A Performance and
Schedulability Analysis of an
Autonomous Mobile Robot
Ala’ Qadi & Steve Goddard
Computer Science & Engineering
University of Nebraska–Lincoln
Jiangyang Huang & Shane Farritor
Mechanical Engineering
University of Nebraska–Lincoln
Highway Robotic Safety Marker System


RSM system is a mobile,
autonomous, robotic,
real-time system that
automates the placement
of highway safety
markers in hazardous
areas.
The RSMs operate in
mobile groups that
consist of a single lead
robot (the foreman) and
worker robots (RSMs).
prototype foreman. A prototype RSM
Tasks Performed by the Foreman

Plan its own path and motion.

Locate RSMs, plan their path,
communicate destinations points, and
monitor performance.
Foreman Design
Sonar Unit
24-sonar ring
circuit board
Main Unit
Communication Unit
Motor Unit
Parallel Port
PIC16F84
MicroController
9XStream OEM RF
Module
PC/104-Plus
(Windows CE OS)
RS232
DM5406
Motor Circuit Board
TCP/IP
RS485
Driving
Motor
Power Unit
Batteries, DC to DC
converters, etc.
Localization Unit
Sick Laser LMS200
Sensor Unit
Rabbit 3000 Microprocessor,
encoders, gyro
Steering
Motor
Foreman Path Planning
Plan its own path and
motion.

1555
15
1115
15o
1
115
1555

Sonar sensors are used to
detect obstacles in the
foreman’s path.
The sonar unit consists of a
ring of 24 active sonar
sensors, with 15
separation, that provides
360 coverage around the
foreman.
15
15

Sonar Sensor Distribution
Foreman Path Planning

Sonar Send Task: Sends a command to its
corresponding sonar sensor to transmit its signal.

Sonar Receive Task: Reads the corresponding
sonar sensor after the signal is echoed back to the
sensor.

Motor-Control Task: Computes the path of the
foreman and controls its speed based on the data
collected from the sonar signals.
Foreman Path Planning Task Set
Task
e
P
d
f
max J
Sonar-Sendi
esend=.085ms
ps
esend
fsendi
0
Sonar-Receivei
erecv=.03ms
ps esend+ erecv+ max Dt frecvi
Path-PlanSpeed-Control
eplan=1.32ms
ps
eplan
fplan
Foreman Motion Control Task Set
max Dt
0
Foreman Path Planning
Zone 0*
Zone 1
Zone 0
D = Dmax
(Sonar Range)
Motion Start
S2
Zone 3
D = Dmax
(Sonar Range)
S4
ps
S3
ps
Case 1: Ideal
Environment
(No Obstacles)
D = Dmax
(Sonar Range)
S1
S0
Zone 2
ps
ps
ps
Time
System
Start
vmax.ps
(0,0)
vmax.ps
Traveled
Distance
vmax.ps
vmax.ps
.
.
.
.
.
.
Foreman
Path Planning
Zone 0*
D = Dmax
(Sonar Range)
Motion Start
D = Dmax
(Sonar Range)
S2
S1
Zone 3
D = Dmax
(Sonar Range)
S3
S4
.
.
.
.
.
.
ps
S0
Zone 2
ps
Case 1: Ideal Environment
(No Obstacles)
Zone 1
Zone 0
ps
ps
ps
Time
ps  frecv2 4  d recv2 4  e plan
System
Start
vmax.ps
(0,0)
vmax.ps
vmax.ps
 23   24  esend  max Dt  erecv  esend  e plan
 23   25  esend 
2 D
 erecv  e plan
340m / s
vmax.ps
Traveled
Distance
vmax i1 
Di  vi  psi
psi1
Foreman Path Planning
Case 2: Obstacles Exist



Maximum Safe Distance Depends on the
obstacles.
Speed might need to be adjusted at scan
points due to obstacles.
This means that the maximum speed for the
zone after the obstacle is also dependent on
the speed before reaching the obstacle.
Example Scenario 1
D=Dmax , No period adjustments
Example Scenario 2
Period adjustments and Sonar Range Adjustments
RSM Motion Planning and Tracking

