Mobile robots “Phoenix-3” and SOFA-2009

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12 Νοε 2013 (πριν από 3 χρόνια και 5 μήνες)

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Mobile robots SOFA
-
2009
and “Phoenix
-
3”

Alex Astapkovitch, head of the Student Design Centre State
University of Aerospace Instrumentation

Alex Burdukov, student, “Phoenix
-
3” project leader


SOFA
-
2009

Virtual robot

benchmark
model

Real robots:

Virtual robots:

2006
-

2007

2007
-

2008

2008
-

2009

“Phoenix
-
3”

-
Phoenix Robotics Group
-

Virtual robot SOFA
-
2009

-

Mobile robots are complex electromechanical devices the real experiments are
very expensive in sense of time and stuff.

-

During Phoenix
-
2 project a virtual environment and simplified robot model were
developed to generate on board cameras images.

-

Phoenix
-
3 project is the third step of Phoenix student research group that consists
from the hardware development and the background theory activities.

-

The strategic goal of the “Phoenix
-
X” projects is a developing of understanding of the
learning strategy for the control system on base of a neuron net.

-

SOFA
-
2009 was started as scientific support for “Phoenix
-
3” project
and still is the part of “Phoenix
-
X” student research activity, but now...

It is a free ticket on fast train for young researches
to Computational Robotics field valley !

Virtual robot SOFA
-
2009

-
Main goal of SOFA is introduction to robotic society the benchmark model
than can be used to investigate neuron net control system learning.

Research activities of Phoenix research group is concerned of “Teaching by
Showing” approach for multi channel real time control systems, based on
artificial neural net.

-
The model has to be as simple as possible and of autonomous differential
drive wheel robot is used as legend.


SOFA
-
2009 benchmark model formulated as system of ordinary
differentional equations:




dx/tx =f(x)+U(t)



X(0)=X0

-
MathCAD 14 was used as a tool due to friendly and fast user interface.

Virtual robot SOFA
-
2009

Kinematics and dynamics models of virtual robot SOFA


axe x

direction
“forward”


φ(t)



robot angle
position


axe
y


axe x

earth fixed frame

R
с

(t)



robot center


position vector



R
0

(t)
-

instant

center of arc

R(t)



instant

rotation radius

φ (t+∆t)
-

φ (t) = ∆ φ (for left wheel) = ∆ φ (for right wheel)

R
0

(t) = R
0

(t+∆t)

Basic relations:

Virtual robot SOFA
-
2009


















































),
(
1
)
(
1
)
(
2
cos
4
)
(
sin
4
)
(
2
2
23
2
2
1
1
13
1
1
2
21
2
22
2
1
2
1
1
11
1
1
2
2
1
2
1
t
U
L
L
k
I
L
R
dt
dI
t
U
L
L
k
I
L
R
dt
dI
I
J
k
J
k
dt
d
I
J
k
J
k
dt
d
Lr
D
dt
d
D
dt
dR
D
dt
dR
m
m
m
m
m
m
m
m
r
r
r
r
w
w
y
c
w
x
c















Model SOFA
-
2009 is defined with
parameters set :




Dw = 0.3


Lr = 0.5


Jr = 0.25


k11 = k22 = 75


k12 = k21 = 10


Rm = 0.1


Lm = 0.01


k13 = k23 = 1.5


Vmax = 12




Vmax is the maximal absolute value for
accumulator voltage.

Model includes dynamic equations, gear model for every wheel, motor model,
control system model.

The simplest as possible model consists of 7 ODE with at least 9 parameters.

Control voltages:


U
1
(t) =0

U
2
(t) = U
max

= 12 V.

Control voltages:


U
1
(t) = U
2
(t) = U
max

=
12 V.

