GENERAL ADAPTIVE GUIDANCE USING NONLTNEAR PRO CONSTRAINT SOLVING METHODS (FAST) Lisa Skalecki* and Marc Martin** Boeing Defense and Space Group Seattle, Washington objectives and constraints are satisfied, and modular software that can be used for a wide variety of vehicles and mission phases without recoding the on-board algorithm. Downloaded by UNIVERSITY OF NEW SOUTH WALES (UNSW) on October 27, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1991-2820 Abstract An adaptive, general purpose, constraint solving guidance algorithm called FAST (Flight Algorithm to Solve Trajectories) has been developed by the authors in response to t h e requirements for the Advanced Launch System (ALS). The FAST algorithm can be used for all mission phases for a wide range of Space Transportation Vehicles without code modification because of the general formulation of the nonlinear programming (NLP) problem, and the general trajectory simulation used to predict constraint values. The approach allows on board re-targeting for severe weather and changes in payload or mission parameters, increasing flight reliability and dependability while reducing the amount of pre-flight analysis that must be performed. The algorithm is described in general in this paper. Three degree of freedom simulation results are presented for application of the algorithm to ascent and reentry phases of an ALS mission, and Mars aerobraking. Flight processor CPU requirement data is also shown. Currently, there are no such systems operating in the field. However, in response to the requirements for the Advanced Launch System (ALS), an adaptive guidance algorithm called FAST (Flight Algorithm to Solve Trajectories) has been developed by the authors. The algorithm allows the vehicle to adapt to winds and atmospheric perturbations in flight, as well as autonomously retarget for changes in payload prior to launch. FAST combines nonlinear programming with the shooting method for two point boundary value problems to calculate a set of command profiles which satisfy the mission constraints. At each guidance update, the on board computer predicts the remainder of the mission by explicitly integrating the trajectory, and solves a nonlinear programming problem if p y of the mission constraints are violated. It has been coded such that it is efficient, general and modular. The FAST algorithm has been successfully used for closed loop guidance analysis for single and multi-stage vertical and horizontal take-off vehicles, low L/D r e -e n t r y and aerobraking. Introduction Current space transportation systems require extensive pre-flight analysis in order to generate and validate nominal trajectory profiles and guidance commands for a given mission. Often, multiple sets of command profiles must be generated pre-flight and stored in the on-board computer to ensure that the mission will not be delayed d u e to environmental conditions, contingencies, or minor last minute changes in mission objectives and constraints. This approach is operationally slow, complex and costly . Prior applications of nonlinear programming techniques to developing adaptive, autonomous guidance algorithms focused on optimization and concentrated on developing code for specific missions and vehicles. Reference 1 demonstrated that the NLP2 optimization package (Reference 2) could be used to determine closed loop guidance commands for a low L/D re-entry vehicle subjected to severe atmospheric dispersions and winds. That work dealt primarily with designing a nominal reentry command profile based on mission and range safety constraints, and developing a multilevel optimization strategy which defines a series of problems to be solved by the NLP2 optimization package. The computational requirements imposed on the flight processor by such an approach, however, are too large for near term application. In addition, while the NLP2 optimization package has been applied to An alternative approach is to make the vehicle more autonomous so that the nominal commands can be targeted and corrected by the vehicle's on-board computer, both prior to and during flight. This level of autonomy can be provided by an integrated guidance and targeting capability that utilizes trajectory optimization or constraint solving techniques to tailor the nominal commands such that the mission * Specialist Engineer, Member AIAA **Senior Engineer, Member AIAA Copyright 0 1991, American Institute of Aeronautics and Astronautics, Inc. All rights reserved. 