Post on 22-May-2018
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Lecture Lecture Lecture Lecture –––– 3333
Optimal Guidance using Optimal Guidance using Optimal Guidance using Optimal Guidance using
Model Predictive Static Programming (MPSP)Model Predictive Static Programming (MPSP)Model Predictive Static Programming (MPSP)Model Predictive Static Programming (MPSP)
Prof. Radhakant PadhiProf. Radhakant PadhiProf. Radhakant PadhiProf. Radhakant Padhi
Dept. of Aerospace Engineering
Indian Institute of Science - Bangalore
Prof. Radhakant Padhi, AE Dept., IISc-Bangalore 2
Outline
� Philosophical overview of guidance
� Applications in Missile Systems
• Strategic Missile Guidance
• Tactical Missile Guidance
� Applications in Space Missions
• Reentry Guidance of a Reusable Launch Vehicle
• Formation Flying of Satellites
• Soft-landing on Moon
� Summary
2
Guidance of Aerospace Vehicles: Guidance of Aerospace Vehicles: Guidance of Aerospace Vehicles: Guidance of Aerospace Vehicles:
A Philosophical OverviewA Philosophical OverviewA Philosophical OverviewA Philosophical Overview
Prof. Radhakant PadhiProf. Radhakant PadhiProf. Radhakant PadhiProf. Radhakant Padhi
Dept. of Aerospace Engineering
Indian Institute of Science - Bangalore
Achievement in Aerospace:
A Remarkable Journey
� Early attempts: Lot of failures
� "Heavier-than-air flying machines are impossible" - Lord
Kelvin, President, Royal Society, 1895.
� Right Brothers’s first flight: 1903
� History of Flight: Approx. 100 years
� Currently: 1,00,000 flights carrying more than 15 million
passengers daily!
� 37.6 million commercial aircraft flights globally transported more
than 3.5 billion passengers in 2015 with no accident (IATA)
� Quickest & Safest mode of transport
� Other aerospace vehicles: Military aircrafts, missiles, launch
vehicles, spacecrafts, UAVs, MAVs etc.
� Key Enabling Technology: Guidance and Control
20 September 2016 Prof. Radhakant Padhi, AE Dept., IISc-Bangalore 4
3
Navigation, Guidance and Control
� Navigation
• Determination of position and velocity (both
translational and rotational) from sensors
� Guidance
• Online determination of the path to be
followed for mission success
� Control
• Achieving the commanded guidance by
appropriate actuator action accounting for the
flight dynamics20 September 2016 Prof. Radhakant Padhi, AE Dept., IISc-Bangalore 5
Prof. Radhakant Padhi, AE Dept., IISc-Bangalore 620 September 2016
Guidance
4
Prof. Radhakant Padhi, AE Dept., IISc-Bangalore 7
Guidance? What is it??
Question: What is R(s)? How to design it??Unfortunately, books remain completely silent on this!
Controller
H(s)
20 September 2016
Guidance
Mission Objective
APPLIED OPTIMAL CONTROL & STATE
ESTIMATION Prof. Radhakant Padhi, AE Dept., IISc-8
Fundamental Problem of
Strategic Missile Guidance
Guidance
phase
5
APPLIED OPTIMAL CONTROL & STATE
ESTIMATION Prof. Radhakant Padhi, AE Dept., IISc-9
Fundamental Problem of
Tactical Missile Guidance
LOS
M
T
APPLIED OPTIMAL CONTROL & STATE ESTIMATION
Prof. Radhakant Padhi, AE Dept., IISc-Bangalore10
Missile Guidance Laws
� Many classical guidance laws are inspired from “observing nature” (e.g. Proportional Navigation (PN) guidance law is based on ensuring “collision triangle”)
� Control theoretic based guidance laws are usually based on “kinematics” and/or “linearized dynamics”. Hence, they are usually not very effective!
