Massively-Parallel

Stochastic Control and

Automation: A New

Paradigm in Robotics

GPU Technology Conference

26 March 2014

Dr. Jonathan Rogers

Assistant Professor George W. Woodruff School of Mechanical Engineering

jonathan.rogers@me.gatech.edu

404-385-1600

2

GT’s Intelligent Robotics and Emergent

Automation Lab (iREAL)

• Research at the intersection of dynamics, control and

estimation, and vehicle design.

• Robot Vehicle Design and Flight Dynamics – Design of novel autonomous vehicle concepts

– Analysis and tradeoffs of various vehicle designs

– Ex: Morphing autonomous tail sitter aircraft

• Control and Estimation for Complex Systems – Energy-harvesting flight control laws

– Low-cost state estimation solutions

– Ex: Expert system controller for helicopter autorotation

– Ex: Orientation estimation using IR thermal sensors

• GN&C Through Emerging Computational Architectures – Novel stochastic control schemes with GPU-based uncertainty propagation

– Ex: Stochastic GPU-based control for parafoil terminal guidance

3

Motivation

• Decision-Making Under Uncertainty: Critical

difficulty in robotics

– Uncertainty invariably is critical limit to performance

• Example: Power usage for Mars rover

• Example: Voice recognition

• Example: Flying/landing with obstacles and winds

Goal

Forest

Desert Terrain

Grassland and Prairie

Motivation

• Decision-Making Under Uncertainty: Mars rover

power management Anticipated battery remaining at t = 1 hour?

• Rover explores unknown terrain,

energy per distance not precisely

known

• Must predict most likely

remaining battery life in presence

of this uncertainty

5

Motivation

• Decision-Making Under Uncertainty: Speech

recognition

– Robot correlates sounds with known library of words

or phrases

– Uncertainty regarding:

• Words human is speaking

• Human intent

– Robot must take some action anyway!

6

Motivation

• Decision-Making Under Uncertainty: Aerial vehicle

obstacle avoidance

1 2

• Should vehicle fly path 1

or path 2?

• Which is more robust to

wind disturbances?

• Which has less likelihood

of hitting buildings or

lake?

• Must predict effects of

unknown disturbances!

7

Motivation

• Nearly every robotic system must be able to make

decisions in presence of uncertainty

• Uncertainty takes form of:

– Random future disturbances

• Wind gusts

– Uncertain robot dynamics

• How fast will I really go with a given

speed command?

– State estimation error

• Am I really where I think I am?

8

Presentation Overview

• Deterministic Control vs Stochastic Control

– GPU-based uncertainty propagation

• Stochastic Control: Mathematical Formulation

• Example: GPU-Based Autonomous Parafoil

Control

– Simulation

– Experimental results

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min min ,T

t t t T T

t

J E g x u g x

1 , 0,..., 1t t t tx f x u w t T

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“Classical” Deterministic Control

• Standard paradigm in autonomous systems control:

– Use a motion model to predict future behavior

– Make control decision based on model prediction

Target

Give control based on miss distance and

direction of predicted impact location.

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“Classical” Deterministic Control

• Given “obstacle” near target, what is likelihood that I

will hit it given uncertainty?

– Uncertainty due to disturbances, model error, sensor error

– Cannot quantify this risk with a single prediction!

Target

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• Predict hundreds or thousands of trajectories

– Randomize disturbances in each one (Monte Carlo

method)

– Leverage GPU’s to perform in real-time

– Base control inputs off probability density of impacts!

