prospect eleven: princeton university’s autonomous vehicle entry 2005 darpa grand challenge
DESCRIPTION
Applications of Knowing “Where am I” Two Examples:. Prospect Eleven: Princeton University’s Autonomous Vehicle Entry 2005 DARPA Grand Challenge. CoPilot|MinETA Real-Time Dynamic Minimum ETA Sat/Nav. Thursday, February 6, 2006 National Physical Laboratory Teddignton, Middlesex, UK. - PowerPoint PPT PresentationTRANSCRIPT
Prospect Eleven: Princeton University’s
Autonomous Vehicle Entry 2005 DARPA Grand Challenge
Thursday, February 6, 2006National Physical LaboratoryTeddignton, Middlesex, UK
Alain L. KornhauserTeam Leader, Prospect Eleven
Professor, Operations Research & Financial Engineering Princeton University
Co-founder & Board Chair, ALK Technologies, Inc.
Applications of Knowing “Where am I”
Two Examples:
CoPilot|MinETAReal-Time Dynamic
Minimum ETA Sat/Nav
Prospect Eleven: The Making, Testing and Running of
Princeton’s Entry in the 2005 DARPA Grand Challenge
Alain L. KornhauserTeam Leader, Prospect Eleven
Professor, Operations Research & Financial Engineering
Andrew Saxe’08 Gordon Franken’08 Scott Schiffres’06
Brendan Collins’08 Bryan Cattle’07 Rachel Blair’06
Josh Herbach’08 Anand Atreya’07 Kamil Choudhury’06
Jan 26, 2006
The DARPA Grand ChallengeDefense Advanced Research Projects Administration
• DARPA Grand ChallengeCreated in response to a US Congressional and DoD mandate, it was a field test intended to accelerate research and development in autonomous ground vehicles that will help save lives on the battlefield. The Grand Challenge brought together individuals and organizations from industry, the R&D community, government, the armed services, academia, students, backyard inventors, and automotive enthusiasts in the pursuit of a technological challenge.
• The First Grand Challenge: Across the Mojave, March 2004From Barstow, California to Primm, Nevada offered a $1 million prize. From the qualifying round at the California Speedway, 15 finalists emerged to attempt the Grand Challenge. However, the prize went unclaimed as no vehicles were able to complete the difficult desert route.
• The 2005 Grand ChallengeOctober 8, 2005 in the desert near Primm. Prize increased to $2 million.
Jan 26, 2006
18 -month Life Cycle of Prospect Eleven
2004 2005
Jan Jan Automate Brakes
Feb Feb Install Computers
Mar 2004 Grand Challenge Mar Mount GPS
Apr Announcement of 2005 GC Apr Work on Machine Vision
May Decide to get involved May 1st Site Visit
Jun Hire 5 summer interns Jun Not top 40, Alternate Status
Jul Literature survey Jul Re-Do Stereo Vision
Aug Literature survey Aug 15 2nd Site Visit
Sep Submit Application Sep 27 National Qualifying Event
Oct Oct 8 2005 Grand Challenge
Nov Receive salvaged 05 Canyon Fall Break
Take care of unfinished business
Dec Automate Steering Dec
Jan 26, 2006
Prospect Eleven & Competition
Jan 26, 2006
Constraints• Very little budget
• Simplicity
Guiding Principles
Objective• Enrich the academic experience of the students
Jan 26, 2006
http://www.pcmag.com/slideshow_viewer/0,1205,l=&s=1489&a=161569&po=2,00.asp
Homemade“Unlike the fancy “drive by wire” system employed by Stanford and VW, Princeton’s students built
a homemade set of gears to drive their pickup. I could see from the electronics textbook they were using that they were learning as they went.”
Jan 26, 2006
Teamwork
Real-time Decision SystemAndrew Saxe’08
Object Detection SystemBrendan Collins’08
Mechanical SystemsGordon Franken’08
Planning SystemsJosh Herbach’08
Electronic SystemsBryan Cattle’07
Computing SystemsAnand Atreya’07
Control SystemsScott Schiffres’06
Organizational SystemsRachel Blair’06
Team LeaderAlain Kornhauser*71P03
Jan 26, 2006
Mechanics
Design and Fabrication of:• Vehicle Actuators
– Steering– Brakes– Transmission
• Sensor Housings– Stereo Camera– GPS Antennae
• System Protection– Shock-absorbing computers– Secure installation of components
Jan 26, 2006
Vehicle Actuators• Steering
– Motor from Bosch cordless drill.– Modified gears mounted directly to
steering wheel.– Rotary encoder used for position
feedback.• Brakes
– Bicycle brake cable used to depress pedal.