� Nonlinear optimal control theory is a “natural tool” to obtain effective missile guidance laws
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MPSP for Strategic Missile GuidanceMPSP for Strategic Missile GuidanceMPSP for Strategic Missile GuidanceMPSP for Strategic Missile Guidance(with solid motors)(with solid motors)(with solid motors)(with solid motors)
Prof. Radhakant Padhi
Dept. of Aerospace Engineering
Indian Institute of Science - Bangalore
Prof. Radhakant Padhi, IISc-Bangalore 12
Fundamental Problem of
Strategic Missile Guidance
Guidance
phase
20 September 2016
7
Prof. Radhakant Padhi, IISc-Bangalore 13
Introduction:
Liquid Engines vs. Solid Motors
Liquid Engines
� Quick firing is not possible
� Sloshing and TWD effect
� Higher cost
� Thrust cut-off facility
� Burnout time is certain
� Manipulative T-t curve
� Guidance is easier
Solid Motors
� Quick firing is possible!
� No sloshing and TWD effects
� Lower cost
� No thrust cut-off facility
� Burnout time is uncertain
� Non-manipulative T-t curve
� Guidance is difficult..!
20 September 2016
Prof. Radhakant Padhi, IISc-Bangalore 14
System Dynamics
: Local radius
: Velocity
: Flt. path angle
: Range angle
: Shear angle
(guidance parameter)
20 September 2016
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Prof. Radhakant Padhi, IISc-Bangalore 15
Free-Flight and Hit Equation
FF Equation Hit Equation
Reference: P.Zarchan, Tactical and Strategic Missile Guidance, 5th Edition, AIAA, 2007.
20 September 2016
Prof. Radhakant Padhi, IISc-Bangalore 16
Numerical Result:With Nominal Thrust
20 September 2016
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Prof. Radhakant Padhi, IISc-Bangalore 17
Numerical Result:With Uncertainties in Motor Performance
20 September 2016
Prof. Radhakant Padhi, IISc-Bangalore 18
Numerical Result:With online re-adjustment of Thrust-time curve
20 September 2016
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Prof. Radhakant Padhi, IISc-Bangalore 19
Comparison Between MPSP and
Nonlinear Programming
Cost function computation
0 20 40 60 80 100 120 140 1600
5
10
15
Time (sec)
Thru
st d
eflection a
ngle
(deg)
NLP
MPSP
20 September 2016
Prof. Radhakant Padhi, IISc-Bangalore 20
A Hybrid Design For Energy-
Insensitive Guidance
� Step 1: Assume that the motor is guaranteed to burn up to a certain duration of predicted burnout time (say 90%). Design the MPSP Guidance
� Step 2: Switch over to Dynamic inversionguidance, which assures that the free flight equation is satisfied for the remaining time continuously.
� Motivation: To eliminate VTP requirement
20 September 2016
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Prof. Radhakant Padhi, IISc-Bangalore 21
Numerical Results:MPSP + Dynamic Inversion
Height Error at the Target
20 September 2016
MPSP Guidance of AntiMPSP Guidance of AntiMPSP Guidance of AntiMPSP Guidance of Anti---- Ballistic Tactical Ballistic Tactical Ballistic Tactical Ballistic Tactical
Missiles under Partial IGC FrameworkMissiles under Partial IGC FrameworkMissiles under Partial IGC FrameworkMissiles under Partial IGC Framework
Prof. Radhakant Padhi
Dept. of Aerospace Engineering
Indian Institute of Science - Bangalore
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Prof. Radhakant Padhi, IISc-Bangalore 23
Missile for missile (air) defense:
A typical engagement scenario
20 September 2016
Prof. Radhakant Padhi, IISc-Bangalore 24
Challenges
� Very high speed targets
• Very less engagement time
• Very high line-of-sight rate
� Zero/Near-zero miss distance is desired
� Impact angle constraint (mission requirement)
� Directional warhead
� Latax saturation (due to less dynamic pressure) should be avoided
20 September 2016
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Prof. Radhakant Padhi, IISc-Bangalore 25
Three Loop Conventional Design Partial IGC Design
Philosophy of Partial Integrated
Guidance & Control (PIGC)
� Exploits the inherent time scale separation property between
faster rotational and slower translational dynamics
� Operates in a Two Loop Structure:
� Commanded body rates generated in outer loop – MPSP
� Commanded deflections generated in inner loop – Dyn. Inv.
