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NASA NTRS2007

Guidance Algorithms for Non-Drifting Trajectory Generation and Control in RendezVous Missions into Elliptical Orbits

Safety requirement represents one of the most critical aspect when defining the operational profile for a RendezVous mission. This requirement specially affects the design of the guidance algorithms that need to be tailored to guarantee what is normally referred to as Passive Trajectory Protection . The basic idea of passive trajectory protection is to design all the trajectory elements in an approach sequence such that if, at any point of the trajectory, thrust control ceases, the resulting free drift motion will remain collision free during a certain amount of time. This paper deals with the design and performances assessment of specific guidance algorithm addressing this issue. Firstly the problem is addressed for circular orbit using the Traveling Ellipse formulation for the relative motion. Secondly a solution for the RendezVous into a generic elliptical orbit is presented. This is based on a reduced transition matrix obtained through a description of the relative motion based on the first order variation of the orbital elements.

DiSotto, Emanuele↗
NASA NTRS2007

Analysis of Capture Trajectories to the Vicinity of Libration Points

Spacecraft capture trajectories to the periodic orbits of the L1 and L2 points in the restricted Hill three-body problem are studied. The specific focus is on transfer to these vicinities from interplanetary trajectories. This application is motivated by future proposals to place "Deep Space ports" at the Earth and Mars L1 or L2 points. These spaceports are considered as candidate gateways for interplanetary transfers in the future. We utilize stable manifolds for capture trajectories to periodic orbits around the libration points. As a result, the cost of capture into a periodic orbit is also reduced relative to direct capture into a parabolic orbit. The way of linking between interplanetary transfer trajectories and the stable manifold is also discussed.

Nakamiya, M.↗
NASA NTRS2008

Trajectory-Oriented Approach to Managing Traffic Complexity: Operational Concept and Preliminary Metrics Definition

This document describes preliminary research on a distributed, trajectory-oriented approach for traffic complexity management. The approach is to manage traffic complexity in a distributed control environment, based on preserving trajectory flexibility and minimizing constraints. In particular, the document presents an analytical framework to study trajectory flexibility and the impact of trajectory constraints on it. The document proposes preliminary flexibility metrics that can be interpreted and measured within the framework.

Idris, Husni↗
NASA NTRS2008

Rapid Trajectory Optimization for the ARES I Launch Vehicle

A simplified ascent trajectory optimization procedure has been developed with application to NASA's proposed Ares I launch vehicle. In the interest of minimizing bending loads and ensuring safe separation of the first-stage solid rocket motor, the vehicle is con- strained to follow a gravity-turn trajectory. This reduces the design space to just two free parameters, the pitch rate after a short vertical rise phase to clear the launch pad, and initial launch azimuth. The pitch rate primarily controls the in-plane parameters (altitude, speed, flight path angle) of the trajectory whereas the launch azimuth primarily controls the out-of-plane portion (velocity heading.) Thus, the optimization can be mechanized as two one-dimensional searches that converge quickly and reliably. The method is compared with POST-optimized trajectories to verify its optimality.

Dukeman, Greg A.↗
NASA NTRS1963

Space Flight Handbooks. Volume 3- Planetary Flight Handbook: Supplementary Trajectory Data: Venus to Earth and Mars to Earth - Part 3