1843 Downloaded by UNIVERSITY OF NEW SOUTH WALES (UNSW) on October 27, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1991-2820 closed loop guidance for other missions and vehicles (Reference 3). separate sets of code had to be developed and maintained for each because the code was not generalized to handle a wide variety of vehicles or missions. Analysis showed that using constraint solving only, rather than optimizing an objective function subject to constraints, resulted in feasible CPU requirements as well as improved targeting accuracy for low L/D re-entry. The FAST constraint solving guidance algorithm was then developed based on the NLP approach of Reference 1 with the additional requirements that the code be: 1) modular and general such that it can be applied to many types of vehicles and missions without recoding 2) computationally efficient such that is is feasible for real time implementation on a currently available flight processor 3) robust such that it can be applied to problems such as retargeting for weather, changes in payload, inclination etc., without extensive pre-flight analysis. The FAST guidance algorithm currently offers advantages not only over other NLP implementations, but also over other guidance approaches such as calculus of variations (COV), finite element methods, and collocation. COV approaches, such as the GUIDE algorithm described in Reference 4, provide the capability to efficiently generate optimal trajectories for closed loop guidance. They are, however, limited in that they must be explicitly recoded for each application and mission. While symbolic manipulation algorithms can be used to make the process more efficient, an "expert" level of human effort is required and separate algorithms would have to be coded for each mission as well as each phase of the mission (ascent, re-entry). Another optimal control approach based on finite element methods and the weak Hamiltonian principle is described in Reference 5. While it was demonstrated that the weak Hamiltonian approach could accurately and efficiently s o l v e trajectory optimization problems, again, the method implies that separate sets of code must be developed for each particular problem. Another disadvantage is that the weak Hamiltonian formulation has not yet been developed to the extent that it can handle inequality constraints. solution in the presence of large dispersions. However, work to date has shown that they are too computationally demanding for near term guidance application. Improvement in flight processor speeds and s p a r s e nonlinear programming methods are necessary before such methods become feasible for real time application. The key to developing cost effective, adaptive and autonomous guidance algorithms is that they be general as well as efficient. The cost of software design is not minimized if the software has to be recoded for new vehicles, missions, or such simple changes as new constraints. Nonlinear programming shooting methods have traditionally been CPU intensive and therefore not considered feasible for real time application. The IUS Gamma Guidance algorithm (Reference 7), which uses nonlinear programming for exoatmospheric g u i d a n c e , uses analytic relationships rather than the shooting method to evaluate the sensitivity of the constraints to the command variables. The shooting method is used during the iterative steps taken by t h e algorithm. While this approach works well for exo-atmospheric application, it is difficult to derive general and accurate analytic sensitivity matrices for endo-atmospheric flight. Recent improvements in flight processor speeds have eliminated the need for this simplification, e enabling shooting methods to become feasible. I n this paper we present a nonlinear programming, constraint solving algorithm that uses the shooting method and is feasible for on board guidance with currently available flight processors. The algorithm is easily applied to a variety of missions and vehicles. The key to developing this algorithm was designing an efficient, general trajectory simulation a n d modularizing the software. This was accomplished by using modern programming languages and techniques, and considering t h e implications of flight processor timing requirements during algorithm development. FAST Guidance Algorithm Overview The FAST adaptive guidance algorithm can be used to solve linear and/or nonlinear, equality and/or inequality constraints imposed at specific points or over regions of flight. The algorithm essentially has three components: 1) Constraint Solving Non-Linear Programming Algorithm 2) General 3 DOF Vehicle Simulation 3) Guidance Executive Logic Collocation methods such as those described in Reference 6 are promising, as they can be generalized, and can reliably converge to a 1844 Inputs to the guidance algorithm required prior to flight are obtained from a mission data load, which defines the current mission objectives and constraints, and the on-board database, which contains vehicle specific data such as aerodynamic characteristics, etc. During flight, the guidance algorithm requires the current vehicle state to initialize the guidance simulation. This includes the current time, position, velocity, propellant levels, and command values. Position and