Measuring Cooperative Robotic Systems Using
Simulation-Based Virtual Environment
Xiaolin Hu
Computer Science Department
Georgia State University, Atlanta GA, USA 30303
Bernard P. Zeigler
Arizona Center for Integrative Modeling and Simulation
University of Arizona, Tucson AZ, USA 85721
Agenda
•
Background on DEVS and Model Continuity
•
The Virtual Measuring Environment
•
The Robotic Convoy Example
•
Preliminary Simulation Results
•
Future Work
DEVS (Discrete Event System Specification)
• Derived from mathematical dynamical system theory
• Based on a formal M&S framework
• Supports hierarchical model construction

Atomic model

Coupled model
• Explicit time modeling
Experimental Frame
real
Source
System
Simulator
behavior database
Modeling
Relation
Simulation
Relation
Model
DEVS Formalism
A Discrete Event System Specification (DEVS) is a structure
M = <X,S,Y,int,ext,con,, ta>
where
X is the set of input values.
S is a set of states.
Y is the set of output values.
int: S  S is the internal transition function.
ext: Q  Xb  S is the external transition function, where
Q  {(s,e) | s  ?S, 0  e  ta(s)} is the total state set,
e is the time elapsed since last transition,
Xb denotes the collection of bags over X.
con: S  Xb  S is the confluent transition function.
: S  Yb is the output function.
+
ta: S  R 0, is the time advance function
A Background on Model Continuity for
Robotic Software Development
The control logic to
be designed
Control
model
Control
model
Sensor/actuator
Virtual
Sensor/actuator
Sensor/actuator
interface
Real
environment
Environment
model
Real
environment
Robotic system to be Modeling
Designed
Simulation &
Test
Mapping
System in
Execution
A Virtual Measuring Environment
Simulation-based
measuring using robot
models and the
environment model
A virtual measuring environment
– an intermediate step that allows
models and real robots to work
together within a “virtual
environment”
Real system measuring
with all real robots
within a real physical
environment
This virtual measuring environment will bring simulationbased study one step closer to the reality.
Realization of the Virtual Measuring Environment
•
Model Continuity allows the same control models used in simulation to
be deployed to real robots for execution. The couplings among these
models are maintained from simulation to execution.
•
The clear separation between the control model and sensor/actuator
interface make it possible for the control model to interact with different
types of sensors/actuators, as long as the interface functions between
them are maintained.
•
The control model of a real robot can use real sensors/actuators to interact
with the real environment and virtual sensor/actuators to interact with a
virtual environment.
•
A real robot can communicate with robot models simulated on
computers, resulting in a system with combined real and virtual robots.
Architecture of the Virtual Measuring
Environment
virtual environment
virtual sensors
HIL actuators
virtual obstacle
virtual counterpart
of the real robot
Control
Model
virtual robots
wireless
communication
computer
mobile robot
An Incremental Measuring Process
Robot
Model
Robot
Model
Robot
Model
Real
Robot
Real
Robot
Real
Robot
Virtual Virtual
Sensor Actuator
Virtual Virtual
Sensor Actuator
Virtual Virtual
Sensor Actuator
Virtual HIL
Sensor Actuator
Real
Real
Sensor Actuator
Real
Real
Sensor Actuator
Virtual Environment
Virtual Environment
Real Environment
(a)
(b)
(c)
Conventional
simulation
Robot-in-the-loop
simulation
Real system
measurement
Experimental Frames
•
input stimuli: specification of the class of admissible input time-dependent
stimuli. This is the class from which individual samples will be drawn and
injected into the model or system under test for particular experiments.
•
control: specification of the conditions under which the model or system will be
initialized, continued under examination, and terminated.
•
metrics: specification of the data summarization functions and the measures to
be employed to provide quantitative or qualitative measures of the input/output
behavior of the model. Examples of such metrics are performance indices,
goodness-of-fit criteria, and error accuracy bound.
•
analysis: specification of means by which the results of data collection in the
frame will be analyzed to arrive at final conclusions. The data collected in a
frame consists of pairs of input/output time functions.
