Guidance equations for quasi-optimum space maneuvers
Approximate time optimum guidance equations for planetary ascent and descent trajectories at constant thrust flat body two-dimensional case
GUIDANCE↗
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Results for “DESCENT TRAJECTORY”
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Fast Optimization for Aircraft Descent and Approach Trajectory
We address problem of on-line scheduling of the aircraft descent and approach trajectory. We formulate a general multiphase optimal control problem for optimization of the descent trajectory and review available methods of its solution. We develop a fast algorithm for solution of this problem using two key components: (i) fast inference of the dynamical and control variables of the descending trajectory from the low dimensional flight profile data and (ii) efficient local search for the resulting reduced dimensionality non-linear optimization problem. We compare the performance of the proposed algorithm with numerical solution obtained using optimal control toolbox General Pseudospectral Optimal Control Software. We present results of the solution of the scheduling problem for aircraft descent using novel fast algorithm and discuss its future applications.
Luchinsky, Dmitry G.↗
A Study of the Positions and Velocities of a Space Station and a Ferry Vehicle During Rendezvous and Return
A study is made of the families of non-thrusting ascent trajectories of a ferry vehicle during rendezvous with an orbiting body, referred to as a space station. It is shown that these trajectories may also be interpreted as descent trajectories of the ferry from the station to the earth. The rendezvous trajectories start at the end of the boost period (assumed to be 60 miles) and terminate at the station. The equations of motion are derived and results are shown for two typical orbits of the station: a 300-mile circular orbit and a 100-to-500-mile elliptical orbit. Trajectories are described in terms of a rotating coordinate system fixed in the station and launch conditions are tabulated in terms of non-rotating inertial coordinates. Boundaries are given in terms of launch (at time of booster burnout) and rendezvous conditions for the example cases. The considerations used to calculate these boundaries and the significance of some of the trends are discussed.
TRAJECTORY↗
A semigraphical method for a deorbit trajectory design study
Semigraphical method to aid selection of descent trajectory compatible with mission constraints
Green, R. N.↗
Some redesignation characteristics attributed to slowing the LM landing approach trajectory
Redesignation characteristics of LM due to slowdown of descent trajectory
Moore, T. E.↗
Flight Management System Execution of Idle-Thrust Descents in Operations
To enable arriving aircraft to fly optimized descents computed by the flight management system (FMS) in congested airspace, ground automation must accurately predict descent trajectories. To support development of the trajectory predictor and its error models, commercial flights executed idle-thrust descents, and the recorded data includes the target speed profile and FMS intent trajectories. The FMS computes the intended descent path assuming idle thrust after top of descent (TOD), and any intervention by the controllers that alters the FMS execution of the descent is recorded so that such flights are discarded from the analysis. The horizontal flight path, cruise and meter fix altitudes, and actual TOD location are extracted from the radar data. Using more than 60 descents in Boeing 777 aircraft, the actual speeds are compared to the intended descent speed profile. In addition, three aspects of the accuracy of the FMS intent trajectory are analyzed: the meter fix crossing time, the TOD location, and the altitude at the meter fix. The actual TOD location is within 5 nmi of the intent location for over 95% of the descents. Roughly 90% of the time, the airspeed is within 0.01 of the target Mach number and within 10 KCAS of the target descent CAS, but the meter fix crossing time is only within 50 sec of the time computed by the FMS. Overall, the aircraft seem to be executing the descents as intended by the designers of the onboard automation.
Stell, Laurel L.↗
Multi-Modal Active Perception for Autonomously Selecting Landing Sites on Icy Moons
Selecting suitable landing sites is fundamental to achieving many mission objectives in planetary robotic lander missions. However, due to sensing limitations, landing sites which are both safe and scientifically valuable often cannot be determined reliably from orbit, particularly, in icy moon missions where orbital sensing data is noisy and incomplete. This paper presents an active perception approach to Entry Descent and Landing (EDL) which enables the lander to autonomously plan informative descent trajectories, acquire high quality sensing data during descent and exploit this additional information to select higher utility landing sites. Our approach consists of two components: probabilistic modeling of landing site features and approximate trajectory planning using a sampling based planner. The proposed framework allows the lander to plan long horizons paths and remain robust to noisy data. Results in simulated environments show large performance improvements over alternative approaches and show promise that our approach has strong potential to improve science return of not only icy moon missions but EDL systems in general.
