Time-Optimal UAV Trajectory Planning for 3D Urban ......Task 1 needs 10% UAVs Task 4 needs 40% UAVs Task 3 needs 30% UAVs Task 2 needs 20% UAVs A group of unknown number of UAVs

University of Pennsylvania GRASP1

Time-Optimal UAV Trajectory Planning for 3D Urban Structure Coverage

Peng Cheng Jim Keller Vijay Kumar

GRASP LabUniversity of Pennsylvania

The 2008 ICRA Workshop onCooperative Control of Multiple Heterogeneous UAVs for Coverage and

Surveillance


Intelligence Surveillance and Reconnaissance (ISR) tasks

Motivation

ONR, Code 30


Motivation3D city maps, such as Google Maps®

New York, Google Maps ®


MotivationAn FAA approved UAV for city law enforcement in Miami


Goal3D Coverage for Reconnaissance and Surveillance in Urban Environments

Two Problems:1. Cooperative coverage with multiple UAVs

Task allocation with minimal communication in finite timeScalable and decentralizedAd-hoc organization

2. 3D coverage of urban structuresComplete coverage with optimality guaranteeDynamic constraints of fixed-wing UAVsLimited field of view of the onboard camera

An Almost Communication-Less Approach to Task Allocation for Multiple UAVsPeng Cheng Vijay Kumar

ThA1: Path Planning Algorithms; Thur. 10:20-10:40am


Task 1 needs 10% UAVs

Task 3 needs 30% UAVsTask 4 needs 40% UAVs

Task 2 needs 20% UAVs

A group of unknown number of UAVs


Positive min. fwd. speed

Limited turning rate

Limited turning rate

Each UAV:• Does not know the total number of UAVs• Does know the task specification and bounded region• Has GPS provide compass and synchronized clock• Has fixed-wings must fly forward (Dubin’s car)• Has limited omni directional sensing range • Has no communication between UAVs

Objective:Determines a task to accomplish in finite time


An Example

Initial configurations Intended task allocation

Task Allocation

1

2 3

4

Allocate the UAVs to provide persistent coverage of the border of the sea. 25% of UAVs are respectively allocated to the 1st and 2nd closed curves, 37.5% for the 3rd curve, and 12.5% for the 4th curve.

Video


Our Solution

Decentralized and scalable with minimal communication (O(1) computation time and O(1) memory with respect to the number of UAVs)Establishes consensus on the total number and task allocation of UAVs in finite timeApplicable for a large group of fixed-wing UAVswith ad-hoc organization

Thur. 10:20-10:40amThA1: Path Planning Algorithms


3D Coverage Problem

Achieve a complete coverage of a building with an onboard camera on a fixed-wing UAV

φ


Challenges

Complicated and coupled dynamics of the UAVComplicated to compute the covered surface area of the buildingHard to provide performance guarantee on

Complete coverageTime optimality


A Search-Based Solution

Sensor footprint of the onboard camera

Area of interest Expensive to compute a solutionHard to provide guarantee on complete coverage


Pattern-Based Solutions - I


Area of interest


Pattern-Based Solutions - II


Area of interest Hard to quantify the time optimality whileincorporating system dynamics


Our Objectives

Compute a coverage plan in real-timeApplicable for the fixed-wing UAVsProvide performance guarantee

Complete coverageTime optimality

Simplified dynamics and

building models

Improved pattern-based

coverage +


A Simplified UAV Model

Decoupled dynamicsIn x-y plane, the Dubin’s car model

In z direction, the double integrator model

( vf has a positive lower bound for the fixed-wing UAVs)


Simplified Building Models

( )FBO

The hemisphere model

The cylinder model


Constant Coverage Rate

O

A C

DB

Tight lower bound on the time to achieve complete coverage of the hemisphere


The Lower Bound on Coverage Time


Coverage Plan for the Hemisphere Model

Constant factor optimality: T ≤ k TL ≤ k Topt


Constant Factor Optimality

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Multiple UAV Persistent Coverage

UAVsofnumber the:

rate refreshing :

n

T

TTn

f

f

all=


Multiple UAV Multiple Buildings

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( )FBO( )FBO

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Preliminary Results with Dynamic Models

