditions that may significantly differ from the real conditions experienced further by aircraft. The forecast uncertainties result in uncertainties in conflict prediction, and thus, conflict resolution becomes less efficient. This work considers wind uncertainties in order to improve the robustness of conflict resolution in the NAT. First, the influence of wind uncertainties on conflict prediction is investigated. Then, conflict resolution methods accounting for wind uncertainties are proposed.

wind uncertainties↗
NASA NTRS2016

Benefits of Using Pairwise Trajectory Management in the Central East Pacific

Pairwise Trajectory Management (PTM) is a concept that utilizes airborne and ground-based capabilities to enable airborne spacing operations in oceanic regions. The goal of PTM is to use enhanced surveillance, along with airborne tools, to manage the spacing between aircraft. Due to the enhanced airborne surveillance of Automatic Dependent Surveillance-Broadcast (ADS-B) information and reduced communication, the PTM minimum spacing distance will be less than distances currently required of an air traffic controller. Reduced minimum distance will increase the capacity of aircraft operations at a given altitude or volume of airspace, thereby increasing time on desired trajectory and overall flight efficiency. PTM is designed to allow a flight crew to resolve a specific traffic conflict (or conflicts), identified by the air traffic controller, while maintaining the flight crew's desired altitude. The air traffic controller issues a PTM clearance to a flight crew authorized to conduct PTM operations in order to resolve a conflict for the pair (or pairs) of aircraft (i.e., the PTM aircraft and a designated target aircraft). This clearance requires the flight crew of the PTM aircraft to use their ADS-B-enabled onboard equipment to manage their spacing relative to the designated target aircraft to ensure spacing distances that are no closer than the PTM minimum distance. When the air traffic controller determines that PTM is no longer required, the controller issues a clearance to cancel the PTM operation.

Chartrand, Ryan↗
NASA NTRS2016

Trajectory Design Employing Convex Optimization for Landing on Irregularly Shaped Asteroids

Mission proposals that land spacecraft on asteroids are becoming increasingly popular. However, in order to have a successful mission the spacecraft must reliably and softly land at the intended landing site with pinpoint precision. The problem under investigation is how to design a propellant optimal powered descent trajectory that can be quickly computed onboard the spacecraft, without interaction from the ground control. The propellant optimal control problem in this work is to determine the optimal finite thrust vector to land the spacecraft at a specified location, in the presence of a highly nonlinear gravity field, subject to various mission and operational constraints. The proposed solution uses convex optimization, a gravity model with higher fidelity than Newtonian, and an iterative solution process for a fixed final time problem. In addition, a second optimization method is wrapped around the convex optimization problem to determine the optimal flight time that yields the lowest propellant usage over all flight times. Gravity models designed for irregularly shaped asteroids are investigated. Success of the algorithm is demonstrated by designing powered descent trajectories for the elongated binary asteroid Castalia.

Pinson, Robin M.↗
NASA NTRS2017

Comparison of the Effects of Velocity and Range Triggers on Trajectory Dispersions for the Mars 2020 Mission

Mars 2020, the next planned U.S. rover mission to land on Mars, is based on the design of the successful 2012 Mars Science Laboratory (MSL) mission. Mars 2020 retains most of the entry, descent, and landing (EDL) sequences of MSL, including the closed-loop entry guidance scheme based on the Apollo guidance algorithm. However, unlike MSL, Mars 2020 will trigger the parachute deployment and descent sequence on range trigger rather than the previously used velocity trigger. This difference will greatly reduce the landing ellipse sizes. Additionally, the relative contribution of each models to the total ellipse sizes have changed greatly due to the switch to range trigger. This paper considers the effect on trajectory dispersions due to changing the trigger schemes and the contributions of these various models to trajectory and EDL performance.

Dutta, Soumyo↗
NASA NTRS2017

Low-Thrust Many-Revolution Trajectory Optimization via Differential Dynamic Programming and a Sundman Transformation

Low-thrust trajectories about planetary bodies characteristically span a high count of orbital revolutions. Directing the thrust vector over many revolutions presents a challenging optimization problem for any conventional strategy. This paper demonstrates the tractability of low-thrust trajectory optimization about planetary bodies by applying a Sundman transformation to change the independent variable of the spacecraft equations of motion to the eccentric anomaly and performing the optimization with differential dynamic programming. Fuel-optimal geocentric transfers are shown in excess of 1000 revolutions while subject to Earths J2 perturbation and lunar gravity.

Aziz, Jonathan↗
NASA NTRS2017

Low-Thrust Many-Revolution Trajectory Optimization via Differential Dynamic Programming and a Sundman Transformation

Low-thrust trajectories about planetary bodies characteristically span a high count of orbital revolutions. Directing the thrust vector over many revolutions presents a challenging optimization problem for any conventional strategy. This paper demonstrates the tractability of low-thrust trajectory optimization about planetary bodies by applying a Sundman transformation to change the independent variable of the spacecraft equations of motion to the eccentric anomaly and performing the optimization with differential dynamic programming. Fuel-optimal geocentric transfers are shown in excess of 1000 revolutions while subject to Earths J2 perturbation and lunar gravity.

Aziz, Jonathan D.↗