Parts 2 and 3 present tabulations of trajectory data for scheduling flights to and from Venus and Mars during the period 1960-2000. Part 2 contains information for outbound flights to these planets; Part 3 contains information for trajectories returning from the planets to Earth. Each Part contains data for single-plane transfers, as well as for broken-plane transfers which employ a midcourse plane-change to eliminate the high speed "ridges." The mathematical analyses employed for all calculations are described in Part 1 of this handbook. To facilitate the construction of round-trip trajectories, the date at the target planet is held fixed while the trip duration is varied in 10-day increments from zero days to the length of that planet's synodic period with Earth. Dates of arrival at the target planet are presented in the extreme right-hand column of Part 2, and dates of departure from the target planet are presented in the extreme left-hand column of Part 3. Thus, by holding Part 2 directly to the left of Part 3, the analyst may easily and rapidly scan all trip possibilities which involve any desired stopover time at the target planet. Within approximately 200 days of each conjunction or opposition, data are presented in 10-day increments at the target planet. Only those trips are listed for which the hyperbolic excess speeds at either or both ends of the trajectory do not exceed 0.6 EMOS (Earth Mean Orbital Speed). For the remaining mission regions, the requirements are so smoothly varying that a 50-day interval in dates at the target planet may be employed; the 10-day interval in trip times is, however, preserved here. In these regions, only those trips are listed for which either or both speeds do not exceed 0.3 EMOS.

Source record↗
NASA NTRS2009

Spacecraft Station-Keeping Trajectory and Mission Design Tools

Two tools were developed for designing station-keeping trajectories and estimating delta-v requirements for designing missions to a small body such as a comet or asteroid. This innovation uses NPOPT, a non-sparse, general-purpose sequential quadratic programming (SQP) optimizer and the Two-Level Differential Corrector (T-LDC) in LTool (Libration point mission design Tool) to design three kinds of station-keeping scripts: vertical hovering, horizontal hovering, and orbiting. The T-LDC is used to differentially correct several trajectory legs that join hovering points. In a vertical hovering, the maximum and minimum range points must be connected smoothly while maintaining the spacecrafts range from a small body, all within the law of gravity and the solar radiation pressure. The same is true for a horizontal hover. A PatchPoint is an LTool class that denotes a space-time event with some extra information for differential correction, including a set of constraints to be satisfied by T-LDC. Given a set of PatchPoints, each with its own constraint, the T-LDC differentially corrects the entire trajectory by connecting each trajectory leg joined by PatchPoints while satisfying all specified constraints at the same time. Vertical and horizontal hover both are needed to minimize delta-v spent for station keeping. A Python I/F to NPOPT has been written to be used from an LTool script. In vertical hovering, the spacecraft stays along the line joining the Sun and a small body. An instantaneous delta-v toward the anti- Sun direction is applied at the closest approach to the small body for station keeping. For example, the spacecraft hovers between the minimum range (2 km) point and the maximum range (2.5 km) point from the asteroid 1989ML. Horizontal hovering buys more time for a spacecraft to recover if, for any reason, a planned thrust fails, by returning almost to the initial position after some time later via a near elliptical orbit around the small body. The mapping or staging orbit may be similarly generated using T-LDC with a set of constraints. Some delta-v tables are generated for several different asteroid masses.

Chung, Min-Kun J.↗
NASA NTRS2010

Space Shuttle Day-of-Launch Trajectory Design and Verification

A top priority of any launch vehicle is to insert as much mass into the desired orbit as possible. This requirement must be traded against vehicle capability in terms of dynamic control, thermal constraints, and structural margins. The vehicle is certified to a specific structural envelope which will yield certain performance characteristics of mass to orbit. Some envelopes cannot be certified generically and must be checked with each mission design. The most sensitive envelopes require an assessment on the day-of-launch. To further minimize vehicle loads while maximizing vehicle performance, a day-of-launch trajectory can be designed. This design is optimized according to that day s wind and atmospheric conditions, which will increase the probability of launch. The day-of-launch trajectory verification is critical to the vehicle's safety. The Day-Of-Launch I-Load Uplink (DOLILU) is the process by which the Space Shuttle Program redesigns the vehicle steering commands to fit that day's environmental conditions and then rigorously verifies the integrated vehicle trajectory's loads, controls, and performance. The Shuttle methodology is very similar to other United States unmanned launch vehicles. By extension, this method would be similar to the methods employed for any future NASA launch vehicles. This presentation will provide an overview of the Shuttle's day-of-launch trajectory optimization and verification as an example of a more generic application of dayof- launch design and validation.