Locate RSMs, plan their path, communicate
destinations points, and monitor performance.
A laser scanner is used to determine the location
of the RSMs.
RSM Motion Planning and Tracking
Task Set
Task
e
p
d
f
max J
Scanning
12ms
pl
pl
0
0
Detecting
.0172n2+.1695n+12.69
pl
pl
0
0
Predicting
3.8n
pl
pl
0
0
Planning
16ms
1500ms 1500ms
0
0
Way Point
8.33ms
1500ms 1500ms
0
0
Window
Resizing
2ms
0
0
pl
pl
Relation Between RSM Location Estimation
Error and the Laser Scan Period
80
25
70
20
Distance Error (cm)
Distance Error (cm)
60
15
10
50
40
30
20
5
10
0
0
0
100
200
300
400
500
600
700
800
900
1000
50
100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000
Laser Sampling Rate (ms)
Laser Sampling Rate (ms)
Maximum Error
Average Error
 average  0.0219  pl  0.2517
 max  0.616  12.467
Characteristics of the Task Set



Some tasks have variable periods that
depend on the system performance
parameters.
The accuracy of RSM position prediction is
dependant in pl. (Higher accuracy with
smaller period.)
The foreman’s maximum traveling speed
is dependant on ps. (Higher speed means
smaller periods.)
Proposed Solution


Combine both task
sets into one task
set with fixed priority.
Analyze the task set
and devise the
minimum number of
online scheduling
tests with minimum
overhead.
Task
Index
Task
p
Priority
1
Sonar Sendi
ps
1
2
Plan Speed
ps
2
3
Sonar Receivei
ps
3
4
Scanning
pl
4
5
Detecting
pl
5
6
Predicting
pl
6
7
Window
Resizing
pl
6
8
Planning
1500
7
9
Way Pointi
1500
8
Combined Task Set
Task Set Analysis
Offline Tests

Theorem 4.1: All Sonar Send tasks (Task 1) will
always their deadlines if
ps  23   24  esend  max Dt  erecv  esend  e plan.
Task Set Analysis
Offline Tests

Theorem 4.1: All Sonar Send tasks (Task 1) will
always their deadlines if
ps  23   24  esend  max Dt  erecv  esend  e plan.

Theorem 4.2: The Path-Plan/Speed-Control task
(Task 2) will always meet their deadlines if
ps  23   24  esend  max Dt  erecv  esend  e plan.
Task Set Analysis
Offline Tests

Theorem 4.1: All Sonar Send tasks (Task 1) will
always their deadlines if
ps  23   24  esend  max Dt  erecv  esend  e plan.

Theorem 4.2: The Path-Plan/Speed-Control task
(Task 2) will always meet their deadlines if
ps  23   24  esend  max Dt  erecv  esend  e plan.

Theorem 4.3: All Sonar Receive tasks (Task 3)
will always their deadlines if
ps  23   24  esend  max Dt  erecv  esend  e plan.
Task Set Analysis
Online Tests
 Theorem 4.4: All tasks will meet their deadlines if
Equations (9) and (10) hold.
 e  DEM
i
p  pi
 e  DEM
p 1500
i
Ti , i 1,... 3
Ti , i 1,...3
( pl )  pl
(1500)  1500
(9)
(10)
Period Adjustments

Task periods pl and/or ps may need to be
adjusted to achieve the desired performance
metrics in the following cases:



Adjusting the speed of the foreman—either because
we want to move faster from one position to the other
or because there is an obstacle in the path.
Increasing the accuracy of RSM path prediction.
Increasing the number of RSMs being controlled.
On Going And Future Work

Developing an application-level control
algorithm that can make dynamic
performance/schedulability tradeoffs.

Generalizing the modeling and schedulability
analysis presented here so that it can be
applied more easily to tasks of other real time
mobile autonomous systems.
Questions??