autonomy↗
Near-Optimal Re-Entry Trajectories for Reusable Launch Vehicles
A near-optimal guidance law for the descent trajectory for earth orbit re-entry of a fully reusable single-stage-to-orbit pure rocket launch vehicle is derived. A methodology is developed to investigate using both bank angle and altitude as control variables and selecting parameters that maximize various performance functions. The method is based on the energy-state model of the aircraft equations of motion. The major task of this paper is to obtain optimal re-entry trajectories under a variety of performance goals: minimum time, minimum surface temperature, minimum heating, and maximum heading change; four classes of trajectories were investigated: no banking, optimal left turn banking, optimal right turn banking, and optimal bank chattering. The cost function is in general a weighted sum of all performance goals. In particular, the trade-off between minimizing heat load into the vehicle and maximizing cross range distance is investigated. The results show that the optimization methodology can be used to derive a wide variety of near-optimal trajectories.
Chou, H.-C.↗
Scientific considerations for a common Saturn/Uranus atmospheric entry probe.
Development of a scientific rationale for an atmospheric probe designed to be capable of entry into either Saturn or Uranus. The effects of the NASA Monograph model atmospheres (SP 8091 and SP 8103) on the entry and descent trajectory specify instrument sampling design. The cool model atmospheres require descents to the vicinity of 20 bars to satisfy the objectives while about 4 bars is sufficient for the warm models. The measurement performance for a descent sampling time of 44 minutes shows that the atmosphere can be reconstructed from measured data. The required total probe entry weight is 103 kg, of which about 15 kg is for the science instruments. The descent data rate varies from 32 to 51 bps, depending upon the mode of transmitting preentry data. The resulting common probe can be redirected in flight between Saturn and Uranus.
Ledbetter, K. W.↗
A Study of the Positions and Velocities of a Space Station and a Ferry Vehicle During Rendezvous and Return
A study is made of the families of non-thrusting ascent trajectories during rendezvous with an orbiting space station and the descent trajectories to the earth's atmosphere. Equations of motion are derived and results are shown for two typical orbits of the station (one circular and one elliptic orbit}. Boundaries of launch (at time of booster burnout) and rendezvous conditions are given and the effects of delays in launch time are discussed.
Eggleston, John M.↗
Transitioning from Free-Flight to TRACON Airspace: The Ground Perspective of User-Preferred Descents
Free-flight is considered to play a major role in the future air traffic environment. Studies are underway addressing different concepts for free-flight and self separation in enroute airspace. One common opinion throughout the different concepts is that the airspace surrounding major airports, the Terminal Radar Approach CONtrol (TRACON) will not be a free flight area. This means that aircraft in this area are completely controlled by air traffic controllers, who may be supported by decision support system like the Center TRACON Automation System (CTAS). How the transition from the free-flight area (enroute airspace) to the terminal area will take place is currently unclear, This paper describes a study at NASA Ames Research Center addressing the perspective of air traffic controllers handling user-preferred (FMS-optimized) descent trajectories during this transition phase. Two major issues in enabling user preferred descents from the controllers' point of view are predictability and controllability. In an environment in which the air traffic services are highly responsive to user preferences controllers need to know, where and when aircraft will change their trajectory and they need to have appropriate means and procedures at hand to control the aircraft according to the overall traffic situation. Predictability shall be enhanced by: 1) Indicating airspace corridors for descending aircraft; 2) Modify the controller interface; 3) Using a ground based conflict probe; 4) Making use of downlinked intent information from the aircraft FMS; and 5) Requiring to fly pilots on user preferred trajectories coupled to the FMS in the lateral and vertical axis. Additional controllability shall be achieved by supporting the controllers with CTAS center tools: 1) Traffic Management Advisor (TMA); 2) Conflict Probing and Trial Planning (CP/TP); and 3) Enroute Descent Advisor (E/DA). The paper describes the general concept and the modifications to current systems required to enable the concept. It explains the experiment design and discusses the results with regard to controller acceptability and usability. Potential benefits and drawbacks of the overall concept are indicated.