– Motor-driven linear actuator.– Load-cell used for tension feedback.– Also: pneumatic e-brake, for fail-safe
operation.• Transmission
– Ability to shift from forward to reverse.– Not used due to several issues:
• Slow actuation• Difficulty interfacing with vehicle
transmission• Not open up an Achilles heel.
Drill motor
Steel Gears
Rotary Encoder
bike cable
brake pedalmotormotor
Load cell
Jan 26, 2006
Sensor Housings
• Stereo Camera– Camera rated for “indoor
office use only” !!!– Water & air tight enclosure– Mounts for photographic
filters
• GPS Antennae– 4 GPS receivers– Need good location on top
of vehicle for best data.– Wooden boom also
supported rotating beacon
Jan 26, 2006
System Protection
• Shock Absorption for computers.– Old way: Computers were
wrapped in foam.– New way: Computers are
rack-mounted on shock-isolating feet.
• Secure installation of other components.– Batteries, wires, power
supplies, air compressor…– The “shake test”
Shock-absorbing
feet
Jan 26, 2006
Stereo Vision System
• Principle of Operation: Difference between two cameras gives depth information
• Steps:– Compute disparity image
– Find obstacles in each column
– Approximate with rectangles
– Filter in time domain
Jan 26, 2006
Challenges
– Quantization
– Noise
– Lighting condition
– Field of view
– Occlusion
– Range
Jan 26, 2006
The left camera sees:
Point Grey Bumblebee
Focal Length: 4mm
Resolution: 640x480
Black & White
Jan 26, 2006
The right camera sees:
Point Grey Bumblebee
Focal Length: 4mm
Resolution: 640x480
Black & White
Jan 26, 2006
Yielding a disparity map:
Intensity indicates distance: the lighter, the closer
White indicates an invalidated location.
Jan 26, 2006
Processing in each column:
Intensity indicates confidence that an obstacle exists at that location. A darker line indicates a higher confidence.
Jan 26, 2006
Bounding with rectangles:
Darker rectangles indicate higher confidence.
Jan 26, 2006
Data Representation
Reference:
http://www.darpa.mil/grandchallenge/TechPapers/Stanford.pdf
vs.
Jan 26, 2006
Tracking
Jan 26, 2006
Navigation
• Blind-Man’s Cane Approach:– Find best instantaneous velocity vector (heading and
speed) within visible cone ahead.
? Desired V
Jan 26, 2006
Step 1: Tube Projection
Jan 26, 2006
Angle
Distance
Gap Identification
Shoot the Gap
V
Jan 26, 2006
Examples of “Shoot the Gap”
‘Gotta’ Reverse
Not without Problems
May Get Squeezed Yippes!
Jan 26, 2006
Interfacing to Existing Vehicle DataExisting electronic information available on ’05 GMC Canyon:• Engine status – temp, RPM, diagnostic codes,...• Transmission – what gear are we in?
4WD on/off• Car traction control – are wheels slipping,
are we really moving?• Wheel speed/odometry – how far have we moved?
how fast?• Throttle is electronic
All monitored & used by Prospect Eleven
Jan 26, 2006
OBD-II Interface10101110101...
Throttle voltage
ABS Wheel Encoders Left
Right
Counters
“Data-acquisition card”
Digital inputs
ADC
101001...
DAC
101001...