20 September 2016
MPSP for Tactical Missile Guidance MPSP for Tactical Missile Guidance MPSP for Tactical Missile Guidance MPSP for Tactical Missile Guidance
with Impact Angle Constraintwith Impact Angle Constraintwith Impact Angle Constraintwith Impact Angle Constraint
Prof. Radhakant PadhiProf. Radhakant PadhiProf. Radhakant PadhiProf. Radhakant Padhi
Dept. of Aerospace Engineering
Indian Institute of Science - Bangalore
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Prof. Radhakant Padhi, IISc-Bangalore 27
Why Impact Angle Constrained
Guidance?
� Enhancement of warhead lethality (e.g. front-attack)
� Terminal trajectory shaping for attacking weak locations of targets (e.g. top attacks for tanks)
� Mission demand (e.g. bunker buster mission, terrorist hideouts in urban areas, water reservoir attack etc.)
� Coordinated attack by multiple munitions
� Countermeasure by enhanced stealthiness
� Range enhancement (indirectly)
� increase in observability of the target
20 September 2016
Prof. Radhakant Padhi, IISc-Bangalore 28
Motivations
� Classical (PN) guidance laws are usually adequate to assure small miss distance, but are silent on impact angle.
� Optimal control theory based techniques are available, but they rely on “linearized kinematics”…need to do better than that!
� The aim here is to develop a nonlinear optimal guidance law with 3-D impact angle constraints, using nonlinear point-mass dynamic models.
20 September 2016
15
Prof. Radhakant Padhi, IISc-Bangalore 29
Challenges
� Strong (nonlinear) coupling between elevation angle and azimuth angle dynamics should be accounted for.
� Zero/Near-zero miss distance requirement cannot be compromised.
� Impact angle constraints in 3D (i.e. two angle constraints at the same time) must be ensured.
� Latax demand has to be as minimum as possible.
20 September 2016
Prof. Radhakant Padhi, IISc-Bangalore 30
3D Engagement Geometry
20 September 2016
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Prof. Radhakant Padhi, IISc-Bangalore 31
Missile and Target Dynamics
Missile Model
State
Control
Target Model
20 September 2016
Prof. Radhakant Padhi, IISc-Bangalore 32
Assumptions about target
�
20 September 2016
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Prof. Radhakant Padhi, IISc-Bangalore 33
Stationary Targets
MPSP Vs. APN: A Comparison
Constraint in
single angle
20 September 2016
Prof. Radhakant Padhi, IISc-Bangalore 34
Stationary Targets
MPSP Vs. APN: A Comparison
Latax CommandsConstraint in
single angle
20 September 2016
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Prof. Radhakant Padhi, IISc-Bangalore 35
Stationary Targets:
Same initial conditions & Different
Terminal Constraints
Various
constraints in
both angles
20 September 2016
Prof. Radhakant Padhi, IISc-Bangalore 36
Stationary Targets:
Different initial conditions for Same
Terminal Constraints
Initial condition
perturbation
with same
terminal
constraint
20 September 2016
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Prof. Radhakant Padhi, IISc-Bangalore 37
Stationary Targets:
Perturbation in initial conditions
(Angle Histories)
20 September 2016
MPSP for ReMPSP for ReMPSP for ReMPSP for Re----entry Guidance of aentry Guidance of aentry Guidance of aentry Guidance of a
ReReReRe----usable Launch Vehicle (RLV)usable Launch Vehicle (RLV)usable Launch Vehicle (RLV)usable Launch Vehicle (RLV)
Prof. Radhakant PadhiProf. Radhakant PadhiProf. Radhakant PadhiProf. Radhakant Padhi
Dept. of Aerospace Engineering
Indian Institute of Science - Bangalore
Co-workers: Omkar Halbe, Scientist, Airbus, Germany and
S. Mathavaraj, Scientist, ISAC/ISRO, Bangalore
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Prof. Radhakant Padhi, AE Dept., IISc-Bangalore 39
Typical trajectory of a RLV
Reentry
Segment
Prof. Radhakant Padhi, AE Dept., IISc-Bangalore 40
Objective and Challenges
� Objective• To develop advanced nonlinear and optimal guidance
for a reusable launch vehicles (RLV) in the descent phase, with special emphasis on the critical re-entry segment.
