1

Dynamic Speed and Sensor Rate Adjustment for Mobile Robotic Systems

Ala’ Qadi, Steve GoddardUniversity of Nebraska-Lincoln

Computer Science and Engineering Department

Jiangyang Huang, Shane FarritorUniversity of Nebraska-Lincoln

Mechanical Engineering Department

2

Introduction: Mobile Robotic Systems

As real-time systems, computations must be completed within established response times.

As spatial systems, the computation performed and their timeliness will be dependent on: The location of the platform in its

environment. The velocity with which the platform is

moving. The existence of objects in the environment.

3

Challenges

Task execution requirements change as the platform moves in the environment.

Platform velocity is dependent on the rate system can collect and process data.

Dynamic changes in the environment (obstacle) might lead to overload conditions.

4

Contributions

An abstract analysis methodology for mobile real-time systems that integrates spatio-temporal properties: processing windows. zone abstractions.

Dynamic adjustment algorithm: maintains a maximum speed less than or equal to the

desired speed. maintains schedulabilty by adjusting

processing window. platform speed.

5

Processing windows

Processing Window: The time interval from the instant the platform starts collecting data to the moment the platform must finish processing the data.

A processing window is the deadline for execution of one or more interdependent tasks.

6

Zones: No Motion

2-Dimensional Zone Example

We define a zone as the area for which the platform collects and processes sensor information, creates a map for the area and plans its path through the area.

B

i

F

ii

i

ttwrD

−==

7

Zones: Mobile System

In MotionIn motion, safety area included

MiSABrD −−=RadiusZone

8

Zones: Definitions

Planning Point Fi =(tiF ,Li

F)

Data Collection Point Bi=(tiB ,Li

B)

Two-Dimensional Zones

LiF =(xi

F,yiF,i

F)

LiB =(xi

B,yiB,i

B)

Fi =(tiF,xi

F,yiF,i

F)

Bi=(tiB,xi

B,yiB,i

B)

9

Zones: Zone Processing Windows

Maximal Scanning Minimal Scanning

),[, F

i

F

i

F

i

F

iittWttw

11 ++=−= ),[, F

i

B

i

B

i

F

iittWttw =−=

10

Dynamic Processing Windows

Changes in the platform environment.

Increasing the maximum possible platform speed.

Increasing performance for processing window related task.

11

Sensor Impact on Processing Window Length

The zone processing window of the platform is dependent on sensor parameters: number of sensor n. set of delays between sensor readings/invocations . set of sensor range and sensitivity R. set of sensor tasks execution times E. feasibility function g is dependent on the sensors and the

associated tasks and parameters.

Independent delays, R, Sensor range dependent delays

),,( ≥ Engw

),,,( RIEngw ≥

12

Schedulabilty Impact on Processing Window Length

Any mobile real-time platform will have a set of tasks

is set of tasks associated with the zone processing window w.

is a (possibly empty) set of periodic tasks with higher priority than .

is a (possibly empty) set of periodic tasks with lower priority than

.

}TTT{Thplpw

UU=w

T

lpT

hpT

wT

wT

13

Schedulabilty Impact: Fixed Priority Scheduling

)(

)(

21

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

Eq

pe

epe

pe

p

epe

pep

ep

pep

Eqep

pep

j

ii

i

j

ii

j

j

ii

j

ii

i

j

j

ii

j

ii

i

jjj

i

j

ii

j

jj

i

j

ii

j

jj

∑

∑∑∑

∑∑

∑

∑

−

=

=

=

−

=

−

=

−

=

−

=

−

=

−≥⇒≥⎟⎟

⎠

⎞⎜⎜⎝

⎛−

++≥

⋅⎟⎟⎠

⎞⎜⎜⎝

⎛++≥

⋅⎥⎥

⎤⎢⎢

⎡+≥

boundlooser aget to for subsitutecan weBecause ⎥⎥

⎤⎢⎢

⎡++≤⎥

⎥

⎤⎢⎢

⎡≤

i

j

i

j

i

j

i

j

i

j

pp

pp

pp

pp

pp

11

14

Combining the sensor bound with the schedulabilty bound.

If , to find the lower bound on w, Solve

The same procedure can be extended if .

)(),,,(hpT

3Eqepw

RIEngwi

ii

⋅⎥⎥

⎤⎢⎢

⎡+≥ ∑

∈

Φ=lp

T

Φ≠lp

T

15

Motion Impact on Processing Window Length

The maximum speed at which the platform can travel is related to the rate the environment can be scanned and signals processed.

The speed of the platform for a zone is dependent on The radius of the zone. The zone-processing window. The speed of the platform in the previous zone. The existence of obstacles in the zone.