Virtual robot SOFA
-
2009

TEST_1. Moving forward with speed 4/5 m/sec

TEST_2. Rotation around left wheel with ang. speed
π
/4 r/s

SOFA
-
2009 model testing Rc(0)
X,Y

= 0
φ
(0) = 0

Virtual robot SOFA
-
2009

Transfer
function

Vout

Vin

Actor layer neuron

Vmax, Vmin

Uout Left Motor

Uout Right Motor

AFSS

APS

ASS



Sensor

layer

Left motor control channel

W
left

= [w
0l
,w
1l
,w
2l
]


Right motor control channel

W
right

= [w
0r
,w
1r
,w
2r
]


Uin left

Uin right

APS


Angle Position Sensor

ASS


Angle Speed Sensor

AFSS


Angle Final Speed Sensor


Example of neuron control system:

Virtual robot SOFA
-
2009


S
1
(T
1
) S
2
(T
1
) .. S
n
(T
1
)



S
1
(T
2
) S
2
(T
2
) .. S
n
(T
2
)


……………………



S
1
(T
p
) S
2
(T
p
) .. S
n
(T
p
)



w
1


w
2





w
n

A
1
(T
1
)


A
1
(T
2
)




A
1
(T
p
)

*

=

S * w = Ua

Matrix form

One step learning paradigm idea:

min

F(w) = (Sw
-

Ua, Sw


Ua) +


⡷,w⤠


w

Tixonov regularization

w = (S
T

S +


䔩E

1

S
T

Ua

Weights calculation

Virtual robot SOFA
-
2009

Experiment with virtual robot includes at least three steps:




sample generating and neuron net control system learning ;



simulation of the robot dynamics with "learned "neuron net control system;



research experiments.


1. SAMPLE GENERATING AND NEURON NET LEARNING



Final position

vector X(T1),

velocity


vector V(T1)


SOLUTION

TABLE

[t
i
, X (t
i
) ]

Sensor

System

Model

Weight Matrix Calculation


W= (S
t
S
+γE)
-
1
S
t

Ua

NEURON

NET

CONTROL

SYSTEM

STRUCTURE



Cauchy

problem

solution for

[
T0
-
T1]

Control voltage matrix

(vector Ua(t) for every motor ),

that corresponds to robot mission

Initial

position

vector X0

Robot model

Virtual robot SOFA
-
2009

Initial and final
positions, control net
structure depends on
research

PROBLEM

NEURON

NET

CONTROL

SYSTEM

MODEL



Cauchy

Problem

Solution



POST

PROCCESINGS

NEURON

NET

CONTROL

SYSTEM

MODEL



Cauchy

problem

solution


and

estimation



Initial

position

Final
position

Robot
model

2. CONTROL SIMULATION

3. NUMERICAL EXPERIMENTS

Examples are presented in applications to articles and in site
http://guap.ru/guap/sdc

Virtual robot SOFA
-
2009

Example of the supervised learning for π/4 rotate

to left sample:

S
ample rotation to left with maximal velocity


learning sample of control voltages for left and
right motors


preliminary estimation of the training


estimation of the robot dynamics under neuron net
control system for π/4 rotate to left for limited and
unlimited actor voltage

Virtual robot SOFA
-
2009

rotation to left on
π

with limited and unlimited
Vmax

motor currents for limited and unlimited voltage

phase portrait for unlimited case: start point
(0,0),final (3.14,0)

phase portrait for limited Vmax: start
point (0,0),final (3.14,0)

Sample of autonomous operation

for π rotate t
ask:

Virtual robot SOFA
-
2009

-
MathCAD 14 example code presented in article as appendix to articles


A. Astapcovitch “Virtual mobile robot SOFA
-
2009 for Computational


Robotics Research”;


A. Burdikov “
Autonomous Robot “PHOENIX
-
3”


SOFA 2009_TEST1_2.xmcd



-

SOFA model test

SOFA 2009_A_LEARNING.xmcd


-

learning to rotate

SOFA 2009_DISTANCE_LEARNING.xmcd

-

learning to move ahead

SOFA 2009_AD_LEARNING.xmcd


-

learning to reach the prescribed






2D point

-

Virtual robot SOFA
-
2009 with neural net control system and learning
procedure can be downloaded for free from the site
http://guap.ru/guap/sdc

-

Site section SOFA
-
2009 has examples:

Autonomous Robot “PHOENIX
-
3”

Autonomic robot Phoenix
-
3 is designing to be able to patrol the determined area with
the purpose of detection the centers of the flame. In case of the flame detection the
robot should come nearer and use the onboard fire extinguisher to eliminate flaming.
For orientation the video shock
-
proof camera with the rotary mechanism and a zoom
lens is supposed to be used.