� Challenges• Path constraints: Structural load, Thermal load, Angle
of attack boundary• Terminal constraints: Final position and velocity• Optimal online trajectory generation• Robustness wrt. uncertainties in parameters • Real-time computability, Smoothness in guidance
command etc.
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Prof. Radhakant Padhi, AE Dept., IISc-Bangalore 41
RLV Guidance using MPSP:
System Dynamics (Spherical Rotating Earth)Ref: Vinh et al., “Hypersonic and Planetary Entry Mechanics”, 1980
Reentry point
End Point
Curvilinear Abscissa
Kinematic Equations over Spherical Rotating Earth
Prof. Radhakant Padhi, AE Dept., IISc-Bangalore 4242
RLV Guidance using MPSP:
System Dynamics (Spherical Rotating Earth)Ref: Vinh et al., “Hypersonic and Planetary Entry Mechanics”, 1980
Dynamic Equations over Spherical Rotating Earth
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Prof. Radhakant Padhi, AE Dept., IISc-Bangalore 43
RLV Guidance using MPSP:
Problem Formulation
� Normalized State Vector
� Control Vector
� Output Vector
� Goals
Terminal
Coordinates
Intermediate
Control for
Bank Angle
Profile
Prof. Radhakant Padhi, AE Dept., IISc-Bangalore 44
RLV Guidance using MPSP:
Problem Formulation
Normalization of State Variables
� Absolute values of state variables are not of the
same order of magnitude
� May create disparity during the control and state
update process
� State variables are normalized using the desired
final values
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Prof. Radhakant Padhi, AE Dept., IISc-Bangalore 45
RLV Guidance using MPSP:
Performance Index Selection
“Soft” Path Constraints where
� Minimize normal load only if value close to bound
� Exponential weight of nominal NL profile to achieve this
� Minimize deviation (error) of updated profile from nominal one
� Maintain control profile in the vicinity of nominal profile
Prof. Radhakant Padhi, AE Dept., IISc-Bangalore 46
RLV Guidance using MPSP:
Performance Index Selection
� For smoothness, minimize distance CD
� Equivalent to minimizing distances AB, BD and AD
� AB is nominal profile
� Min (BD) = min (J2)
� Min (AD) = min (J3)
24
Prof. Radhakant Padhi, AE Dept., IISc-Bangalore 4747
RLV Guidance using MPSP:Nominal Trajectory with 8 Initial Conditions
Smooth Profile
Trim Bounds not
ViolatedStable Lateral Profile
Prof. Radhakant Padhi, AE Dept., IISc-Bangalore 4848
Guidance Simulation Results:8 Cases of Initial Condition Perturbations
Smooth Trajectories,
Terminal Constraints Met
25
Prof. Radhakant Padhi, AE Dept., IISc-Bangalore 4917 February 2010 49
Guidance Simulation Results:8 Cases of Initial Condition Perturbations
Path Constraints Met
1. Normal Load < 3g
2. Heat Flux < 60 W/cm^2
3. Dynamic Pressure < 25 kPa
Prof. Radhakant Padhi, AE Dept., IISc-Bangalore 50
Summary of Results
� MPSP is a potential technique to
implement for Re-entry guidance as it
leads to:
• Very good terminal accuracy
• Path-constraints are met
• Maximum normal load is below 3g at all time
• Bank-angle reversals are in the middle
• Shows good amount of robustness
• Computational time is small