velocity i s obtained from the navigation system while current propellant levels are estimated based on the number of engines operating. Command values (such as the position of flaps, etc) are obtained from other sensors. Output consists of the table of guidance commands, which is used by the control system. The constraint solving algorithm is loosely based on a subroutine in the NLP2 optimization package which is used to find a feasible point before optimizing. The problem is to solve for the n command variables u such that the m constraint equations: Ce ( x, u, t ) = 0 Ci ( x, u, t ) 2 0 (Equality constraints) (Inequality constraints) Downloaded by UNIVERSITY OF NEW SOUTH WALES (UNSW) on October 27, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1991-2820 are satisfied, where x is the state of the vehicle and t is time. The constraint values are predicted using an explicit 3 degree of freedom trajectory simulation with a 4th order Runge-Kutta integrator, which has been generalized to allow application to a wide variety of environments and vehicles. The environmental models allow general oblate planet models, atmospheres, and winds to be included in the guidance trajectory predictor. The vehicle models allow multiple stages, multiple engines, and complex descriptions of the aerodynamic force a n d moment coefficients. The mission is simulated as a series of events, which represent changes in the environmental or vehicle definition. A static moment balance option, which gimbals the engines to balance the aerodynamic moment in the pitch and yaw planes, increases simulation accuracy for non symmetric configurations. Vehicle attitude may be specified using inertial euler angles, relative euler angles, o r aerodynamic angles. The guidance executive logic includes the code used to read and process the guidance input file, which models the on-board database and mission data load, and controls communication between the guidance algorithm and the onboard computer. The algorithm makes minimal assumptions on the vehicle characteristics, steering command profiles, mission objectives or constraints. These parameters are obtained either from the onboard database or /mission data load, which can "be standardize to p r o v i d e operational efficiency. Bas'cally, the modular guidance approach is similqr to the concept of a fighter pilot loading a tape of his flight plan - he doesn't need to remove and reprogram his on-board computers. The mission data load (information that changes depending on mission or day of launch) is minimized because the vehicle would be able to autonomously target the initial flight profile on-board prior to launch from a set of standard nominal command profiles stored in the on-board database. 3 The algorithm can be applied to a wide variety of vehicles and missions because of the capability to define variables, equations, and tables within an on board database or mission data load. A standard equation reader has been built into the algorithm, with multidimensional table lookups treated as standard functions. Therefore, the basic trajectory sirnulation modelled within the algorithm can be easily extended with user defined constants, variables, and integrals. Figure 1 shows a portion of the guidance input file used to simulate the mission data load and on-board database for closed loop computer simulations, to illustrate how easy it is to define the mission and the constraints. The guidance command tables are initialized in the COMMAND section. Inertial pitch angle (inpitch) and inertial roll angle (inRoll) are standard commands for launch vehicles. Anything that makes sense and has an effect on the vehicle's flight can be commanded. The sign designates commands that the guidance can vary to satisfy the constraints, while an "=" sign designates a fixed value that cannot be altered. The mission constraints are defined in the CONSTRAINT section. Constraints can be standard trajectory variables or user defined Since the algorithm can predict the remaining trajectory, commands are generated to the e n d of the mission or phase, resulting in a table of commands rather than simply instantaneous commands (See Table 1). This table is modified during each guidance update if any constraints are not satisfied. The control system then can get instantaneous commands by interpolating from this table. This feature aids in increasing flight reliability, since a set of converged guidance commands is always available for the entire mission. "-" 1845 varied (eg. drop booster weight at "dropBoost" event), and are designated by "+" signs on the graphics. The inertial pitch angle is commanded at 12 "nodes" along the trajectory, while the inertial roll angle is commanded at only 5 nodes. Downloaded by UNIVERSITY OF NEW SOUTH WALES (UNSW) on October 27, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1991-2820 variables. The example shown