Mobile robots “Phoenix-3” and SOFA-2009 Alex Astapkovich, head of the Student Design Centre State University of Aerospace Instrumentation Alex Burdukov,

Mobile robots “Phoenix-3” and SOFA-2009

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

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

Saint-Petersburg State University of Aerospace Instrumentation

Saint-Petersburg, 2009

Mobile robots SOFA-2009 Mobile robots SOFA-2009 and “Phoenix-3” and “Phoenix-3”

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

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

SOFA-2009Virtual robotbenchmark

model

Real robots:Real robots:

Virtual robots:Virtual robots:

2006 - 20072006 - 2007 2007 - 20082007 - 2008 2008 - 20092008 - 2009

““Phoenix-3”Phoenix-3”

-Phoenix Robotics Group-

Virtual robot SOFA-2009Virtual 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-2009Virtual 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.


Kinematics and dynamics models of virtual robot SOFA Kinematics and dynamics models of virtual robot SOFA

axe x

direction “forward”

φ(t) – robot angle position

axe y

axe xearth fixed frame

Rс (t)– robot center position vector

R0 (t) - instant center of arc

R(t) – instant rotation radius

φ (t+∆t)- φ (t) = ∆ φ (for left wheel) = ∆ φ (for right wheel) R0 (t) = R0 (t+∆t)

Basic relations:


),(1

)(1

)(

)(

)(2

cos4

)(

sin4

)(

2223

22

1113

11

221

2222

121

1111

12

21

21

tULL

kI

L

R

dt

dI

tULL

kI

L

R

dt

dI

tIJ

k

J

k

dt

d

tIJ

k

J

k

dt

dLr

D

dt

d

D

dt

dR

D

dt

dR

mmm

m

mmm

m

rr

rr

w

w

y

c

w

x

c

Model SOFA-2009 is defined with parameters set :

Dr = 0.3 Lr = 0.5 Jr = 0.25k11 = k22 = 75k12 = k21 = 10 Rm = 0.1Lm = 0.01k13 = 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:

U1(t) =0U2(t) = Umax = 12 V.

Control voltages:

U1(t) = U2(t) = Umax = 12 V.


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


Transfer function

Vout

Vin

Actor layer neuronVmax, Vmin

Uout Left Motor

Uout Right Motor

AFSS

APS

ASS

Sensorlayer

Left motor control channelWleft = [w0l,w1l,w2l]

Right motor control channelWright = [w0r,w1r,w2r]

Uin left

Uin

APS – Angel Position Sensor ASS – Angel Speed SensorAFSS – Angel Final Speed Sensor

Example of neuron control system:Example of neuron control system:


S1(T1) S2(T1) .. Sn(T1)

S1(T2) S2(T2) .. Sn(T2)

……………………

S1(Tp) S2(Tp) .. Sn(Tp)

w1

w2

wn

A1(T1)

A1(T2)

A1(Tp)

* =

S * w = Ua Matrix form

One step learning paradigm idea:

min F(w) = (Sw - Ua, Sw – Ua) + (w,w) w

Tixonov regularization

w = (ST S + E) –1 ST Ua Weights calculation

Virtual robot SOFA-2009Virtual robot SOFA-2009Experiment 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 positionvector X(T1),velocity vector V(T1)

SOLUTION TABLE [ti, X (ti) ]

Sensor System Model

Weight Matrix Calculation W= (StS+γE) -1St 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 positionvector X0

Robot model


Initial and final positions, control net structure depends on researchPROBLEM

NEURON NET CONTROL SYSTEM MODEL

Cauchy Problem Solution

POSTPROCCESINGS

NEURON NET CONTROL SYSTEM MODEL

Cauchy problem solution andestimation

Initialposition

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

http://guap.ru/guap/sdc


Virtual robot SOFA-2009Virtual robot SOFA-2009Example of the supervised learning for π/4 rotate to left sample:

Sample 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


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 task:


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

A. Astapcovich “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”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:Project legend:


-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”Autonomous Robot “PHOENIX-3”Control system structure during autonomous operation:

Controller ASK-Lab

Left and RightMotor Control

Bridges

Rotating camera(sensor)

Multichannel 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


Wi-Fi AP Computer

Video link

RF-transmitter

cam. output 1

cam. output 2

Pad 1 (robot)

Pad 1 (fire extinguisher)

OperatorRadio 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.


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”Autonomous Robot “PHOENIX-3”Ultrasonic Orientation System.

1 – MCP 2510 CANbus controller chip;

2 – PIC18F458 microcontroller chip;

3 – 16-bit counter;

4 – former of an ultrasonic pulses;

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.

2

31

4 6

5

8

7

CANbus module structure:

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


It was demonstrated with 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 and 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:


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



Documents

Mobile robots “Phoenix-3” and SOFA-2009 Alex Astapkovich, head of the Student Design Centre State University of Aerospace Instrumentation Alex Burdukov,