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Satellite Formation Flying (SFF) Satellite Formation Flying (SFF) Satellite Formation Flying (SFF) Satellite Formation Flying (SFF)
through MPSPthrough MPSPthrough MPSPthrough MPSP
Prof. Radhakant PadhiProf. Radhakant PadhiProf. Radhakant PadhiProf. Radhakant Padhi
Dept. of Aerospace Engineering
Indian Institute of Science - Bangalore
Co-worker: Girish Joshi, Scientist, ISAC/ISRO, Bangalore
Satellite Formation Flying
Two or more satellites flying in prescribed orbits at a
fixed separation distance for a given period of time
forming a large virtual spacecraft
Trailing FormationCluster Formation
Constellation
(Image Source: en.wikipedia.org, newsscientist.com)
52Prof. Radhakant Padhi, AE Dept., IISc-Bangalore
27
Satellite Formation Flying:
Advantages & Objectives
� Advantages
• Higher redundancy: Improved fault tolerance
• On orbit configuration: Coordinated multi missions
• Lower individual launch mass: Reduced launch
cost and increased mission flexibility
• Minimal financial loss in case of failure
� Objectives
• Reconfigure the formation of satellites to new
desired relative orbit: Minimize terminal errors
• Minimize the control effort required
53Prof. Radhakant Padhi, AE Dept., IISc-Bangalore
System Dynamics and Problem
Formulation
Hill’s reference Frame:
• Chief Satellite Centered non inertial reference frame
54
h: Angular momentum Vector
Prof. Radhakant Padhi, AE Dept., IISc-Bangalore
28
Prof. Radhakant Padhi, AE Dept., IISc-Bangalore
55
System Dynamics
� Complete nonlinear SFF system dynamics (Hill’s Equations)
56
Formation flying of satellite using
MPSP:
State Vector
Control Vector
Output Vector
Final time(tf)
Selected from LQR method (time at
which tracking error becomes small)
Prof. Radhakant Padhi, AE Dept., IISc-Bangalore
29
Circular Chief Satellite Orbit:
Results and Discussion
57
Position Error units : km ; Velocity Error units : km/sec
Stateerror
LQR MPSP(Itr No. 5)
0.1683
0.00012
-0.1042
-0.0002
0.2003
0.00008
Prof. Radhakant Padhi, AE Dept., IISc-Bangalore
Results and DiscussionPosition States Error History LQR, MPSP
58
LQR MPSP
Prof. Radhakant Padhi, AE Dept., IISc-Bangalore
30
Results and DiscussionVelocity States Error History LQR, MPSP
59
LQR MPSP
Prof. Radhakant Padhi, AE Dept., IISc-Bangalore
Results and DiscussionControl History LQR, MPSP
60
LQR Control MPSP Control
Prof. Radhakant Padhi, AE Dept., IISc-Bangalore
31
Prof. Radhakant Padhi, AE Dept., IISc-Bangalore 61
Numerical Results:
Output Error Convergence
Error
in
states
Initial
Error
Iteration
1
Iteration
2
Iteratio
n 3
Iteratio
n 4
1.0e-
003
Iteration
5
1.0e-004
Iteration
6
1.0e-004
Iteration
7
1.0e-005
x 0.0275 0.0374 0.0214 0.0024 -0.0388 -0.7360 -0.1512 -0.1345
X_dot 0.0000 0.0001 0.0000 0.0000 0.0002 -0.0014 -0.0004 -0.0004
Y -0.0223 0.0832 0.0315 0.0047 0.1959 -0.8402 -0.2370 -0.2949
Y_dot -0.0000 -0.0000 0.0000 0.0000 0.0012 -0.0003 -0.0004 -0.0007
z 0.0456 -0.1314 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000
Z_dot 0.0000 -0.0000 0.0000 0.0000 -0.0000 -0.0000 -0.0000 -0.0000
Results and DiscussionComposite Plot for MPSP solution for different
initial conditions :
62Prof. Radhakant Padhi, AE Dept., IISc-Bangalore