in Figure 1 is for a vehicle delivering a payload to a 28.5 degree orbit with perigee at 80 nautical miles. Note that this is an input file, and modification or recompilation of the guidance algorithm is not required to create new variables, events, or constraints. The retargeted trajectory satisfies all of the mission constraints, and the vehicle is ready to be launched. The algorithm used 3.04 CPU seconds to perform the pre-launch targeting shown in Figure 2, assuming a MIPS R3000 flight processor with a 20 MHz clock rate. The FAST algorithm is written entirely in Modula-2 (Reference 8), a modern programming language based on Pascal. Use of Modula-2 has allowed the on-board database and mission data load to be modelled in a format that is easy to read and understand (See Figure l), as well as allowing a general, yet efficient, high fidelity trajectory simulation to be developed. Modula-2 is very similar to Ada, and is, in fact, often used as an Ada training tool. This feature will simplify the eventual conversion of the algorithm to Ada for implementation on a flight processor. The benefit of using Modula-2 for algorithm development is that it is easier to learn than Ada and does not have the slow compilation or overhead of Ada, which allows rapid prototyping on time shared computers. The results of guidance dispersion analysis on the two stage ALS launch vehicle ascent trajectory are tabulated in Table 2. The nominal reserve propellant for this case is 12699 lbs, with approximately 5200 lbs allocated for dispersions (the rest is for engine out). The vehicle follows open loop commands during first stage flight. The FAST guidance algorithm performs updates every 20 seconds after booster separation. The guidance injection accuracy requirements for the generic ALS launch vehicle are: To demonstrate the FAST adaptive guidance algorithm, results of three degree of freedom closed loop simulations are presented for a generic ALS launch vehicle, a low L/D re-entry vehicle and an aerobraking vehicle. The algorithm has also been successfully applied to single stage to orbit (SSTO) vertical and horizontal take-off. apogee perigee inclination +/- 1 nm +/- 1 nm +/- 0.1 degree Rote that the algorithm is relatively insensitive to the dispersions, resulting in small injection accuracy e r r o r s and r e s e r v e propellant requirements within the allocated margin, Therefore, the overall GN&C injection accuracy error will be primarily due to navigation errors (particularly errors in knowledge of the engine cut-off velocity), which cannot be corrected by guidance. ALS Ascent The closed loop simulation that incorporates t h e FAST guidance algorithm includes interactive graphics capability. Figure 2 shows a screen dump of the algorithm in target mode for ALS ascent application. Prior to launch, the vehicle's on-board computer would be able to retarget the initial standard optimal trajectory stored in the database for current weather conditions or changes in payload, etc. Figure 3 shows the detailed results from the 100 closed loop simulations through winter dispersed GRAM (Global Reference Atmospheric Model) winds and atmospheres. The FAST guidance algorithm is given only the monthly mean wind and atmosphere profile in order to predict the trajectory. The actual vehicle flies through the dispersed profiles. Note that the resulting apogee, perigee and inclination errors are well within the guidance tolerances. While q-alpha and q-beta were not imposed as guidance constraints for this example, their resulting maximum values were monitored and plotted. The ALS vehicle used for this example can tolerate q-alphas near 6500 p,sf-deg. The constraints imposed are listed on the left side of the screen. When a constraint is satisfied a "*" is shown after the constraint value. The number of function evaluations, which includes evaluations to form the Jacobian matrix, is shown above the constraint values. The Jacobian is the matrix of sensitivities of the constraints to perturbations in the command variables and is used by the constraint solver to update the command tables. The resulting reserve propellant is shown in Figure 3 to illustrate that the constraint solver does not drive the solution away from the optimum. Thus, adding optimization of Events are used to define the steering command nodes as well as points along the guidance simulated trajectory where input data is to be 1846 Downloaded by UNIVERSITY OF NEW SOUTH WALES (UNSW) on October 27, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1991-2820 parameters such as final reserve propellant would only increase the amount of CPU used per update, with negligible impact on the final injection accuracy and actual reserve propellant. Optimization would only serve to improve t h e pre-launch or on-orbit targeting capabilities, and will eventually be added to the FAST algorithm for these purposes