micromouse presentation

Ng Beng Kiat Taiwan2009 1

Introduction

Does not cover microcontroller

Demo

Body design Physics

Sensor & Alignment

PID control --

Speed Profile

DC Motor sizing

DC Motor driver

Battery

Search Algorithm???


Photo of top and bottom of Min5


Minimum mechanical design & construction PCB used as robot body () PCB is tough and strong Good soldering to withstand crash Sensors must be well supported (hot glue )


DEMO


1.0 Body Design Physics ()( )

Centre of gravity & weight transfer

Moment of inertia ()

Robot weight () heavier or lighter?

Robot wheel () bigger or smaller?


1.1 Centre of gravity & weight transfer (&)

When Robot is not accelerating/decelerating, all weight is on tires

If there is no weight on tires -> no grip

Acceleration () () High c.g.

x d

Weight on tire

= (robot weight)(d-x)/d

Reaction ()

Mouse weight

Resultant force

Fig 1: Weight transfer when accelerating

weight transferred here


Lighter or slimmer motors to lower c.g.

More weight on tires, hence more grip for acceleration

Resultant force acts through c.g.

acceleration() Lower c.g.

x d

Weight on tire

= (robot weight)(d-x)/d

reaction

Resultant force

Fig 2: Weight transfer when accelerating (low cg)

x is smaller


Stepper motor based micromouse has high c.g.

Has a higher tendency to roll over if cornering at high speed. ()

Always keep the robot c.g. as low as possible

Make robot as wide as possible () Make your robot like F1 car

Fig 3 : Weight transfer when cornering()

Centrifugal force = (vv)/(2r)

Resultant force


1.2 Moment of inertia ()

High moment of inertia

motor

r

I = mr2

m = motor weight

r

motor

Low moment of inertia


When moment of inertia is high, rotational acceleration () is

reduced for the same torque .

Torque = I (F = ma)

() = ()

Keep heavy parts like motors, battery etc as close to robot centre as possible

()()

If moment of inertia is high, stronger motor is required, -> bigger battery

too!


1.3 Robot weight ()

Question : Does a heavier mouse provides more acceleration (has more grip )? Question: ()?

Force (Newton) = mass(kg) acceleration(m/s2)


Force available to propel the robot forward depends on motor power

and friction force .

If motor is powerful enough, then friction is the limiting factor ()

Friction force = FN u u = coefficient of friction FN = mass g

g = 9.8 m/s2

tire


If motor exerts a force greater than friction force, tires will skid ().

To prevent skidding, driving force < friction force

o Friction = FN u = mass g u

o Therefore acceleration limit = gu

o If u=0.7, then acceleration limit is about 7m/s2.

u = 0.7 7m/s2

Acceleration is independent of mass. Limited by tires.

Keep robot weight low -> reduce motor size -> reduce battery capacity.


1.4 Robot wheel

Question : A bigger wheel or a smaller wheel?

Tire friction is reduced by dirt ()

Clean tires before run

A smaller wheel would need to rotate more times for the same distance o Pick up more dirt() o If maze if dirty, performance will be affected

Bigger wheels raise the c.g. ()


Weight of wheels and shaft affect the robots c.g. Keep wheels & shaft as light as possible

Use light and thin material if possible

Lower c.g. higher c.g.

Smaller wheel, lower c.g. Bigger wheel, lower c.g.


Big wheel will roll easily over steps or humps()

Hump or step Hump or step


Wider wheel will also be less affected by unevenness. ()

On a flat and clean surface, tire diameter and width has negligible impact on performance. ()

Too wide and its hard to turn

A bigger surface allows the wheel to

ride over unevenness


1.5 Four wheel drive ?

During acceleration, weight is transferred to back wheels (

)

During deceleration, weight is transferred to front wheels Good for straight acceleration/deceleration ()

Complex and hard to build ()

My dream mouse !!!

c.g.

x

More weight Less weight

acceleration


1.6 Skid Pads

Skid pad (Teflon)

Must be rocking

1mm

Wheels on floor

Wheels hanging in

the air


2.0 Sensors & Alignment

Side sensor

Front sensor

Diagonal sensor

Figure: Mouse sensors layout

receiver

transmitter

shield


2.1 Sensor circuit and operation

Left and right front sensors pulsed separately to avoid interference

Figure : Transmitter circuit diagram

IR LED

LeftFront

diagonal

side

rightFront


Figure : Receiver circuit diagram


Tx1

Rx1

Tx2

Rx2

From Tx2

Figure : Timing diagram of sensors signals()