32
Prof. Radhakant Padhi, AE Dept., IISc-Bangalore 63
Rendezvous (Docking)
VariableDesired Final States
Error in States(LQR)
Error in States(MPSP)
x -1.1086 km -56.1m 4 mm
y 2.0209 km 39.1m 9 mm
z 0.3579 km -57.1m 0 mm
x_dot 0.0006 m/s 0 m/s 1.3 mm/s
y_dot 1.4 m/s 0.1m/s 2.2 mm /s
z_dot 2.4 km/s 0m/s 0.0 m/s
Computational Time (in Matlab): Approx. 20 sec (for one iteration)
Prof. Radhakant Padhi, AE Dept., IISc-Bangalore 64
Summary of Results
� MPSP is a potential technique to
implement for Satellite formation flying
as it leads to:
• Very good terminal accuracy
• Less number of iterations
• Computational time per iteration is small
� Current/Future work
• Evaluation in a Real-time platform
• Possible implementation in hardware
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FuelFuelFuelFuel----Optimal Guidance of a Lunarcraft Optimal Guidance of a Lunarcraft Optimal Guidance of a Lunarcraft Optimal Guidance of a Lunarcraft
for Soft Landing on Moonfor Soft Landing on Moonfor Soft Landing on Moonfor Soft Landing on Moon
Prof. Radhakant PadhiProf. Radhakant PadhiProf. Radhakant PadhiProf. Radhakant Padhi
Dept. of Aerospace Engineering
Indian Institute of Science - Bangalore
Co-workers: Avijit Banerjee & Kapil Sachan, Students, IISc, Bangalore
66
A Typical Lunar Mission
Prof. Radhakant Padhi, IISc-Bangalore20 September 2016
34
67
Soft-Landing Mission
Prof. Radhakant Padhi, AE Dept., IISc-Bangalore
Alt
itu
de
18 km
100 m
4 m
100 km
0
4 x 800
2 x 800
Attitude Hold
Phase
Rough Braking Phase Precision
Braking Phase
50°
E
D
C
B
50°
A
Vv = 0 m/s
VH = 1690 m/s
Vv = 0
VH = 0
F
Down Range
10 km 4.2 km 0
Vv = 0 m/s
VH = 1630 m/s
Vv = 2m/s
VH = 0
2 x 800
Pitch-In Phase
Hovering
Phase
Final Descent
Phase
LIRAPLIRAP,
AltimeterLIRAP, Altimeter, Pattern Matching
Camera, Velocity Sensors LIRAP, Altimeter, Velocity
Sensors, HDA Camera
68
7 km
2 km
35
69
Problem to be Explored:
Optimal Soft-landing of Lunar Module
Prof. Radhakant Padhi, AE Dept., IISc-Bangalore
Objective
� To develop an optimal and robust Guidance algorithm for soft landing of the lander
� The algorithm should ensure:
• Soft landing at the designated site
• Minimum fuel consumption
• Non-violation of mission and hardware constraints
• Robustness for uncertainties (due to engine
misalignment, CG shift, fuel slosh etc.)
• Real-time computability for onboard implementation
Prof. Radhakant Padhi, AE Dept., IISc-Bangalore 70
36
System Dynamics in 2D
Prof. Radhakant Padhi, AE Dept., IISc-Bangalore 71
Prof. Radhakant Padhi, AE Dept., IISc-Bangalore 72
Objective: Fuel Minimization
� Minimum fuel consumption is ensured by maximizing
the landed mass, i.e. by minimizing
� However, minimization of Ja is equivalent minimizing
Jb, where
� So, the cost function selected is:
37
Terminal Vertical Orientation
Prof. Radhakant Padhi, AE Dept., IISc-
Bangalore
73
• To ensure the terminalvertical orientation
Control Weight Profile
Computation of guess control
� Considering The altitude as a function of time
� Considering initial and terminal conditions
Prof. Radhakant Padhi, AE Dept., IISc-Bangalore 74
38
Computation of guess control
(cont..)