Harrington, Brian E.↗
NASA NTRS2009

Performance of Trajectory Models with Wind Uncertainty

Typical aircraft trajectory predictors use wind forecasts but do not account for the forecast uncertainty. A method for generating estimates of wind prediction uncertainty is described and its effect on aircraft trajectory prediction uncertainty is investigated. The procedure for estimating the wind prediction uncertainty relies uses a time-lagged ensemble of weather model forecasts from the hourly updated Rapid Update Cycle (RUC) weather prediction system. Forecast uncertainty is estimated using measures of the spread amongst various RUC time-lagged ensemble forecasts. This proof of concept study illustrates the estimated uncertainty and the actual wind errors, and documents the validity of the assumed ensemble-forecast accuracy relationship. Aircraft trajectory predictions are made using RUC winds with provision for the estimated uncertainty. Results for a set of simulated flights indicate this simple approach effectively translates the wind uncertainty estimate into an aircraft trajectory uncertainty. A key strength of the method is the ability to relate uncertainty to specific weather phenomena (contained in the various ensemble members) allowing identification of regional variations in uncertainty.

Lee, Alan G.↗
NASA NTRS2010

Improving Separation Assurance Stability Through Trajectory Flexibility Preservation

New information and automation technologies are enabling the distribution of tasks and decisions from the service providers to the users of the air traffic system, with potential capacity and cost benefits. This distribution of tasks and decisions raises the concern that independent user actions will decrease the predictability and increase the complexity of the traffic system, hence inhibiting and possibly reversing any potential benefits. One such concern is the adverse impact of uncoordinated actions by individual aircraft on the stability of separation assurance. For example, individual aircraft performing self-separation may resolve predicted losses of separation or conflicts with some traffic, only to result in secondary conflicts with other traffic or with the same traffic later in time. In answer to this concern, this paper proposes metrics for preserving user trajectory flexibility to be used in self-separation along with other objectives. The hypothesis is that preserving trajectory flexibility will naturally reduce the creation of secondary conflicts by bringing about implicit coordination between aircraft. The impact of using these metrics on improving self-separation stability is investigated by measuring the impact on secondary conflicts. The scenarios analyzed include aircraft in en route airspace with each aircraft meeting a required time of arrival in a twenty minute time horizon while maintaining separation from the surrounding traffic and using trajectory flexibility metrics to mitigate the risk of secondary conflicts. Preliminary experiments showed promising results in that the trajectory flexibility preservation reduced the potential for secondary conflicts.

Idris, Husni↗
NASA NTRS2010

Definition and Demonstration of a Methodology for Validating Aircraft Trajectory Predictors

This paper presents a new methodology for validating an aircraft trajectory predictor, inspired by the lessons learned from a number of field trials, flight tests and simulation experiments for the development of trajectory-predictor-based automation. The methodology introduces new techniques and a new multi-staged approach to reduce the effort in identifying and resolving validation failures, avoiding the potentially large costs associated with failures during a single-stage, pass/fail approach. As a case study, the validation effort performed by the Federal Aviation Administration for its En Route Automation Modernization (ERAM) system is analyzed to illustrate the real-world applicability of this methodology. During this validation effort, ERAM initially failed to achieve six of its eight requirements associated with trajectory prediction and conflict probe. The ERAM validation issues have since been addressed, but to illustrate how the methodology could have benefited the FAA effort, additional techniques are presented that could have been used to resolve some of these issues. Using data from the ERAM validation effort, it is demonstrated that these new techniques could have identified trajectory prediction error sources that contributed to several of the unmet ERAM requirements.