only. Reference 1 where the third phase angle of attack command was not used until the vehicle was actually flying in the third phase. The use of nodes, as done here with the FAST algorithm, rather than phases of constant commands, as done in Reference 1, allows greater flexibility in defining a strategy. During ascent, guidance update rates are on the order of 20-30 seconds. Table 2 and figure 3 illustrate that the maximum CPU used for each dispersed case is well below 2 seconds. The CPU intensive guidance updates occur early in the ascent phase where the atmospheric and wind effects have the most impact and the predicted trajectories are the longest. A two second delay in obtaining the updated guidance command tables has a negligible effect on the final accuracy since any errors incurred due to t h e delay are corrected in later updates. To verify this, the closed loop simulation was modified to implement a computer delay such that the updated guidance commands could not be used until the CPU time required for processing h a d elapsed. There was no significant change in orbital injection accuracy, CPU requirements, or constraint values. The constraints imposed on the re-entry problem are the aeromaneuver terminal latitude and longitude error in nautical miles at 15,000 ft altitude, as well as the maximum bank angle rate. Figure 4 shows two sets of targeting errors for 100 closed loop simulations through GRAM dispersed winter winds and atmospheres. Both sets use vehicle atmospheric angle of attack and bank angle command profiles as guidance variables. For the first case, the guidance uses monthly mean wind and atmospheric data, and is able to guide the vehicle to within 1.5 nm of the target. The second case utilizes a ground or aircraft based lidar system which measures a n d uplinks the eastward and northward wind components from 0 to 60,000 f t altitude. With the lidar system, the FAST guidance algorithm is able to obtain pinpoint accuracy (within 0.02 nm 122 ft) for all 100 cases. - Low L/D R e - e m e The constraint solving algorithm was also applied to re-entry of a generic, low L/D (-0.2) vehicle. Re-entry typically consists of a de-orbit burn to t h e proper re-entry orbit, an aeromaneuver phase, and a parachute or other terminal guidance phase. The goal is to minimize the aeromaneuver targeting error so that recovery operations are simplified, reducing the operating cost of the system. The FAST guidance algorithm can also be applied to high L/D re-entry. For this application, however, the bank angle should not be directly commanded due to its highly nonlinear nature. An alternate command, such as the vertical or horizontal component of the L/D, is more linear and therefore would be more reliable. Mars Aerobraking The FAST algorithm has also been applied to an aerobraking Mars mission with a vehicle L/D of 0.5. The approach trajectory is a hyperbolic orbit with C3 (twice the specific mechanical energy) of 50 k m 2 / s e c 2 . The targeted final orbit is highly elliptic (3644 km by 37183 km radius). The imposed constraints are velocity at periapsis to give the correct apoapsis, the final inclination (30 deg), the final longitude of ascending node (0 deg), and the maximum bank rate (30 deg/sec). The bank angle at 18 nodes is used as the guidance command, with a fixed angle of attack. During the aeromaneuver phase, the guidance commands consist of the bank angle and angle of attack at various nodes along the trajectory. Low L/D, precision re-entry is a much more difficult problem than ascent. As the vehicle approaches the target, it loses control authority (the bank angle and angle of attack become less effective) and experiences severe atmospheric and wind perturbations. This is in contrast to the ascent case, where atmospheric and wind perturbations are less significant since the vehicle exits the sensible atmosphere as it approaches the target. Figure 5 shows resulting trajectories for flight through 5 different atmospheres including t h e Viking1 and Viking2 measured atmospheres. The guidance has information only on the mean (Marsnhme) atmosphere. The resulting delta-V required to correct the final apoapsis and periapsis are shown as well as the resulting inclination errors, argument of periapsis errors Therefore, the guidance commands at each node are not always active. Instead, commands near the end of the trajectory are reserved for use during later updates, so that corrections made during upper atmospheric flight do not saturate the commands near the end of the trajectory. 