An Architecture with Experimental Frames
Control model
of robots
Define input stimuli,
control, metrics,
analysis from the
measuring point of view
Robot
Models
Models of
sensors and
actuators
Experimental
Frames
Environment
Model
Model how the environment
reacts/interacts with robots
A Robot Convoy Example
FReadyIn
Robotn
FReadyOut
…
…
BReadyIn
FReadyOut
Robot3
FReadyIn
BReadyOut
BReadyIn
FReadyOut
Robot2
FReadyIn
BReadyIn
Robot1
BReadyOut
BReadyOut
• Robots are in a line formation with each robot has a front neighbor
and a back neighbor.
• The system try to maintain the coherence of the line formation
• A robot’s movements are synchronized with its neighbors
• A robot (except the leader robot) goes through a basic “turn – move
– adjust – inform” routine.
• No global communication/coordination exists.
Robot Model
FReadyIn
FReadyIn
BReadyIn
BReadyIn
Convoy
moveComplete
move
FReadyOut
FReadyOut
BReadyOut
BReadyOut
move
Avoid
moveComplete
HWInterface activity
•
Based on Brooks’ Subsumption Architecture
•
The Avoid model controls a robot to move away if the robot collides with
anything. The Convoy model is fully responsible to control a robot to convoy in
the team.
•
HWInterface activity is responsible for the sensor/actuator hardware interfaces.
Formula of Movement
D
Ri-1
di
Ri
i
i-1
Ri
Ri-1
i-1
i
di-1
a
tg i 
d i 1 * sin( i 1   i )
a  d i 1 * cos( i 1   i )
d i 1 * sin( i 1   i )
di 
D
sin  i
 i    i   i 1   i 1   i   i
i
Environment Model
move1
…
…
moveN
startMove TimeManager1
Robot1 t1
…
…
startMove TimeManagerN
RobotN tN
moveComplete1 SpaceManager
…
…
Robot1 (x, y)
…
…
sensorData1
…
…
RobotN (x, y)
moveCompleteN Obstacles (x, y)
sensorDataN
•
This TimeManager determines how long it takes for a robot to finish a movement.
•
The SpaceManager is a model of the experimental floor space, including the size,
shape and position of the work area, the static objects and robots.
•
In this example we have ignored the detailed dynamic processes of a movement.
Two Noise Factors
a
Random numbers are used to
simulate the noises and variances
in robots’ movement.
D
d
Distance noise factor (DNF): the ratio of the maximum distance
variance as compared to the robot’s moving distance.
Angle noise factor (ANF): the ratio of the maximum angle
variance as compared to the robot’s moving distance.
Formation Coherence
The formation coherence is
affected by the noise factors.
45
40
35
30
25
20
15
10
5
0
11033
10245
9457
8669
7881
7093
6305
5517
4729
3941
3153
2365
1577
1
DNF=0.1, ANF=0.08
789
position error
average position error with 30 robots
simulation steps
Ei (t )  ( xi (t )  xi d esired (t )) 2  ( y i (t )  yi d esired (t )) 2
(4)
xi desired (t )  xi 1 (t )  D * cos i 1 (t )
(5)
yi desired (t )  yi 1 (t )  D * sin i 1 (t )
(6)
E (t )
E (t )  
i
N
(7)
We use the average position
error of the robot team as the
indicator for the convoy
system’s formation
coherence: the smaller the
error is, the more coherent the
convoy system is.
The position error does not
accumulate over time –
coherent.
Noise Sensitivity
Position errors vs. noise factors
position errors
45
40
35
Series1
30
Series2
Series3
25
9572
9009
8446
7883
7320
6757
6194
5631
5068
4505
3942
3379
2816
2253
1690
1127
564
1
20
simulation steps
Series 1: DNF = 0.04, ANF = 0.04, average = 35.08
Series 2: DNF = 0.1, ANF = 0.08, average = 35.69
Series 3: DNF = 0.2, ANF = 0.1, average = 36.61
The system is insensitive to
the noise factors as long as
these factors are within a
safe boundary.
Scalability
Position error vs. number of robots
40
position error
35
30
DNF=0.1, ANF=0.08
25
20
15
0
10
20
30
40
50
number of robots
•
It shows that the average position error increases as the number of
robot increases.
•
If this trend holds true with more robots, the system is not scalable
in the sense that it will eventually break as more robots are added
into the system.
A Future Experimental Setup
Environment Model
Robot_1
…
…
…
…
Robot_k
Robot_n
Real environment
abstract sensors –
abstract motor
abstract sensors –
HIL motor
real sensors –
HIL motor
For example, we can check the back robot’s position errors based on the
position and direction of its front robot in the physical environment.
Thank you