Vivona, Robert A.↗
NASA NTRS2011

The Best Estimated Trajectory Analysis for Pad Abort One

I. Best Estimated Trajectory (BET) objective: a) Produce reconstructed trajectory of the PA-1 flight to understand vehicle dynamics and aid other post flight analyses. b) Leverage all measurement sources taken of vehicle during flight to produce the most accurate estimate of vehicle trajectory. c) Generate trajectory reconstructions of the Crew Module (CM), Launch Abort System (LAS), and Forward Bay Cover (FBC). II. BET analysis was started immediately following the PA-1 mission and was completed in September, 2010 a) Quick look version of BET released 5/25/2010: initial repackaging of SIGI data. b) Preliminary version of BET released 7/6/2010: first blended solution using available sources of external measurements. c) Final version of BET released 9/1/2010: final blended solution using all available sources of data.

Kutty, Prasad↗
NASA NTRS2010

Multi Sector Planning Tools for Trajectory-Based Operations

This paper discusses a suite of multi sector planning tools for trajectory-based operations that were developed and evaluated in the Airspace Operations Laboratory (AOL) at the NASA Ames Research Center. The toolset included tools for traffic load and complexity assessment as well as trajectory planning and coordination. The situation assessment tools included an integrated suite of interactive traffic displays, load tables, load graphs, and dynamic aircraft filters. The planning toolset allowed for single and multi aircraft trajectory planning and data communication-based coordination of trajectories between operators. Also newly introduced was a real-time computation of sector complexity into the toolset that operators could use in lieu of aircraft count to better estimate and manage sector workload, especially in situations with convective weather. The tools were used during a joint NASA/FAA multi sector planner simulation in the AOL in 2009 that had multiple objectives with the assessment of the effectiveness of the tools being one of them. Current air traffic control operators who were experienced as area supervisors and traffic management coordinators used the tools throughout the simulation and provided their usefulness and usability ratings in post simulation questionnaires. This paper presents these subjective assessments as well as the actual usage data that was collected during the simulation. The toolset was rated very useful and usable overall. Many elements received high scores by the operators and were used frequently and successfully. Other functions were not used at all, but various requests for new functions and capabilities were received that could be added to the toolset.

Prevot, Thomas↗
NASA NTRS2011

Hayabusa Re-Entry: Trajectory Analysis and Observation Mission Design

On June 13th, 2010, the Hayabusa sample return capsule successfully re-entered Earth s atmosphere over the Woomera Prohibited Area in southern Australia in its quest to return fragments from the asteroid 1998 SF36 Itokawa . The sample return capsule entered at a super-orbital velocity of 12.04 km/sec (inertial), making it the second fastest human-made object to traverse the atmosphere. The NASA DC-8 airborne observatory was utilized as an instrument platform to record the luminous portion of the sample return capsule re-entry (~60 sec) with a variety of on-board spectroscopic imaging instruments. The predicted sample return capsule s entry state information at ~200 km altitude was propagated through the atmosphere to generate aerothermodynamic and trajectory data used for initial observation flight path design and planning. The DC- 8 flight path was designed by considering safety, optimal sample return capsule viewing geometry and aircraft capabilities in concert with key aerothermodynamic events along the predicted trajectory. Subsequent entry state vector updates provided by the Deep Space Network team at NASA s Jet Propulsion Laboratory were analyzed after the planned trajectory correction maneuvers to further refine the DC-8 observation flight path. Primary and alternate observation flight paths were generated during the mission planning phase which required coordination with Australian authorities for pre-mission approval. The final observation flight path was chosen based upon trade-offs between optimal viewing requirements, ground based observer locations (to facilitate post-flight trajectory reconstruction), predicted weather in the Woomera Prohibited Area and constraints imposed by flight path filing deadlines. To facilitate sample return capsule tracking by the instrument operators, a series of two racetrack flight path patterns were performed prior to the observation leg so the instruments could be pointed towards the region in the star background where the sample return capsule was expected to become visible. An overview of the design methodologies and trade-offs used in the Hayabusa re-entry observation campaign are presented.