Project legend:

Autonomous Robot “PHOENIX
-
3”

-
There are several steps in neural system synthesis using “teaching by
showing” methodology.

-

During the 1st step robot’s movement are controlled by a traditional control
system or by operator. During this procedure robot’s sensors information and
control commands are written to onboard laptop.

-
This data is used on the 2nd step for neural regulator coefficients
determination.

-

It means that the control system has to have at least two basic modes of
operations: operator control mode and autonomous operation.

-

Operator control mode is used during the learning phase.

Autonomous Robot “PHOENIX
-
3”

Control system structure during autonomous operation:


Controller ASK
-
Lab

Left and Right

Motor Control

Bridges

Rotating
camera

(sensor)

Multichan
nel Video
IP
-
codec
ASK
-
Lab

Laptop

Fire
extinguisher
engine

Actors

Sensors

RS
-
232

Rotating
camera

(position
motors)

RS
-
485

Ethernet

Ultrasonic
Orientation
System

CANbus

Still
Camera

Autonomous Robot “PHOENIX
-
3”

Wi
-
Fi
AP


Computer

Video link

RF
-
transmitter

cam. output
1

cam. output
2

Pad 1 (robot)

Pad 2 (
fire
extinguisher
)

Operator

Radio link

Control system structure for operator control mode
:

-
During Phoenix
-
2 experiments, two control schemes were tested


one with analog and
one with digital control channel.

-
It was noticed, that digital control system has significant delays in the channel, so it was
decided to use an analog control system for Phoenix
-
3 project.


Autonomous Robot “PHOENIX
-
3”

Analog
joysticks

RF
-
transmitter

RF
-
receiver

Controller

Laptop

Actors and
sensors

Two channel RF
-
control system
.

-
Phoenix
-
3 project implements two channel control system: one for robot
movement control and another for control on board equipment.

-
Hitec FOCUS 6 RC
-
equipment was used during experiments. It includes a
control pad and receiver module.

Autonomous Robot “PHOENIX
-
3”

Ultrasonic Orientation System.

1


MCP 2510 CANbus controller chip;

2


PIC18F458 microcontroller chip;

3


16
-
bit counter;

4


ultrasonic pulses generator;

5


ultrasonic receiver;

6


ultrasonic transmitter;

7


frequency divider;

8


quartz generator.

-

Ultrasonic distance measuring module based on MuRata MA40S8S and MA40S8R
devices was developed.

Has a net structure based on CANbus.

-

Developed module can measure of distances up to to 2 m. with accuracy resolution
approx. 0,2 mm.


2

3

1

4

6

5

8

7

CANbus module structure:

5

6

Autonomous Robot “PHOENIX
-
3”

It

was

demonstrated

during

Phoenix
-
1

project

that

camera

inclination

sensor

is

the

necessary

element

of

control

system
.


Video subsystem.

“Phoenix
-
3” video subsystem of the robot includes a rotary shock
-
proof camera with
the rotary mechanism, a zoom lens and a two
-
channel video digitizing module with an
Ethernet interface.

SEN
=

S1

S2

SN

This column is filed by “hand ” with
camera inclination angle

value specific for every learning sample
SI.

Algorithm of using fixed inclination angle:

Autonomous Robot “PHOENIX
-
3”

-
More info about project “Phoenix
-
3” can be find on the site
http://guap.ru/guap/sdc