1001 11011001 0101
Transmission position
Tension on thebrake pedal
100 lb
Jan 26, 2006
Other thoughts
Jan 26, 2006
Feedback Control SystemsSpeed Control Module:
– Receives desired speed from Navigation– Decides how to modulate throttle and brake– Requirements
• Gracefully reach and maintain desired speed• Smooth acceleration and braking
– To minimize skidding on loose sand wet grass
• Strict adherence to speed limit– Minimize overshoot
Steering Control Module– Receives desired heading angle and speed from Navigation– Converts to desired steering wheel angle– Constrains wheel angle as function of speed to avoid roll-over.– Control Coefficients tuned to trade off response and overshoot
Jan 26, 2006
Speed Control -- Implementation
• Proportional Integral Control– Output = KPev + ∫KIevdt + KD (dev∕dt)
– Where evelocity = Vdesired – Vcurrent
• KP term deals with the bulk of error
• KI integrates up error to eliminate steady state error
• KD reduces overshoot and ringing by slowing response
Speed ControlDesired Speed
Current Speed
Latest Speeds
Percent Throttle
Percent Brake Tension
Jan 26, 2006
Why P11 stopped after 9.4 miles
• We store a list all obstacles we are currently concerned about– Each time a new obstacle is received, we add it to this list– Each obstacle needs to have its relative position updated each time
we get new vehicle position information• It gets these updates by subscribing to the RelativeFrameUpdated event
• When we have passed an obstacle by more than twenty feet, we remove it from the list– However, we were not unsubscribing the obstacle from the
RelativeFrameUpdated eventThus, nine miles down the road, our computer was still processing a bush it saw near the beginning of the course!
C# is a powerful language, but it has to be used carefully
Timeline of Accomplishments of Princeton’s “Prospect Eleven” DARPA Grand Challenge Team
May 2004 - Nov 2005
Segment Description Images Videos
“Going Back” Oct 30-Nov 2, ‘05
After completing 10 miles in GCE, Prospect Eleven returns to the desert to “complete” the 2005 and the 2004 Grand Challenge coursesGPS tracks for 3 days
2004 DGCNov 2, ‘05
GPS Tracks 0.3mbRun Images 3mb
Cruisin’04 2.5mb
Return to Beer Bottle Pass, Nov 1, ‘05
GPS Tracks 0.3mb
2005 DGC, Oct 31, ‘05
GPS Tracks 0.1mbRun Images 3mb
Cruisin’05 16mbGate’05 3mb, Gate2 ’05 4mb
Changing “one line”, Oct 30, ‘05 Images 0.2mb FixingCalibrating
2005 GCEOct. 8, ‘05
DARPA Grand Challenge Event, 132 mile course in desert around Primm, NV; 23 entries; Prospect Eleven is #10 seed
Run Summary Start_11mbPassBy_29mbSummary 17mb
NQESep 27-Oct 5, 05
National Qualifying Event held at California Speedway. 43 “bots” competing for 23 positions on 2.2 mile course
NQE Course CrashOutside_7mbCrashInside_4mbPrefectRun5_9mb
Run-up to NQEAug 17-Sep 26
Modifications and testing after invitation as one of three “Alternates” to the NQE
2nd Site VisitAug 16, ‘05
2nd chance at demonstrating capabilities of P11 to DARPA officials at West Windsor athletic fields after earning “Alternate status
Pre-2nd_SiteVisit_6mb
1st Site VisitMay 3, ‘05
Demonstration of Prospect Eleven’s capabilities and potential to DARPA officials, mixed performance
Automation of P11Nov ’04-May ‘05
Conversion of a GMC 05 Canyon to Prospect Eleven: Automation of brake, throttle, steering; GPS; vision
P11 Tech Paper
Application & PrepMay ‘04-Nov ’05
Putting the team together, planning, organization, & literature search.