1847 ascent, re-entry and aerobraking missions for a variety of space transportation vehicles. The same algorithm was used for all of the applications, with no recoding required in order to perform the analysis, demonstrating that a single guidance algorithm can be used for all mission phases as well as for a wide variety of vehicles. Downloaded by UNIVERSITY OF NEW SOUTH WALES (UNSW) on October 27, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1991-2820 and longitude of ascending node errors. Since there were no specified accuracy requirements when this study was performed, the constraint tolerances were arbitrarily set at 50 m/sec, 1 deg and 1 deg respectively for velocity at periapsis, inclination and longitude of ascending node constraints. Figure 6 shows results of 100 closed loop simulations through dispersed winds and atmospheres generated using the MarsGRAM (Reference 10) model for a low density day. The statistical mean and standard deviation, assuming a normal distribution, are also shown for each parameter. The CPU data presented for applications of the FAST guidance algorithm demonstrates that nonlinear programming shooting methods are feasible for current flight processor implementation. Restrictive approaches that involve using analytic sensitivity matrices are no longer advantageous. In view of the historically rapid improvement in processor speed, CPU requirements will become even less of an issue in the years to come. The benefits to operational efficiency and in-flight reliability of a general approach such as the FAST algorithm are too significant to ignore. T h e ability to autonomously and quickly perform pre-launch targeting within the vehicle's flight computer simplifies the ground operations (no need to upload a new solution since the computer can generate the retargeted solution by itself) and increases the launch reliability and dependability (the vehicle can retarget for actual environmental conditions). The resulting inclination and longitude of ascending node errors are well within t h e specified tolerances of 1 deg. While the argument of perigee was not constrained, as there was insufficient control authority using only the bank angle profile for guidance commands, the results show that 'the. errors are at least bounded. Further research is required to determine an approach for actively constraining the argument of perigee. The resulting delta V's to correct the final orbit are relatively small, indicating that the FAST guidance algorithm is a good candidate for application to aerobraking flight. The maximum CPU used per run is also plotted, again assuming a MIPS R3000 processor with a 20 MHz clock rate. The guidance update rate varies from 5 to 20 seconds during the aeromaneuver phase. While 2 CPU seconds may seem to be rather large for an update rate of 5 seconds, it is important to keep in mind that processors historically double in speed every 18 months on the average. Figure 7 shows the historical trend for MIPS CMOS processors and VAX CMOS processors. CMOS processors do not r e q u i r e cooling, so their performance can be related to flight processor performance. 0 However, while the shooting method works well when the initial estimate of commands is close enough to the actual solution, and the constraints are well behaved, it is difficult to apply to problems where a reasonable estimate of the solution is not available. An example of this is engine out during ascent. Unless multiple initial command profiles are stored pre-flight, or some correction factor is developed and applied to the stored profile in order to force the initial guess to be in the neighborhood of the final solution, the algorithm may not be able to converge. A solution to this problem is to utilize multiple shooting, which is more capable of solving problems with poor initial estimates, or highly nonlinear constraints. This would further increase the reliability and autonomy of the algorithm. Multiple shooting takes advantage of knowledge of the form of the state vector as a function of time, which, for guidance application, can be taken from the previous update. The application of multiple shooting to guidance is the subject of another paper by the authors (Reference 11). Another advantage to using the FAST constraint solving guidance algorithm for missions such as this is that it can also be used for re-entry. Thus, the same algorithm can be used for landing on Mars. This reduces the amount of on board software that must b e coded and validated. The only additional data required is defining the target conditions, constraints and commands that should be used to guide the vehicle during re-entry. These are all part of the mission data load. Conclusion The FAST constraint solving, adaptive guidance algorithm has been successfully applied to 1848 References 1. Cramer, Bradt, and Hardtla, "NLP Re-entry Guidance: Developing a Strategy for Low L/D Vehicles", AIAA-88-4123-CP, AIAA Guidance, Navigation and Control Conference, August 1988. 2. Betts, John T., "Nonlinear Programming Algorithm NLP2 Documentation", The Aerospace Corporation, April 1987. Downloaded by UNIVERSITY OF NEW SOUTH WALES (UNSW) on October 27, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1991-2820 Command tables at time = 24 seconds 3. Cramer, Bradt and Hardtla, "Launch Flexibility Using NLP Guidance and Remote Wind Sensing", AIAA-90-3330-CP, AIAA Guidance, Navigation and Control Conference,. August 1990. 