Cassell, Alan M.↗
NASA NTRS2011

Dynamic Weather Routes: A Weather Avoidance Concept for Trajectory-Based Operations

The integration of convective weather modeling with trajectory automation for conflict detection, trial planning, direct routing, and auto resolution has uncovered a concept that could help controllers, dispatchers, and pilots identify improved weather routes that result in significant savings in flying time and fuel burn. Trajectory automation continuously and automatically monitors aircraft in flight to find those that could potentially benefit from improved weather reroutes. Controllers, dispatchers, and pilots then evaluate reroute options to assess their suitability given current weather and traffic. In today's operations aircraft fly convective weather avoidance routes that were implemented often hours before aircraft approach the weather and automation does not exist to automatically monitor traffic to find improved weather routes that open up due to changing weather conditions. The automation concept runs in real-time and employs two keysteps. First, a direct routing algorithm automatically identifies flights with large dog legs in their routes and therefore potentially large savings in flying time. These are common - and usually necessary - during convective weather operations and analysis of Fort Worth Center traffic shows many aircraft with short cuts that indicate savings on the order of 10 flying minutes. The second and most critical step is to apply trajectory automation with weather modeling to determine what savings could be achieved by modifying the direct route such that it avoids weather and traffic and is acceptable to controllers and flight crews. Initial analysis of Fort Worth Center traffic suggests a savings of roughly 50% of the direct route savings could be achievable.The core concept is to apply trajectory automation with convective weather modeling in real time to identify a reroute that is free of weather and traffic conflicts and indicates enough time and fuel savings to be considered. The concept is interoperable with today's integrated FMS/datalink. Auxiliary(lat/long) waypoints define a minimum delay reroute between current position and a downstream capture fix beyond the weather. These auxiliary waypoints can be uplinked to equipped aircraft and auto-loaded into the FMS. Alternatively, for unequipped aircraft, auxiliary waypoints can be replaced by nearby named fixes, but this could reduce potential savings. The presentation includes an overview of the automation approach and focuses on several cases in terms of potential savings, reroute complexity, best auxiliary waypoint solution vs. named fix solution, and other metrics.

McNally, B. David↗
NASA NTRS2012

Patched Conic Trajectory Code

PatCon code was developed to help mission designers run trade studies on launch and arrival times for any given planet. Initially developed in Fortran, the required inputs included launch date, arrival date, and other orbital parameters of the launch planet and arrival planets at the given dates. These parameters include the position of the planets, the eccentricity, semi-major axes, argument of periapsis, ascending node, and inclination of the planets. With these inputs, a patched conic approximation is used to determine the trajectory. The patched conic approximation divides the planetary mission into three parts: (1) the departure phase, in which the two relevant bodies are Earth and the spacecraft, and where the trajectory is a departure hyperbola with Earth at the focus; (2) the cruise phase, in which the two bodies are the Sun and the spacecraft, and where the trajectory is a transfer ellipse with the Sun at the focus; and (3) the arrival phase, in which the two bodies are the target planet and the spacecraft, where the trajectory is an arrival hyperbola with the planet as the focus.

Park, Brooke Anderson↗
NASA NTRS2013

Mars Sample Return Using Commercial Capabilities: ERV Trajectory and Capture Requirements