DAPRPA Grand Challenge Event, October 07, 2005
The Day Before 2005 Grand Challenge Event
L2R: Rachel Blair’06, Dan Chiou’05, Prof. Alain Kornhauser*71 P03, Ben Essenburg’05, Bryan Cattle’07, Josh Herbach’08. Jeff Jones*05, Kamil Chihoudy’06, Scott Schiffres’06, Anand Atreya’07; Launch Team: Andrew Saxe’08, Brendan Collins’08, Gordon Franken’08
DAPRPA Grand Challenge Event, October 08, 2005
The DARPA Grand Challenge Event Team 2005 Grand Challenge Event
DAPRPA Grand Challenge Event, October 08, 2005
The Launch of Prospect Eleven 2005 Grand Challenge Event
DAPRPA Grand Challenge Event, October 08, 2005
Return of Prospect Eleven @ 8 Mile Mark
2005 Grand Challenge Event
DAPRPA Grand Challenge, Unfinished Business, October 31, 2005
Approaching Beer Bottle Pass 19:02
2005 Grand Challenge Course
DAPRPA Grand Challenge, Unfinished Business, October 31, 2005
Beer Bottle Pass 19:10 PST
2005 Grand Challenge Course
DAPRPA Grand Challenge, Unfinished Business, November 1, 2005
The Assent: 17:00Rerun to Beer Bottle
Pass
DAPRPA Grand Challenge, Unfinished Business, November 1, 2005
The Assent: 17:01Rerun to Beer Bottle
Pass
DAPRPA Grand Challenge, Unfinished Business, November 2, 2005
12:252004 Grand Challenge Course
DAPRPA Grand Challenge, Unfinished Business, November 2, 2005
14:262004 Grand Challenge Course
DAPRPA Grand Challenge, Unfinished Business, November 2, 2005
The Finish 18:44 2004 Grand Challenge Course
L2R: Prof. Alain Kornhauser*71 P03, Andrew Saxe’08, Bryan Cattle’07, Scott Schiffres’06
Prospect Eleven’sUnfinished Business
October 31-November 2, 2005DARPA Grand Challenge ’04 & ’05 Courses
GPS Tracks and Timing Maps
DAPRPA Grand Challenge, Unfinished Business, October 31, 2005
Finish, ’05 Course
Jan 26, 2006
Start 7:53:30 PSTFinish 19:35:49Elapsed Time 11:43:49Pause Time ~2:55:49Autonomous Time 8:48:59
8:44:48 1:10 Pause
10:48:04 3:45 Open & pass thru gate
9:52:53 8:14 Open gate & pass through
13:18:531:10 Pause
18:20:53 38:50 prepare inside video
19:00:21 – 0:56 Adjust Camera19:02:53 – 1:52 Wait for chase car
10:37:37 5:54 Open & pass thru gate
18:02:502:08 Pause
11:15:155:14 Pause at ranch, go thru gate
11:29:5242:00 Pull chase car out of mud
13:16:051:32 Rejoin course
10:53:332:15 Pause
14:16:032:23 remove rubble blocking I-15 underpass
12:42:354:40 Pause
12:33:511:19 Pause
15:13:311:30 Wait for traffic to clear on NV 161
16:03:071:53 Pause
16:07:484:32 to take pictures
16:12:5011:44 negotiate bulldozed area
16:31:172:12 Survey another bulldozed area
8:20:555:20 Pictures at Primm return
8:31:428:53 Take down fence & pass through
GPS Tracks & Timing of Prospect Eleven’s Autonomous run of the 05 GC Course 10/31/05
Jan 26, 2006
Red: 8:00 Outbound 10/31Deviation to avoid “lake”
Yellow: 16:30 Return 10/31Deviation to avoid “lake”
Blue: 8:00 Outbound 11/2Lake dried sufficiently, no deviation required.
GPS Tracks & Timing of Prospect Eleven Diverting Around Not-so-dry Lake 05 GC Course 10/31/05
DAPRPA Grand Challenge, Unfinished Business, November 1, 2005
Return to Beer Bottle Pass
GPS Tracks of return to Beer Bottle Pass 11/01/05
DAPRPA Grand Challenge, Unfinished Business, November 1, 2005
Return to Beer Bottle Pass 2005 Grand Challenge Course, 1.9 miles
Start Down: 17:10:17
End Up: 17:04:48Duration: 0:10:21
Start Up: 16:54:27
End Down: 17:18:04
Duration: 0:7:47
GPS Tracks & Timing of Prospect Eleven’s Autonomous run up then back down Beer Bottle Pass 11/02/05
Jan 26, 2006
7:28:334:35 negotiate bulldozed area
7:55:2633:08 Divert to get gas for P11
8:39:1311:50 take pictures
8:34:014:30 take pictures
10:13:432:10 cross road