4. Tylee, and Hardtla, "Adaptive Guidance for Future Launch Vehicles", AIAA-88-4124CP, AIAA Guidance, Navigation and Control Conference, August 1988. 5. Hodges, Calise, Bless and Leung "A Weak Hamiltonian Finite Element Method for Optimal Guidance of an Advanced Launch Vehicle", American Control Conference Proceedings, 1989. 6. Bradt, Jessick, Hardtla, "Optimal Guidance for Future Space Applications", AIAA-872401-CP, AIAA Guidance, Navigation and Control Conference, August 1987. 7. Hardtla, John, "Gamma Guidance for the Inertial Upper Stage (IUS)", AIAA-78-1292, AIAA GN&C Conference, 1978. 8. Wirth, Nicklaus, "Programming in Modula2", 3rd edition, Springer-Verlag, New York, 1985. 9. time inpitch inRoll 25.0 30.0 68.2 11 2.7 155.9 180.3 205.4 229.7 251 .O 271.7 292.4 313.2 333.9 -17.4 -20.8 -46.7 -69.9 -80.0 -79.4 -87.1 -92.8 -96.8 -99.6 -103.2 -1 06.4 -1 09.6 -90.9 -91.o -91.3 -91.6 -91.6 -91.6 -91.7 -91.7 -91.7 -91 .8 -91.8 -91.8 -91.9 Table 1 : Sample FAST Comn md Tables On Board Database: ( - means command t h a t g u i d a n c e c a n v a r y ) COMMAND 0 DEFINE i n P i t c h AT f i r s t AT c l e a r T o w e r AT d r o p B o o s t AT time230 AT d r o p F a i r i n g AT time350 AT time400 AT t i m e 4 2 5 AT l a s t DEFINE inRoll AT f i r s t AT c l e a r T o w e r AT d r o p B o o s t AT d r o p F a i r i n g AT l a s t Justus, Fletcher, Gramling and Pace, "The NASAMSFC Global Reference Atmospheric Model", NASA Contractor Report 3256, 1980. = 0.000000EO = 0.000000EO - 74.873666 - 70.862320 - 81.765260 - 90.932520 - 97.843471 - 101.17229 - 103.89821 = - 180.00000 - 180.00000 -91.217530 - 91.350888 - 91.547421 -- = - Mission Data Load: CONSTRAINT AT l a s t AT l a s t AT l a s t AT l a s t AT l a s t 10. Johnson, James, Justus and Chimonas, "The Mars Global Reference Atmosphere Model (Mars - GRAM)", Technical Report for NASA Grant No NAG8-078, October, 1989. coreprop > 5000 height 80 0 inFlight = ink1 = 25766.0 inclination = 28.5 AUXILIARY DEFINE h e i g h t DEFINE qAlpha 11. Skalecki, L., and Martin, M., "Application of Multiple Shooting to Closed Loop Guidance", I A F -9 1 - 3 2 6 , IAF 42nd International Astronautical Congress, 1991. = = TOL TOL TOL TOL TOL = = 1 0.001 = 0.001 = 0.01 0.001 = ( r a d i u s - e q u a t o r b d ) /6076.1155 dynPres * a t t a c k Figure 1: Sample Database and MDL 1849 FLIGHT function final 22 ........................ , (clearTower) oostProp coreprop - 400000 21745.32* 25766.00 * i n c l i n a t i o 28.50000* Downloaded by UNIVERSITY OF NEW SOUTH WALES (UNSW) on October 27, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1991-2820 ................ ,................500000 Retargetedbrajectory f i n a l t r a j e c t o r y with outputs.. Figure 2: ALS Ascent Targeting * Table 2: ALS Ascent 1850 . Max CPU (sec) vs Run I D 150 200 250 Reserve P r o p ( a s ) vs Run I D , : Downloaded by UNIVERSITY OF NEW SOUTH WALES (UNSW) on October 27, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1991-2820 1080 2060 3040 , j . . j ; i i j 4020 P e r i a e e E r r o r vs ADOUM E r r o r h m ) 150 200 250 I n c l i n a t i o n E r r o r (deg) vs Run I D - 0.25 0 150 0.25 U 2 00 250 AM Dispersions WITH BANK AND ANGLE OF ATTACK CONTROL WITH BANK, ANGLE OF ATTACK CONTROL, AND LIDAR 2 2 s i h h E Y Y L2 E o t 1 o t longitude error (nm) longitude error (nm) erornanuever Figure 4: LOW LI 1851 Guldance knows Marsnhme, Vehlcle flles through: -..-... MARSNHME COSPARVL xrmmm 100 VIKING1 ...... VIKING2 3M) 200 COSPARVH TIME (sec) Downloaded by UNIVERSITY OF NEW SOUTH WALES (UNSW) on October 27, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1991-2820 I ! I DeltaV IncErr ArgPerErr (m=)(deg) -200 l i ........... 1...................... 100 200 i ......... 300 100 TIME (sec) LonAsc NCdeER 6%) (deg) MARSNHME 17.3 -.008 -.018 -.WOO5 COSPARVL 125.2 ,139 -5.6 ,056 COSPARVH 248.7 .i49 4.5 ,015 ,042 1.4 ,002 VIKING1 89.6 VIKING2 40.5 -.024 -.0004 -.8 200 300 TIME (sec) Figure 5: Mars Aerocapture Guided Trajectories C3 = 50 I1A..................I .................. i RG PFR ERROR : Mean 2 .................i.................. ...... ..... -2M)oo 125 150 175 -0.051, Slarna = 0.643 deg ..... I ........... ................... I RUNID 125 150 RUNID 175 39 deg 150 .................. L 125 150 I 175 125 5 deg 150 175 RUN ID MAX GPU : Mean = 1.99. Siarna = 0.456 sec 3 .................................... i................. j,.................. .................. .................. :................................ : 0 125 1852 150 o : 0 RUNID Downloaded by UNIVERSITY OF NEW SOUTH WALES (UNSW) on October 27, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1991-2820 40 30 20 10 Introduction Date .* lntr 1853 n

1/--страниц