Prevot, Thomas↗
Analysis of Flight Management System Predictions of Idle-Thrust Descents
To enable arriving aircraft to fly optimized descents computed by the flight management system (FMS) in congested airspace, ground automation must accurately predict descent trajectories. To support development of the predictor and its uncertainty models, descents from cruise to the meter fix were executed using vertical navigation in a B737-700 simulator and a B777-200 simulator, both with commercial FMSs. For both aircraft types, the FMS computed the intended descent path for a specified speed profile assuming idle thrust after top of descent (TOD), and then it controlled the avionics without human intervention. The test matrix varied aircraft weight, descent speed, and wind conditions. The first analysis in this paper determined the effect of the test matrix parameters on the FMS computation of TOD location, and it compared the results to those for the current ground predictor in the Efficient Descent Advisor (EDA). The second analysis was similar but considered the time to fly a specified distance to the meter fix. The effects of the test matrix variables together with the accuracy requirements for the predictor will determine the allowable error for the predictor inputs. For the B737, the EDA prediction of meter fix crossing time agreed well with the FMS; but its prediction of TOD location probably was not sufficiently accurate to enable idle-thrust descents in congested airspace, even though the FMS and EDA gave similar shapes for TOD location as a function of the test matrix variables. For the B777, the FMS and EDA gave different shapes for the TOD location function, and the EDA prediction of the TOD location is not accurate enough to fully enable the concept. Furthermore, the differences between the FMS and EDA predictions of meter fix crossing time for the B777 indicated that at least one of them was not sufficiently accurate.
Stell, Laurel↗
Fast Sensitivity-Based Optimal Trajectory Updates for Descent Operations Subject to Time Constraints
The ability to meet a controlled time of arrival during a continuous descent operation will enable environmentally friendly and fuel efficient descent operations while simultaneously maintaining airport throughput. Previous work showed that guidance strategies based on a frequent recalculation of the optimal trajectory during the descent result in excellent environmental impact mitigation figures while meeting operational constraints in the presence of modelling errors. However, the time lag of recalculating the trajectory using traditional optimisation algorithms could lead to performance degradation and stability issues. This paper proposes an alternative strategy, which allows for fast updates of the optimal trajectory based on parametric sensitivities. Promising results show that the performance of this method is comparable to that of instantaneously recalculating the optimal descent trajectory at each time sample.
Dalmau, Ramon↗
Predictability of Top of Descent Location for Operational Idle-Thrust Descents
To enable arriving aircraft to fly optimized descents computed by the flight management system (FMS) in congested airspace, ground automation must accurately predict descent trajectories. To support development of the trajectory predictor and its uncertainty models, commercial flights executed idle-thrust descents at a specified descent speed, and the recorded data included the specified descent speed profile, aircraft weight, and the winds entered into the FMS as well as the radar data. The FMS computed the intended descent path assuming idle thrust after top of descent (TOD), and the controllers and pilots then endeavored to allow the FMS to fly the descent to the meter fix with minimal human intervention. The horizontal flight path, cruise and meter fix altitudes, and actual TOD location were extracted from the radar data. Using approximately 70 descents each in Boeing 757 and Airbus 319/320 aircraft, multiple regression estimated TOD location as a linear function of the available predictive factors. The cruise and meter fix altitudes, descent speed, and wind clearly improve goodness of fit. The aircraft weight improves fit for the Airbus descents but not for the B757. Except for a few statistical outliers, the residuals have absolute value less than 5 nmi. Thus, these predictive factors adequately explain the TOD location, which indicates the data do not include excessive noise.
Stell, Laurel L.↗
Navigation Prediction Performance During OSIRIS-REx Proximity Operations at (101955) Bennu
The OSIRIS-REx (Origins, Spectral Interpretation, Resource Identification and Security–Regolith Explorer) Orbit Determination team performed covariance analyses prior to the commencement of proximity operations (ProxOps) at (101955) Bennu to determine the expected predicted trajectory performance in order to meet trajectory knowledge requirements throughout each phase of the mission. One of the primary requirements placed on the predicted trajectory performance was based on the performance during orbital phases leading up to the maneuver to initiate the Touch-and-Go (TAG) trajectory descent. Throughout ProxOps the nominal force models being used to predict the spacecraft trajectory were updated in an effort to improve the prediction performance. The most significant models that contributed to prediction performance were of solar radiation pressure, thermal reradiation of the spacecraft, predicted attitude errors, and desaturation maneuvers. Efforts were made throughout all of ProxOps to monitor, trend, predict, and update spacecraft modeling to improve the prediction performance. These efforts were vital to reduce the spacecraft knowledge errors necessary to achieve a TAG target smaller than pre-launch analysis allowed due to the rough terrain of Bennu. Increased precision in predicted trajectory errors allowed for refined uncertainties to be used for future phase planning throughout the mission. The navigation team successfully predicted the spacecraft trajectory throughout all of ProxOps achieving predicted trajectories errors less than originally analyzed.