9:42:261:50 take pictures
10:04:592:07 take pictures
10:28:113:20 take pictures
7:08:36Start ’04 GC Course
GPS Tracks & Timing of Prospect Eleven’s Autonomous run of the 04 GC Course 11/02/05
DAPRPA Grand Challenge, Unfinished Business, November 2, 2005
Jan 26, 2006
14:50:xx4:00 Avoid Washout in 4 spots
15:10:102:04 Inspect burial monument
12:05:250:30 Xing CA 127
12:08:002:00 take pictures
13:08:541:05:56 Fix steering encoder
12:38:032:17 take pictures
12:19:371:50 take pictures
10:57:136:30 take pictures
12:53:360:54 Pause
14:33:152:45 take pictures
14:44:132:47 take pictures
GPS Tracks & Timing of Prospect Eleven’s Autonomous run of the 04 GC Course 11/02/05
DAPRPA Grand Challenge, Unfinished Business, November 2, 2005
Jan 26, 2006
17:16:3315:28 Replace Front Left Blowout
16:12:070:50 Xing road
15:19:004:32 take pictures
15:46:032:07 take pictures
15:38:011:37 take pictures
16:33:152:45 Letting traffic pass on Randall Drive
16:35:141:00 Xing Yermo Road
17:32:274:00 Inspecting Silt Filled underpasses < 4 ft. clearance
18:41:261:10 Pause let cars pass on Stoddar Valley Rd
GPS Tracks & Timing of Prospect Eleven’s Autonomous run of the 04 GC Course 11/02/05
18:18 Top
18:35 Bottom
Daggett Pass
Start 7:08:36Finish 18:44:19 – Arrival at gate of Slash X CafeElapsed Time 11:37:43Pause Time ~03:28:00Autonomous Time 08:09:00
File photo
File photo
File photo
Finish, ’04 Course
Jan 26, 2006
Jan 26, 2006
Accomplishments:• Invited to National Qualifying Event
• Seeded 10th for Grand Challenge
• Accomplished 10 miles of Autonomous Driving in GC
• “Completed” the 2005 & 2004 Courses during Fall Break
Overview:http://orfe.princeton.edu/~alaink/Prospect11/Movies/P11SummaryMovie.wmv
Wasn’t so easy, Outside: http://orfe.princeton.edu/~alaink/Prospect11/Movies/NQE2CrashOutsideView.mov
Wasn’t so easy, Inside: http://orfe.princeton.edu/~alaink/Prospect11/Movies/NQE2CrashInside.mov
Essentially Perfect:http://orfe.princeton.edu/~alaink/Prospect11/Movies/NQE5PerfectRun.mov
Launch at Grand Challenge:http://orfe.princeton.edu/~alaink/Prospect11/Movies/GCE-Start.AVI
Doing Better than 2004’s Best:http://orfe.princeton.edu/~alaink/Prospect11/Movies/GCE_PassBy8Miles.avi
Return to the Desert; 2005 Course:http://orfe.princeton.edu/~alaink/Prospect11/Movies/PGC05_10h29mFastDryLake.AVIhttp://orfe.princeton.edu/~alaink/Prospect11/Movies/PGC05_10h34mFastDryLake.AVI
Return to the Desert; Return to Beer Bottle Pass:
http://orfe.princeton.edu/~alaink/Prospect11/Movies/PGCBB_Small.mov
Return to the Desert; 2004 Course: http://orfe.princeton.edu/~alaink/Prospect11/Movies/PGC04_11h59mCruisin.AVI
Some Videos:
Jan 26, 2006
Lessons Learned• It is non-trivial to “Just Do It”
– You must respect Uncertainty (and plan for it)– Harmonize Accuracy– Time is your Friend
• (only know what you need to know when you need to know it)
– More is not necessarily Better– Always assume your code has bugs
• Stereo Vision Does Work!• Three (3) Regimes of Autonomous Control
– Under “7” mph– Between 7- 25 mph– Above 25 mph
Jan 26, 2006
Operational Processes used byCapital District Advanced Traveler Information System
(CD-ATIS)
CoPilot|MinETA: Real-Time Dynamic Minimum ETA Sat/Nav
by
Alain L. KornhauserCo-founder & Board Chair, ALK technologies, Inc.
Jan 26, 2006
1 6
1
1 1
2
2
2
3
3
3
4
3
5 5
6
6
8
8
9
6
PROBLEM: How to get from A to B•Many Paths
•Each with a Different Value to the Decision Maker
•Each Segment Changing with Uncertainty over Time
Things Change!!
4
Jan 26, 2006
Link Travel TimesHistoric, Actual & Forecast During Day One week-day on one link
Things change!
