Measuring Cooperative Robotic Systems Using Simulation-Based Virtual Environment

 

Xiaolin HuComputer Science Department

Georgia State University, Atlanta GA, USA 30303 

Bernard P. ZeiglerArizona 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

• Derived from mathematical dynamical system theory

• Based on a formal M&S framework

• Supports hierarchical model construction Atomic model Coupled model

• Explicit time modeling

DEVS (Discrete Event System Specification)

Source

SystemSimulator

Model

Experimental Frame

SimulationRelation

ModelingRelation

behavior database

real

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 tobe designed

Realenvironment

Sensor/actuator

Robotic system to be Designed

Controlmodel

Environmentmodel

VirtualSensor/actuator

Simulation & Test

Modeling

Controlmodel

Realenvironment

Sensor/actuatorinterface

System in Execution

Mapping

A Virtual Measuring Environment

A virtual measuring environment – an intermediate step that allows models and real robots to work together within a “virtual environment”

Simulation-based measuring using robot models and the environment model

Real system measuring with all real robots within a real physical environment

This virtual measuring environment will bring simulation-based 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.

virtual environment

virtual obstacle

virtual robots

computer

virtual counterpart of the real robot

ControlModel

virtual sensors HIL actuators

wireless communication

mobile robot

Architecture of the Virtual Measuring Environment

An Incremental Measuring Process

RobotModel

RobotModel

Virtual Environment

Virtual Sensor

Virtual Actuator

Virtual Sensor

Virtual Actuator

(a)

Conventional simulation

RobotModel

RealRobot

Virtual Environment

Virtual Sensor

Virtual Actuator

Virtual Sensor

HIL Actuator

(b)

Robot-in-the-loop simulation

RealRobot

RealRobot

Real Environment

Real Sensor

Real Actuator

Real Sensor

Real Actuator

(c)

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

RobotModels

EnvironmentModel

ExperimentalFrames

Define input stimuli, control, metrics, analysis from the measuring point of view

Model how the environment reacts/interacts with robots

Control model of robots

Models of sensors and actuators

Robot2

BReadyIn

FReadyIn

FReadyOut

BReadyOut

Robot3

BReadyIn

FReadyIn

FReadyOut

BReadyOut

FReadyOutRobotn

FReadyInRobot1BReadyIn

BReadyOut……

A Robot Convoy Example

• 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.

Avoid

Convoy

HWInterface activity

move

FReadyOutFReadyIn

moveComplete

moveComplete move

BReadyIn BReadyOut

FReadyOut

BReadyOut

FReadyIn

BReadyIn

• 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.

Robot Model

i

i-1 i

i-1

adi-1

di

D

RiRi-1

iRi-1

Ri

)cos(*

)sin(*

11

11

iii

iiii da

dtg

Dd

di

iiii

sin

)sin(* 11

iiiiii 11

Formula of Movement

move1 sensorData1

sensorDataN

startMove TimeManager1Robot1 t1

SpaceManager

Robot1 (x, y)

RobotN (x, y)

Obstacles (x, y)

moveComplete1

moveN startMove TimeManagerNRobotN tN

moveCompleteN

……

……

……

……

……

• 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.

Environment Model

Two Noise Factors

Random numbers are used to simulate the noises and variances in robots’ movement.

d

aD

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.

average position error with 30 robots

05

1015202530354045

1

78

9

15

77

23

65

31

53

39

41

47

29

55

17

63

05

70

93

78

81

86

69

94

57

10

24

5

11

03

3simulation steps

po

sit

ion

err

or

DNF=0.1, ANF=0.08

Formation Coherence

22 ))()(())()(()( tytytxtxtE desirediidesirediii (4)

)(cos*)()( 11 tDtxtx iidesiredi (5)

)(sin*)()( 11 tDtyty iidesiredi (6)

NtE

tE i )()( (7)

The formation coherence is affected by the noise factors.

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.

Position errors vs. noise factors

20

25

30

35

40

45

1

56

4

11

27

16

90

22

53

28

16

33

79

39

42

45

05

50

68

56

31

61

94

67

57

73

20

78

83

84

46

90

09

95

72

simulation steps

po

sit

ion

err

ors

Series1

Series2

Series3

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

Noise Sensitivity

The system is insensitive to the noise factors as long as these factors are within a safe boundary.

Position error vs. number of robots

15

20

25

30

35

40

0 10 20 30 40 50

number of robots

po

sit

ion

err

or

DNF=0.1, ANF=0.08

Scalability

• 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.

Robot_1 Robot_k Robot_n……

……

Environment Model

Real environment

abstract sensors – abstract motor

abstract sensors – HIL motor

real sensors – HIL motor

A Future Experimental Setup

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