16

Motion Impact on Processing Window Length

First Zone Z0

01

=−

),,,(max iiii

Dwvvf

),,,( BBB yxB0000

0 =

),,,( BBB yxwF0000

=

Beyond Z0

iiFB =

+1

Motion Bound

17

Example: 2-dimisional Constant Speed

wSr

vw

Swvrv

SwvrDwD

v

MM

Mi

i

i

2−=⇒−⋅−=

−⋅−=

=

max

max

max

max

max

If at any plan point Fi we change the zone processing window wi or change the sensor detection range ri.

1

1

+

−−⋅−=

i

Miii

i wSwvrv

max

18

Motion Impact on Processing Window Length: Obstacles Exist

The distance the platform can safely move is not the zone radius.

Move safe distance between the obstacle and the platform, Xobs.

If Xobs < Di

01

=−

),,,(max obsiii

Xwvvf

19

Processing Window Adjustment Algorithm

Dynamic ProcessingWindow Adjustment

AlgorithmEnvironmentRequirementParameters

Sensor RequirementParameters

SchedulabilityRequirements

Minimum Processing Window Length

Maximum PerformanceParameters

Scheduler

20

Processing Window Speed/Adjustment Algorithm

At the end of w(At the planning point)

Obstacle Exist

No Obstacle

No

Yes

No Yes

No Obstacle

No Yes

Yes

No

AdjustSpeed

YesNo

ii

iMiiidesired

jT j

i

ii

wr

wSwvrv

ep

r_IEngr_IEngw

v

j

and for

/)(

),,,(),,,(

Solve , maximize To

hpT

+⋅−=

⋅⎥⎥

⎤⎢⎢

⎡+=

−

∈

∑

1

maxmin rrr i ≤≤

iMiiii

jT

j

i

ii

wSwvrv

ep

r_ IEngr_ IEngw

j

/)(

),,,(),,,(

hpT

+⋅−=

⋅⎥⎥

⎤⎢⎢

⎡+=

−

∈∑

1

desiredvv <max

iMiiiiislack

desiredi

vSwvwvrt

vv

/))(( 11 +⋅+⋅−=

=

+− iMiiiiislack

i

vSwvwvrt

vv

/))(( 11

max

+⋅+⋅−=

=

+−

minrr

v

i =

maximizeTo

i

jT

j

wrv

ep

r_ IEngr_ IEngw

rr

j

⋅=

⋅⎥⎥

⎤⎢⎢

⎡+=

=

∑∈

2/

),,,(),,,(

maxmax

T

max

max

max

hp

max

max

for),,,(Solve

vXwvvf

obsii0

1=

−

desiredvv <max

desiredvv<

desiredv

desiredvv=

maxmax

T

min

min

min

for),,,(Solve

),,,(),,,(

,maximizeTo

hp

vXwvvf

ep

r_ IEngr_ IEngw

rrv

obsii

jT

j

i

i

j

01

=

⋅⎥⎥

⎤⎢⎢

⎡+=

=

−

∈∑

desiredvv <

max

0max

=

=

slack

i

t

vv

0==

slack

desiredi

tvv

21

Case Study1: Robot Navigation Using Sonar Sensors

Companion is a robot with 24 sonar sensors, 15o apart.

22

Task Processing Graph

n

τtMapTask

PlanTask

So nar

SendSenso r

Receive

planmaprecvsendee

reenRIEng ++⋅+++⋅= )(),,,(

3402τ

DeadReckoning

TaskPID Task

wT

hpT

23

Motion Bounds

No Obstacles

Obstacles Exist1

1

+

−−⋅−=

i

Miii

i wSwvrv

max

obs

ii

i

i

obsiiiX

mv

mv

wvmv

Xwvvf −−⎟⎠⎞

⎜⎝⎛ ++−= −−

− 22

2

11

2

1 max

max

max),,,(

24

Obstacle

Robot Body

Sonar SensorRing

Robot Path

Zone Boundary

Sonar Range Boundary

Simulation

Obstacle

Robot Body

Sonar SensorRing

Robot Path

Zone Boundary

Sonar Range Boundary

Without Processing Window/Speed

Adjustment With Processing Window/Speed

Adjustment

25

Actual Test

Without Processing Window/Speed

Adjustment With Processing Window/Speed

Adjustment

26

Results Summary

without Algorithm with Algorithm

ttotal (s) 96.48 73.17

38.20 48.02

76.40% 96.04%

without Algorithm with Algorithm

ttotal (s) 85.20 65.53

29.74 36.09

29.97 36.85

59.48% 72.18%

59.97% 73.7%

(cm/s)v

(%)/desired

vv

(cm/s)v

(%)/desired

vv

(cm/s)actual

v

(cm/s)/desiredactual

vv

Simulation Result Summary

Actual Test Summary

27

Conclusion

We presented a method for integrating speed requirements of a mobile robotic

platform with real-time fixed priority scheduling.

New abstractions called zones and processing windows were created.

An algorithm for the adjusting zone processing window was developed.

Improved system performance (Speed).