� Considering the linear approximation of transversal velocity profile
� The control guess can be computed from following equations
Prof. Radhakant Padhi, AE Dept., IISc-Bangalore 75
Terminal Mass & Cost Function
Variation with Final Time
Prof. Radhakant Padhi, AE Dept., IISc-Bangalore 76
Variation of the mission cost w.r.t. final flight time
Maximum terminal
mass
Minimum cost
39
77
Optimal Flight Time:
� MPSP computes the fuel optimal guidance command
based on the selected final time
� To selection the optimal : a gradient based off line
computational method is formulated.
� To make the selection online: a neural net based
function learning is incorporated to account for the
variation of initial state of the lunar module.
Prof. Radhakant Padhi, AE Dept., IISc-Bangalore
Neural Net
Optimal flight time
20 September 2016 78
Optimal Flight Time:
� MPSP computes the fuel optimal guidance command
based on the selected final time
� To selection the optimal : a gradient based off line
computational method is formulated.
� To make the selection online: a neural net based
function learning is incorporated to account for the
variation of initial state of the lunar module.
Soft-landing of Lunar Lander
Neural
Net
Optimal flight time
40
Numerical Results: MPSP GuidanceNumerical Results: MPSP GuidanceNumerical Results: MPSP GuidanceNumerical Results: MPSP Guidance
Radhakant Padhi,Radhakant Padhi,Radhakant Padhi,Radhakant Padhi,
Avijit Banerjee, Kapil Sachan, Shyam Mohan Avijit Banerjee, Kapil Sachan, Shyam Mohan Avijit Banerjee, Kapil Sachan, Shyam Mohan Avijit Banerjee, Kapil Sachan, Shyam Mohan
Dept. of Aerospace Engineering
Indian Institute of Science – Bangalore
Simulation Results with Free
Terminal Attitude
20 September 2016 80
Altitude Profile
Soft-landing of Lunar Lander
Mass Profile
Mass consumption
45% of initial mass
41
Simulation Results:
20 September 2016 81
Radial velocity Profile
Soft-landing of Lunar Lander
Transversal velocity history
Numerical Convergence of
MPSP Guidance:
Normalized Terminal Error
Iteration I(normalized)
Iteration II(normalized)
Iteration III
Altitude
Range angle
Transverse
velocity
Radial
velocity
20 September 2016 Soft-landing of Lunar Lander 82
Algorithm
takes only 3
iterations to
converge
High
Terminal
accuracy is
ensured
Average computational time for the complete algorithm is 0.576728
second on “Matlab 2013a” platform
42
Simulation Results:
20 September 2016 83
Thrust magnitude history Thrust direction history
Soft-landing of Lunar Lander
The terminal body orientation constraints is not satisfied
Terminal Vertical Orientation
20 September 2016 Soft-landing of Lunar Lander 84
• To ensure the terminal vertical
orientation
Control Weight Profile
43
Simulation Results:
20 September 2016 Soft-landing of Lunar Lander 85
Thrust direction history
Altitude Profile
Th
rust d
ire
ctio
n
Simulation Results
20 September 2016 86Soft-landing of Lunar Lander
Mass Profile
• Terminal Mass of Module: 485kg (high mass consumption )
• Thrust limit is violated
Thrust magnitude history
44
Remarks:
� Orientation of module, with high
velocity is difficult and demands
more fuel.
� segment-I ensures the a desired
low velocity and altitude
� Terminal vertical orientation
considered during the followed by
segment.
