methodology for path planning with dynamic data driven ......methodology for path planning with...

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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Thank you

Questions?

victorsi@mit.edu

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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.

[7] A. Adler, A. Bar-Gill, and N. Shimkin, “Optimal flight paths for engine-out emergency landing," in Proceedings of the Chinese Control and Decision Conference, 2012, pp. 2908-2915.

[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)