New Stochastic Control Paradigm

Target

Range (m)

Deflection (

m)

5080 5100 5120 5140 5160 5180 5200

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Target

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• Can predict likelihood that we hit obstacle near

target – Can find a trajectory shape that minimizes this risk

– Only possible if we can simulate 1000’s of trajectories

extremely quickly

New Stochastic Control Paradigm

Target

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GPU’s for Real-Time Monte Carlo

• GPU’s are ideal tool for uncertainty propagation

– Assign single trajectory per GPU kernel

– Allows us to perform thousands of predictions on board

vehicle, in real-time

80 90 100 110 120 130 140 150 160-30

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Range (m)

Cro

ss R

ange (

m)

GPU’s for Real-Time Monte Carlo

• Massively-parallel Monte Carlo on GPU’s provides 1-2

order of magnitude runtime reduction over same code

on CPU

– We can run Monte Carlo’s in real-time

M. Ilg., J. Rogers, M. Costello, “Projectile Monte Carlo Analysis Using A Graphics Processing

Unit,” 2011 AIAA Atmospheric Flight Mechanics Conference, Portland, OR, 2011

Runtime

comparison for

six-degree-of-

freedom flight

simulation code

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GPU Co-Processor for Robot Control

• Current paradigm:

– Sensors feed microprocessor

– Microprocessor computes control (autopilot)

Sensors

Micro-

processor

Control Inputs

GPU Co-Processor for Robot Control

• New paradigm:

– Sensors feed microprocessor

– Microprocessor sends current state information to GPU co-

processor

– GPU propagates uncertainty and refines guidance solution

Sensors

Micro-

processor

Control Inputs

GPU Co-processor State

Uncertainty

Estimate

• Real-time Monte

Carlo Simulation

• Quantify uncertainty

Mathematical Foundation

• “Stochastic finite horizon optimal control”

• Dynamic model with stochastic forcing:

• Find control inputs that maximize cost function

– Cost computed as function of PDF over finite horizon

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Stochastic forcing Robot dynamics

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min min ,T

t t t T Tu U

t

J E g x u g x

Terminal cost Stage cost

functions

Mathematical Foundation

• Solving optimization problem requires knowledge of

state PDF over finite horizon

– State PDF is provided by GPU Monte Carlo trajectory

predictions!

– Optimization problem then solved using standard

methods

1

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min min ,T

t t Tu U

t

t TJ E x u xg g

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Cro

ss R

ange (

m)

Range (m)

Deflection (

m)

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Target

Functions of state PDF

Example: Autonomous Parafoils

• Autonomous parafoils widely in use to delivery

supplies – cheap and portable

• Automation & Control is challenging:

– Underactuation (can only bank right and left)

– Stochastic forcing: wind gusts!

– Model error: flexible body, dynamics vary flight-to-flight

– Sensing error: Emphasis on low-cost sensors

Strongly stochastic system!

Current systems can land only

within 100 m of target.

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Challenging Dropzones

• Need control systems that get close to target

– But more importantly do not miss in wrong direction!

Notional desired

landing location

Martian Grand Canyon (Melas Chasma) Banda Aceh, Indonesia following

2004 tsunami

Parafoil Terminal Guidance

• Standard approach geometry

• Approach target downwind

• Turn at proper time with turn

rate 𝜓 (𝑡)

• Land heading into the wind

• Current systems plan final

turn assuming perfect

knowledge of winds

• If winds change during turn,

parafoil misses target

GPU-Based Parafoil Terminal Guidance

• Through massively-parallel Monte Carlo’s, GPU selects

approach path most robust to wind disturbances

F

( )t

3 example trajectory paths:

• Sharp right turn

• Shallow right turn

• Medium left turn

Candidate Trajectories

Constructed by:

• Discretizing turn rates

into N possible values

• Discretizing turn times

into M possible values

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GPU-Based Parafoil Terminal Guidance

• GPU-Based Guidance Workflow

• Monte Carlo’s performed for each trajectory shape

– Optimal shape selected that is most robust to disturbances

Simulation Results

• Example simulation – Wind shift during final turn

• Baseline trajectory (black) lands

far from target due to change in

wind

• Trajectory penalizing error only

performs hard left turn to

dissipate altitude, lands with

almost no error but with

crosswind

• Trajectory penalizing error and

velocity trades impact error to

land into wind

Target

Wind

Wind

mJ d

mJ d kv

GPU

Updates

Simulation Results

• Example Results: Autonomous Parafoils

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Cross Range (ft)

Range (

ft)

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Cross Range (ft)

Range (

ft)

Standard Parafoil Guidance GPU-Based Optimal Guidance

J. Rogers, N. Slegers, “Robust Parafoil Terminal Guidance Using Massively Parallel Processing,” Journal

of Guidance, Control, and Dynamics (AIAA), In Press, 2014.