Jan 26, 2006
Real-Time Dynamic Minimum ETA Sat/Nav
•250 Volunteers using CoPilot|Live commuting to/from RPI
• CoPilot continuously shares real-time probe-based traffic data
• CoPilot continuously seeks a minimum ETA route
“Advance” project Illinois Universities
Transportation Research Consortium
The late 90s
Conducted its version of the abandoned “ADVANCE” (Advanced Driver and Vehicle Advisory Navigation ConcEpt )project
Link
&
Jan 26, 2006
Project Objectives
• Create: real-time data collection from vehicles and dissemination to vehicles of congestion avoidance information which is used to automatically reroute drivers onto the fastest paths to their destinations
• Target locations: small to medium-sized urban areas
• Aspects: operations, observability, controllability, users, information transfer to travelers
Jan 26, 2006
3-month field test
Capital District (Albany), NY, USA
Journey-to-work
200 participants80 Tech Park employees120 HVCC staff & students“Techy” travelers
Network:Freeways & signalized arterialsCongested linksPath choices exist
I 90
I 787
US
HW
Y 4
STATE
HW
Y 32
STATE HWY 2
STATE HWY 151US HW
Y 9
STATE HWY 378
2ND
ST
STATE HWY 155
WASHINGTON AVE
WINTER ST
15T
H S
T
STATE HWY 43
8TH
ST
STA
TE
HW
Y 3
77B
RO
AD
WAY
AV
E
CAMPBELL AVE
ACCESS RD
1ST ST
STATE HWY 136
COUNTY HWY 130
TIBBITS AVE
LIN
CO
LN A
VE
RA
MP
LOU
DO
N R
D
STATE HWY 43
RAMP
RA
MP
RA
MP
RAMP
RA
MP
HVCC
Rensselaer Technology
Park
TroyColonie
North Greenbush
Albany
Experiment Details
Jan 26, 2006
Basic Operational ArchitectureTwo-way cellular data communications between
Customized Live|Server
at ALK
Customized CoPilot|Live
In vehicles
6
Destination
12, 4
3 57
8
Jan 26, 2006
The In-Vehicle “Device”
Sprint PCS Vision card and battery pack: Communication
with the server
CoPilot GPS unit:Determines location
Pocket PC with 256 MB SD card: Software platform and audio
communication with the driver
Other Sat/Nav Platforms
Jan 26, 2006
Every Second
CoPilot|Live Determines “Where am I”, Then…
CoPilot|Live “Where Am I”,
Then…
ALK Server Updates:
TT(mi, mj )
If Momument, mj , is passed
Send mi , mj , ttk(mi, mj )= t(mi) - t(mi)
(52 bytes)
Set i=j
Jan 26, 2006
Every “n” Minutes
ALK Server Builds: set Uk
Sends: TT(mi, mj ) for every (i,j) in Uk
CoPilot|Live … Send… Current Location & Destination,
Last update time (42 bytes)
ALK Server …Send… New TT(mi, mj ) for every (i,j) in Uk
(280 bytes/100arcs)
CoPilot|Live …Updates TT(mi, mj ) in Uk , ETA on current route, Finds new
MinETA route, if MinETA “substantially” better then… Adopt new route
ALK Server …Determines Uk : set of TT(mi, mj ) within “bounding polygon”
of (Location;Destination)k that have changed more than “y%” since last update.
CoPilot|Live Sends: “Where am I”, Dest., Last update Receives/Posts: updatesComputes: MinETA Updates route, if better
Jan 26, 2006
When Available
ALK Server …Receives: Other congestion information from various
source, blends them in TT(mi, mj )
ALK Server Updates:
TT(mi, mj )
Jan 26, 2006
What We HeardI find it interesting how willing I am to listen to a machine tell me
which route to take
I like using it for when I have no idea on how to get somewhere, and it is good for my normal
route because it keeps me out of traffic on route 4.
It is great, it took a while to trust it telling me where to go, but i like it because i
cant get lost! Thanks.
This thing is awesome. I was a little skeptical at first but once i got the hang
of it I don’t know how I went along without it. I think any student commuting
to school will benefit from this.
I'm very impressed with the CoPilot program thus far. The
directions are accurate and it adapts quickly to route changes.
Jan 26, 2006
1
2
3
also Can Watch Vehicles
Jan 26, 2006
North American Monument Network• ~125,000 North American “Monuments”
• ~106 (mi, mj)
• 1st Commercial application in PC*Miler v19 (contains Median Travel Time by Time-of-Day for all NA)
(mi, mj) near Troy (mi, mj) larger area