Mars Sample Return was presented as the highest priority planetary science mission of the next decade [1]. Lemke et al. [2] present a Mars Sample Return mission concept in which the sample is returned directly from the surface of Mars to an Earth orbit. The sample is recovered in Earth Orbit instead of being transferred between spacecraft in Mars Orbit. This paper provides the details of this sample recovery in Earth orbit and presents as such a sub-element of the overall Mars sample return concept given in [2]. We start from the assumption that a Mars Ascent Vehicle (MAV), initially landed on Mars using a modified SpaceX Dragon capsule, has successfully delivered the sample, already contained within an Earth Return Vehicle (ERV), to a parking orbit around Mars. From the parking orbit, the ERV imparts sufficient Delta-V to inject itself into an earthbound trajectory and to be captured into an Earth orbit eventually. We take into account launch window and Delta-V considerations as well as the additional constraint of increased safety margins imposed by planetary protection regulations. We focus on how to overcome two distinct challenges of the sample return that are driven by the issues of planetary protection: (1) the design of an ERV trajectory meeting all the requirements including the need to avoid contamination of Earth's atmosphere; (2) the concept of operations for retrieving the Martian samples in Earth orbit in a safe way. We present an approach to retrieve the samples through a rendezvous between the ERV and a second SpaceX Dragon capsule. The ERV executes a trajectory that brings it from low Mars orbit (LMO) to a Moon-trailing Earth orbit at high inclination with respect to the Earth-Moon plane. After a first burn at Trans-Earth Injection (TEI), the trajectory uses a second burn at perigee during an Earth flyby maneuver to capture the ERV in Earth orbit. The ERV then uses a non-propulsive Moon flyby to come to a near-circular Moon-trailing orbit. To perform the Earth Orbit Rendezvous (EOR), a second Dragon capsule is then launched from Earth and a similar lunar flyby is performed to rendezvous with the ERV. The requirements for rendezvous, close proximity operations and capture of the sample canister are described. A concept of operations for sample retrieval is presented along with design specifications of the ERV, the required modifications to the Dragon capsule, as well as the hardware, software, sensors, actuators, and capture mechanisms used. In our concept, a container is mounted to the front hatch of Dragon, capable of accommodating the sample canister and sealing it from the rest of the capsule. The sample canister is captured using a robotic arm with a magnetic grappling mechanism. Dragon then performs a propulsive maneuver to return to Earth for a controlled re-entry while the ERV (sans sample container) is left in the Moon trailing orbit. Contingency cases and related mitigation strategies are also discussed, including the advantages and disadvantages of performing the ERV rendezvous with a crew.

Faber, Nicolas F.↗
NASA NTRS2013

Visiting Vehicle Ground Trajectory Tool

The International Space Station (ISS) Visiting Vehicle Group needed a targeting tool for vehicles that rendezvous with the ISS. The Visiting Vehicle Ground Trajectory targeting tool provides the ability to perform both realtime and planning operations for the Visiting Vehicle Group. This tool provides a highly reconfigurable base, which allows the Visiting Vehicle Group to perform their work. The application is composed of a telemetry processing function, a relative motion function, a targeting function, a vector view, and 2D/3D world map type graphics. The software tool provides the ability to plan a rendezvous trajectory for vehicles that visit the ISS. It models these relative trajectories using planned and realtime data from the vehicle. The tool monitors ongoing rendezvous trajectory relative motion, and ensures visiting vehicles stay within agreed corridors. The software provides the ability to update or re-plan a rendezvous to support contingency operations. Adding new parameters and incorporating them into the system was previously not available on-the-fly. If an unanticipated capability wasn't discovered until the vehicle was flying, there was no way to update things.

Hamm, Dustin↗
NASA NTRS2014

Pair-Wise Trajectory Management-Oceanic (PTM-O)

This document describes the Pair-wise Trajectory Management-Oceanic (PTM-O) Concept of Operations (ConOps). Pair-wise Trajectory Management (PTM) is a concept that includes airborne and ground-based capabilities designed to enable and to benefit from, airborne pair-wise distance-monitoring capability. PTM includes the capabilities needed for the controller to issue a PTM clearance that resolves a conflict for a specific pair of aircraft. PTM avionics include the capabilities needed for the flight crew to manage their trajectory relative to specific designated aircraft. Pair-wise Trajectory Management PTM-Oceanic (PTM-O) is a regional specific application of the PTM concept. PTM is sponsored by the National Aeronautics and Space Administration (NASA) Concept and Technology Development Project (part of NASA's Airspace Systems Program). The goal of PTM is to use enhanced and distributed communications and surveillance along with airborne tools to permit reduced separation standards for given aircraft pairs, thereby increasing the capacity and efficiency of aircraft operations at a given altitude or volume of airspace.

Jones, Kenneth M.↗