methodology for path planning with dynamic data driven ......methodology for path planning with...
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Methodology for Path Planning with Dynamic Data Driven Flight Capability Estimation
June 16, 2016
17th AIAA/ISSMO Multidisciplinary Analysis and Optimization ConferenceMAO-14: Emerging Methods, Algorithms, and Dynamic Data Driven Systems
Victor Singh, Department of Aeronautics and Astronautics, MITAdvisor: Prof Karen Willcox
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Emergence of Smart Skin Technologies
New sensing “smart” skin technologies can measure
Wind speed
Temperature
Shears and strains
Image Credit: http://www.unmannedsystemstechnology.com/2014/08/bae-developing-smart-skin-technology-to-detect-damage-on-aircraft/
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The DDDAS Paradigm
DDDAS: Dynamic Data Driven Application Systems
Feedback loop of data to computation and simulation
Computation and Simulation
System
Measurements
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Towards a Self Aware UAV
External signals
On board sensors
Damage
Sensors include: GPS, accelerometer, camera, laser, strain sensors
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Objectives
Develop a data-driven path planning approach at the vehicle level that
Integrates computation and simulation with online sensor data
Encompasses multiple sensor types
Accounts for model uncertainty and disturbances
Demonstrate proposed methodology on an example 3D path planning problem where a UAV learns it is damaged and must react accordingly
Quantify performance benefits
BackgroundMethodologyImplementationSimulation & ResultsConclusions & Future Work
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Problem Setup
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Background: Sensing and Detection
Operational Loads Monitoring (OLM)
Structural Health Monitoring (SHM)
[Willis2009, Staszewski2004]
Self-Aware UAV
Path Planner
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Background: Capability Estimation
Determine modified flight envelope using
Least squares
Filtering methods
Statistical inference
[Koolstra2012]
Parameters investigated
Handling: stability/control
Lift, drag, stall, center-of-gravity, and inertia shifts
[Kim2010, Menon2013]
Self-Aware UAV
Path Planner
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Background: Mission Planning
Numerous algorithms
Rapidly exploring random trees
Motion primitives & graph search
Probabilistic road maps
Potential/Navigation functions
Pseudospectral methods
Dynamic programming
[LaValle2006, Meuleau2009, Lopez2009, Ure2013,…]
Self-Aware UAV
Path Planner
BackgroundMethodologyImplementationSimulation & ResultsConclusions & Future Work
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Path Planning: Components
Transition Model
Measurement Model
Constraint Model
Optimization Problem
Goal Obstacles
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Vehicle State, Control, and Measurements
Vehicle State:
Kinematics:
Damage:
Total State:
Control:
Measurements:
kinematic quantities (e.g. GPS/IMU/Camera)
structural health quantities (e.g. Strain Sensors)
Data:
Strain sensors
LIDAR/Camera
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Transitions and Observations
Transition Model
Measurement Model
Uncertainty and disturbances
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The Belief State
Data grows (curse of history)
Represent with sufficient statistic, i.e. the belief state [Thrun2006, Bertsekas2005]
With transition
Observation Transition
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Path Planning: Components
Transition Model
Measurement Model
Constraint Model
Optimization Problem
Goal Obstacles
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Offline Phase: Design and Analysis
Different design conditions (FAA and Proprietary)
Maximum loads
Failsafe
Discrete source damage
Possible Damage Locations
Image Credit: ASWING v598
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Offline Phase: Design and Analysis
Performance parameter examples
Margins of safety (strain/loads)
Aerodynamic limits
Engine limits
This results in massive computational requirements
Surrogates ConstraintsDesign and
Analysis
Vehicle state, control, and damage
configuration
High Fidelity Physics Model
Performance parameter
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Offline Phase: Surrogates
Surrogates ConstraintsDesign and
Analysis
Vehicle kinematic state
Control
Damage configuration
Velocity
Bank angle
Feasible region
Infeasible region
[Lecerf2015]
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Offline Phase: Constraints
Surrogates ConstraintsDesign and
Analysis
In general, we do not know the damage state the vehicle takes online
Constraints adjust based on posterior damage state distribution
Dynamic capability
Vehicle kinematic state
Control
Measurement
Markov Assumption
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Path Planning: Components
Transition Model
Measurement Model
Constraint Model
Optimization Problem
Goal Obstacles
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CPOMDP Formulation
We formulate the planning problem as a Constrained Partially Observable Markov Decision Process (CPOMDP) [Kaebling1998]
Formally, a CPOMDP is a tuple , where
is the vehicle state space.
is the control input space.
is the measurement space.
is the transition probability distribution.
is the observation probability distribution.
is the one step reward function.
is the constraint function.