20 September 2016 Soft-landing of Lunar Lander 87
S-I
S-II
Without angle
constraints With angle
constraint
18 km
7 km
Simulation results:
20 September 2016 Optimal Guidance for Soft Lunar Landing 88
Altitude Profile Mass profile
45
Simulation results:
20 September 2016 Optimal Guidance for Soft Lunar Landing 89
Radial velocity ProfileTransversal velocity history
Simulation results:
20 September 2016 Optimal Guidance for Soft Lunar Landing 90
Thrust magnitude historyThrust direction history
109N discontinuity
Thrust
Bound
46
Remarks:
� Orientation of module, with high
velocity is difficult and demands
more fuel.
� segment-I ensures the a desired
low velocity and altitude
� Terminal vertical orientation
considered during the followed by
segment.
20 September 2016 Soft-landing of Lunar Lander 91
S-I
S-II
Without angle
constraints With angle
constraint
18 km
7 km
Simulation Results:
20 September 2016 Soft-landing of Lunar Lander 92
Altitude Profile Mass profile
47
Simulation Results:
20 September 2016 Soft-landing of Lunar Lander 93
Radial velocity ProfileTransversal velocity history
Simulation results:
20 September 2016 Soft-landing of Lunar Lander 94
Thrust magnitude historyThrust direction history
48
Segmentation:
20 September 2016 Soft-landing of Lunar Lander 95
Initial Terminal Initial Terminal
Altitude 18km 7km 7km 100m
Range angle
Transverse
velocity
1692m/s 300m/s 300m/s 0m/s
Radial
velocity
0m/s -50m/s -50m/s 0.01m/s
Mass 934kg ----------------- 573.6 kg --------------
(495.5kg)
Segment I Segment II
Without terminal angel constraint With terminal angel constraint
PIL Simulation: GPIL Simulation: GPIL Simulation: GPIL Simulation: G----MPSP GuidanceMPSP GuidanceMPSP GuidanceMPSP Guidance
Radhakant Padhi,Radhakant Padhi,Radhakant Padhi,Radhakant Padhi,
Avijit Banerjee, Kapil Sachan, Shyam Mohan Avijit Banerjee, Kapil Sachan, Shyam Mohan Avijit Banerjee, Kapil Sachan, Shyam Mohan Avijit Banerjee, Kapil Sachan, Shyam Mohan
Dept. of Aerospace Engineering
Indian Institute of Science – Bangalore
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Texas Instruments’ TMS320C6748
Advantages of C6748:•Low power applications•Easy memory management•Scalable
Features of LCDK and C6748:•456 MHz C674x Floating point core•2 level cache based architecture•XDS100v2 JTAG debug probe
Processor Details
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Details:
Janani V., Kapil Sachan and Radhakant Padhi, “Validation of Lunar Landing G-MPSP Guidance from
PIL Studies”, Proceedings of IFAC Advances in control optimization of dynamical systems (ACODS)
2016.
Texas Instruments’ CodeComposer Studio(CCStudio V5)� Code Composer Studio
used for interfacing
between processor and
the PC.
� It comprises a C/C++
compiler, source code
editor, project build
environment, debugger
and other features.
Integrated Development Environment (IDE)
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PIL Simulation Procedure
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Quantitative results
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Concluding RemarksConcluding RemarksConcluding RemarksConcluding Remarks
Prof. Radhakant PadhiProf. Radhakant PadhiProf. Radhakant PadhiProf. Radhakant Padhi
Dept. of Aerospace Engineering
Indian Institute of Science - Bangalore
Prof. Radhakant Padhi, AE Dept., IISc-Bangalore 102
Concluding Remarks
� MPSP is a promising technique for optimal guidance
of aerospace vehicles
� Trajectory optimization philosophy is brought into
guidance design (with no hard constraints)
� It is not quite sensitive to the initial guess history of
control history.
� Various challenging aerospace guidance problems
have been (and are being) solved.
� There are interests in DRDO and ISRO to implement
it in various upcoming missions
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Prof. Radhakant Padhi, AE Dept., IISc-Bangalore 103