20% 2%

Simulation Results

• Through simple modification to cost function, terrain

awareness incorporated

J. Rogers, N. Slegers, “Terminal Guidance for Complex Drop Zones Using Massively Parallel Processing,”

2013 AIAA Aerodynamic Decelerator Systems Conference, Daytona Beach, FL, 25-28 March, 2013.

Standard GPU-Based Standard GPU-Based

Experimental Tests

• Powered parafoil constructed to verify simulation results

Canopy Span 6.8 ft

Weight 6 lbs

Forward Speed 14.7 kts

Descent Rate 13.5 ft/s

Max Turn Rate 30 deg/s

Endurance (while

powered)

~15 minutes

Flight Control Architecture Design

• Flight system hardware

Autopilot

Serial Connector

Cable

GPU-ARM

Board (SECO)

GPU Battery (4 cell LiPo) Autopilot Battery

Flight Control Architecture Design

• Guidance system workflow:

– Autopilot controls vehicle

– GPU provides autopilot with optimal path to fly

Autopilot

• GPS

• Baro altimeter

• Gyros

• Accelerometers

• Magnetic

compass

• Wireless comms

• Servo drivers

GPU

NVIDIA Quadro

1000 M (96 cores)

ARM

NVIDIA Tegra 3

ARM Quad-Core

Mobile Processor

SECO CUDA-On-ARM Dev. Board

Parafoil

State • Position

• Velocity

• etc.

Optimal

Trajectory • Turn rate

• Appr. angle

• Turn time

Optimization

Problem Brake

Commands

Example Flights

• GPU-guided case successfully avoids constraint,

standard guidance case does not

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Dow

nra

nge (

m)

Crossrange (m)

Parafoil Position

Projected Impact Point

Target

GPU Updates

Standard Guidance GPU-Based Stochastic Guidance

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Crossrange (m)

Parafoil Position

Projected Impact Point

Target

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Example Flight

• GPU Optimal Trajectory Outputs

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time (s)

Turn

Rate

(deg/s)

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time (s)

F (

deg)

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time (s)

Turn

Tim

e (

s)

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Time (s)

Bra

ke (

in)

GPU Trajectory solutions

• Four GPU solutions show commands

to initiate left turn to create space

from constraint, then final right turn

to approach target.

Dispersion Comparisons

• 11 standard flights, 12 GPU-based flights

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Crossrange (m)

Dow

nra

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Crossrange (m)

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Standard Guidance GPU-Based Stochastic Guidance

• GPU impacts “hug constraint” as seen in simulation

• Missing constraint comes at penalty of somewhat larger miss distance

72% 17%

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Video of GPU-Guided Flight Trajectory

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Conclusion and Final Remarks

• Stochastic guidance and control will become

increasingly important for robotic systems

– GPU enables real-time uncertainty propagation

– Have shown its utility in variety of control tasks

– Extensions underway to many other applications

UAV’s HEV’s Ground

Robots

35

Conclusion and Final Remarks

• Stochastic guidance and control will become

increasingly important for robotic systems

– GPU enables real-time uncertainty propagation

– Have shown its utility in variety of control tasks

– Extensions underway to many other applications

• Research represents first time GPU has been flown

on aerial robotic system for control purposes.

UAV’s HEV’s Ground

Robots

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Questions

• Thanks for attending!