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CPOMDP Formulation
The objective of a CPOMDP is to find a feedback policy that maximizes the total expected discounted reward subject to the constraints be above some threshold:
where
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CPOMDP Formulation
This optimization statement can be recast into the following Bellman equation
where
BackgroundMethodologyImplementationSimulation & ResultsConclusions & Future Work
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Implementation: Setup
Objective: A damaged UAV has to reach a target location while avoiding obstacles
UAV Parameters
6 DOF motion model
Wing Span: 55ft
Cruise Velocity: 161 mph
Cruise Altitude: 25,000 ft
Payload: 500 lb
Range: 2500 nmi
73 Damage test scenarios and 50 trials for each
73 x 50 = 3650 total missions
10 damage scenarios serve as training set
Aurora Flight Sciences: www.aurora.aero
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Implementation: Offline Physics Models
Aero Structural Model: Use a combination of ASWING and VABS
Global Aircraft Behavior: ASWING
– Aerodynamic, structural, and control-response offlexible winged aircraft
Wing Beam Model: VABS
– 2D Finite element solver for wing box cross section
http://web.mit.edu/drela/Public/web/aswing/Active Aeroelasticity and Structures Research Laboratory, The University of Michigan
BackgroundMethodologyImplementationSimulation & ResultsConclusions & Future Work
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Simulation Results: Pristine Case
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Simulation Results: Damaged Case
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Results: Trajectories
Little to moderate damage Moderate to severe damage
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Results: Overall
Baseline policy exceeds capability
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Results: Peak Strain vs Total Time
Structural Failure
Collision
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Results: Peak Strain vs Distance to Goal
Structural Failure
Collision
Goal Reached
BackgroundMethodologyImplementationSimulation/ResultsConclusions & Future Work
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Conclusions
Main Contributions
Developed a flexible methodology that accounts for
– Vehicle capability constraints– Vehicle process noise and disturbances– Measurement process noise and disturbances
Demonstrated methodology on a 3D path planning example of a UAV navigating to a target location.
Implementation results show that a dynamic capability enabled aircraft can
Greatly improve its chances of survivability over baseline
Modify strategy based on received observations about its health
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Future Work
Incorporation of higher fidelity physics based libraries
Joint work with UCSD
Developing a baseline UAV model with full fluid structural interactions with thin shell composite structures [Bazilevs2015]
Progressive damage modeling
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Acknowledgements
This work was supported through funding from the Arthur Gelb Fellowship as well as from AFOSR grant FA9550-11-1-0339 under the Dynamic Data-Driven Application Systems Program. The UAV model was provided by Aurora Flight Sciences.
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References
[1] S. Willis, “OLM: A Hands-On Approach, ” in ICAF 2009, Bridging the Gap between Theory and Operational Practice, 2009, pp 1199-1214
[2] W. Staszewski, G. Tomlinson, and C. Boller, ”Health Monitoring of Aerospace Structures Smart Sensor Technologies and Signal Processing,” John Wiley and Sons Ltd, 1st Ed, 2004
[3] H.J. Koolstra and H.J. Damveld, “Envelope Determination of Damaged Aircraft," in “AIAA Guidance, Navigation, and Control Conference”, 13-16 August, Minneapolis, Minnesota", 2012
[4] M. Lecerf, “Methodology for Dynamic Data-Driven Online Capability Estimation," AIAA, Vol. 0, 2015, pp. 1-15
[5] J. Kim, K. Palaniappan, and P.K. Menon, “Rapid Estimation of Impaired-Aircraft Aerodynamic Parameters," Journal of Aircraft, Vol. 47, No. 4, 2010, pp. 1216-1228.
[6] P.K. Menon, P. Sengupta, S. Vaddi, B. Yang, J. Kwan, “Impaired Aircraft Performance Envelope Estimation," Journal of Aircraft, Vol. 50, No. 2, 2013, pp. 410-424.
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[8] E.M. Atkins, I.A. Portillo, and M.J. Strube, “Emergency Flight Planning Applied to Total Loss of Thrust," Journal of Aircraft, Vol. 43, No. 4, 2006, pp. 1205-1216
[9] N.T. Nguyen, K.S. Krishnakumar, J.T. Kaneshige, P.P. Nespeca, “Flight Dynamics and Hybrid Adaptive Control of Damage Aircraft," Journal of Guidance, Control, and Dynamics, Vol. 31, No. 3, 2008, pp. 410-424.
[10] V. Stepanyan, S. Campbell, and K. Krishnakumar, “Adaptive Control of a Damaged Transport Aircraft using M-MRAC," in “AIAA Guidance, Navigation, and Control Conference, 2-5 August, Toronto, Ontario Canada”, 2010
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References
[11] N. Meuleau, C. Plaunt, D.E. Smith, and T. Smith, “An Emergency Landing Planner for Damaged Aircraft," in “Proceedings of the Twenty-First Innovative Applications of Artificial Intelligence Conference", 2009, pp. 114-121.
[12] I. Lopez and N. Sarigul-Klijn, MICAI 2009: Advances in Artificial Intelligence, chap. Intelligent Aircraft Damage Assessment, Trajectory Planning, and Decision-Making under Uncertainty, Springer Berlin Heidelberg, 2009, pp. 99-111.
[13] N.K. Ure, G. Chowdhary, J.P. How, M.A. Vavrina, J. Vian, “Health Aware Planning Under Uncertainty for UAV Mission with Heterogeneous Teams," in “European Control Conference, 17-19 August, Zurich, Switzerland", 2013.
[14] S. Thrun, W. Burgard, and D. Fox, Probabilistic Robotics, MIT Press, 2006.
[15] Y. Bazilevs et. el, “Isogeometric Fatigue Damage Prediction in Large-Scale Composite Structures Driven by Dynamic Sensor Data,” Journal of Applied Mechanics, Vol 82-9 (2015)