Jason M. Leonard↗
Regression Analysis of Top of Descent Location for Idle-thrust Descents
In this paper, multiple regression analysis is used to model the top of descent (TOD) location of user-preferred descent trajectories computed by the flight management system (FMS) on over 1000 commercial flights into Melbourne, Australia. The independent variables cruise altitude, final altitude, cruise Mach, descent speed, wind, and engine type were also recorded or computed post-operations. Both first-order and second-order models are considered, where cross-validation, hypothesis testing, and additional analysis are used to compare models. This identifies the models that should give the smallest errors if used to predict TOD location for new data in the future. A model that is linear in TOD altitude, final altitude, descent speed, and wind gives an estimated standard deviation of 3.9 nmi for TOD location given the trajec- tory parameters, which means about 80% of predictions would have error less than 5 nmi in absolute value. This accuracy is better than demonstrated by other ground automation predictions using kinetic models. Furthermore, this approach would enable online learning of the model. Additional data or further knowl- edge of algorithms is necessary to conclude definitively that no second-order terms are appropriate. Possible applications of the linear model are described, including enabling arriving aircraft to fly optimized descents computed by the FMS even in congested airspace. In particular, a model for TOD location that is linear in the independent variables would enable decision support tool human-machine interfaces for which a kinetic approach would be computationally too slow.
trajectory prediction↗
Propulsive trajectory optimization to minimize surface contamination
MOTIVATION: We present an optimization technique for propulsive vehicles that autonomously minimizes contamination during surface approach and landing. In addition to short-range hoppers, the optimization technique is also fully applicable to traditional orbit-to-surface landers. This study addresses scenarios where surface alterations from propulsion events are counterproductive or hazardous to the mission objectives. This is of immediate interest for landers (whether human or robotic), that may rely on pristine soils collected in the immediate vicinity of landing sites to accomplish science investigations, mining, or ISRU surface operations. Such missions are averse to various surface-plume interactions such as thermal scoring, physical agitation, and contamination. The capability can be applied with minimal impact to the baseline mission concept. METHODS: Optimization algorithms have been developed to calculate descent trajectories and maneuvers, thrust magnitude, and attitude for various mission cases. These parameters are determined as an optimal solution when minimizing either fuel consumption, contamination deposited at the landing site, or some weighted combination of both. Among constraints imposed on the solution, we examined pitch rate, vertical takeoff and vertical landing (VTVL) requirements, size of the contamination zone, and minimum ground clearance during flight. This tool provides unique, non-intuitive solutions and can be a valuable resource for mission planners. RESULTS: A variety of agile trajectory solutions were obtained, each yielding different reductions in landing site contamination and corresponding to only modest increases in fuel consumption. Several optimal trajectories were obtained by varying the contamination weight in the fitness function. As expected, when the contamination weight is zero, the trajectory appears close to parabolic since the optimization scheme only attempts to minimize for fuel utilization, yielding essentially, the expected ballistic trajectory. Notably for contamination weights greater than zero, trajectory inflections are observed in the descent phase, which manifests as hovering or additional, mini “pseudo hops” before the final touchdown. A trajectory inflection is characterized by arresting the majority of the spacecraft vertical velocity component at a coordinate outside of the landing target, and without violating ground clearance constraints. FUTURE WORK: Our optimization technique is ready for laboratory or field demonstrations to validate the sophisticated maneuvering solutions obtained for fuel optimization and surface preservation. An appropriate testbed would validate the optimal guidance algorithms, the navigation system, and sensor suite by emulating vehicle flight in closed loop robotic tests. Critically, these algorithms could then be ported to flight software for implementation.
surface contamination↗
Mid-Lift-to-Drag Ratio Rigid Vehicle 6-DOF EDL Performance Using Tunable Apollo Powered Guidance
The Mid-Lift-to-Drag ratio Rigid Vehicle (MRV) is a candidate in the NASA multi-center effort to determine the most cost effective vehicle to deliver a large-mass payload to the surface of Mars for a human mission. Products of this effort include six-degree-of-freedom (6DoF) entry-to-descent trajectory performance studies for each candidate vehicle. These high fidelity analyses help determine the best guidance and control (G&C) strategies for a feasible, robust trajectory. This paper presents an analysis of the MRV's G&C design by applying common entry and descent associated uncertainties using a Fully Numerical Predictor-corrector Entry Guidance (FNPEG) and tunable Apollo powered descent guidance.
human↗