27GRASP

Autopilot connected for hardware-in-the-loop testing in lab

Offset view of aircraft from simulator

Active Waypoint

Aircraft location

Autopilot connected for hardware-in-the-loop testing in lab

Offset view of aircraft from simulator

Active Waypoint

Aircraft location

Overview of System

28GRASP

Power Required for Maneuvering Flight

05

1015

05

1015

2025

250

300

350

400

450

500

Flight Path Angle - degrees

Bank Angle - degrees

Pow

er R

equi

red

-Wat

ts

Navigation Limits

Assumption of Decoupled Requirements for Turning and Climbing SegmentsAppropriate for Simulated Flight Conditions:

• Velocity near minimum power required• Maximum angle of bank low in magnitude

29GRASP

Trim Angle of Attack for Maneuvering Flight

05

1015

0

5

10

15

20

25

6

6.5

7

7.5

8

Flight Path Angle - degrees

Bank Angle - degrees

Trim

Ang

le o

f Atta

ck -

degr

ees Flight Plan entirely within range of linear aerodynamics

30GRASP

Simulation Data for Hemispherical Flight Path Over a Building in Lower Manhattan (17 State St.)

Simulation Model:• Nonlinear Equations of Motion• Linear Aerodynamic Forces and Moments

Visualization:• FlightGear v9.9

Air Vehicle Configuration:• Quarter scale Piper Cub J3 • PiccoloTM Autopilot Hardware-in-the-loop

Flight Conditions:• Sea Level/Standard Day Ambient Conditions• Cruise Airspeed set to 15 m/s• Maximum Commanded Angle of Bank set to 15o (minimum radius of turn = 85.7m)• Target Climb Angle: 15o (maximum power)• No winds

Building Height: 208mCamera FOV: 35o

Trajectory Requirements for Air Vehicle:• increase in power required to climb(φ = 0) = mgVηpropsin(γ) ~ 820*sin(γ) [Watts]

• increase in power required to turn(γ = 0) = (mg)2Vηprop ~ 33*sec2(φ)) [Watts]qSπAecos2(φ)

} Dictates 4 Tiers for Complete Coverage; 96 waypoints

31GRASP

FlightGear Scenery Sparse Compared to RealityPermits Execution of Hemispherical Flight Plan

32GRASP

T =0 @ first waypointT =0 @ first waypoint

Launch pointLaunch point

Last point in time historyLast point in time historyReference Point for Reference Point for δδNorthing, Northing, δδEasting Easting measurementsmeasurements

Flight Plan Flight Plan Actual PathActual Path

Map-view of Simulated Flight Path

33GRASP

Cartesian view of flight plan

East - m

North - m

Alt. - m

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35GRASP

0 50 100 150 200 250 300 350 400 4500

100

200

300

400

500

600

Time - sec

delta

Nor

thin

g, d

elta

Eas

ting

and

Alti

tude

from

refe

renc

e - m δδNorthing from Reference:Northing from Reference:

Flight Plan:Flight Plan:Actual Path:Actual Path:

δδEasting from Reference:Easting from Reference:Flight Plan:Flight Plan:Actual Path:Actual Path:

δδAltitude from Reference:Altitude from Reference:Flight Plan:Flight Plan:Actual Path:Actual Path:

Trajectory Following Performance:• Within expected limits for Piccolo except during transition phases

Time History Data

36GRASP

GRASP Autonomous UAV

Flight Test Data/Imagery6August06

Pipersville, PA

Trajectories for Time Optimal Surveillance

37GRASP

Flight Field – Pipersville, Pennsylvania

38GRASP

Autopilot and Camera Installation on Aircraft

Fixed forward-looking camera: 30o down from level attitude

Ground Station Antenna

Autopilot Housing

Airspeed/AltitudeSensor

GPS Antenna

39GRASP

Coverage of Flightline

40GRASP

Landing/Recovery


Conclusion

Real-time trajectory design for fixed-wing UAVsfor coverage of urban structuresPerformance guarantee

Complete coverageConstant-factor time optimality

Verified with the hardware-in-the-loop simulation results

Thank you! Questions!An Almost Communication-Less Approach to Task Allocation for Multiple UAVs

Thur. 10:20-10:40amThA1: Path Planning Algorithms

Documents

Time-Optimal UAV Trajectory Planning for 3D Urban ......Task 1 needs 10% UAVs Task 4 needs 40% UAVs Task 3 needs 30% UAVs Task 2 needs 20% UAVs A group of unknown number of UAVs