IR LED

Pulsing allows higher current to swarm interference () LED on < 10% of time only -> can stand higher current

Pulsing minimize interference from neighbouring sensors

Receiver should be less sensitive -> allows high transmitter output ()

Improve signal noise ratio


2.2 Alignment

Direction offset

Centre of cell

Lateral offset

Longitudinal offset

Figure: Types of positional error


Figure: Correcting direction & lateral offset with diagonal sensor ( 45 )

if( (LALIGN_SEN_VALUE > laSenV3) && (RALIGN_SEN_VALUE < raSenV3)) {

//Too left, adjust right

alignSpeed= (LALIGN_SEN_VALUE - laSenV3)*maxAlignSpeed/laNearLeftRange ;

}

else if( (RALIGN_SEN_VALUE > raSenV3) && (LALIGN_SEN_VALUE < laSenV3) ) {

// Too right, adjust left

alignSpeed = -(RALIGN_SEN_VALUE - raSenV3)*maxAlignSpeed/raNearRightRange);

}

LALIGN_SEN_VALUE

RALIGN_SEN_VALUE


*Almost all turns are preceded by a pole to no-pole transisition

Threshold

eve

Readjust position

Figure: Correcting longitudinal offset with pole detection ()

Assumption :

Lateral and angular offset

is small.


Start of turn end of turn

Use front sensors to adjust

position before turn

Figure: Correcting longitudinal offset with front wall (exploration) ()

Calibrate sensor here


Collision avoidance

Detect pole to adjust

position()

Not use in diagonal run

Figure: Diagonal run. Collision avoidance and position adjustment


3.0 Speed Profile

Rotational speed(wSpeed)

Translational speed (xSpeed)

leftWheelSpeed = xSpeed wSpeed; rightWheelSpeed = xSpeed + wSpeed;

Figure : Speed components of a 2 wheels robot


3.1 Two basic speed profiles

Translational speed

Parameters

Top speed

Acceleration/deceleration

End speed (= curve turn speed)

Distance

Time(s)

Speed (m/s)

Top

speed Acceleration/

deceleration

end speed


Rotational speed ()

3.2 Basic movements

Diagonal & non-diagonal straight runs (wSpeed=0)

Pivot turns (xSpeed=0) ()

Curve turns 90, 180(U), 135(J), 45,V(xSpeed=constant, + wSpeed)

Time(s)

Speed (deg/s)

Top

speed Acceleration/

deceleration


45 degrees (x4)

90 degrees(x4)

180 degrees(x2) 135 degrees (x4)


V turn (x2)


Time(s)

Speed(m/s)

Outer wheel

Inner wheel

Figure : Curve turn speed profile

end

start


3.3 Profile generator and PD loop

No integral term

PD control & Profile generator is executed every msec PWM frequency is 10kHz PWM duty cycle = kp errorn + kd (errorn-errorn-1)

PD -

+ -

Profile

Generator

error speed

PWM

encoder signals

Figure : Profile generator and PD loop

Set topSpeed,

endSpeed,

acceleration, distance

motor


3.4 Straight speed profile C code

// At the beginning of profile, targetSpeed = topSpeed;

// Keep checking for deceleration condition

void SpeedProfile() {

decelerationRequired = (curSpeed2 endSpeed2)/(2distance);

if (decelerationRequired>deceleration) targetSpeed = endSpeed;

if (curSpeedtargetSpeed) curSpeed -= deceleration;

distance += curSpeed;

}

distance - ; curSpeed -; endSpeed - ; acceleration - ; deceleration -


Time(s)

Speed(m/s)

Figure : Speed profile

t2 t1

s2

s1

d

A

B

Calculating deceleration:

A+B = (S1t2)/2

B = S2(t2 - t1)/2

d = S1/t2 = S2/( t2 - t1)

o t2 = S1/d o (t2 - t1) = S2/d

A = (S1t2 )/2 -B = (S1t2)/2 - S2(t2 - t1)/2

= (S12- S2

2)/2d

d = (S12- S2

2)/2A


3.5 PD loop and gyroscope

PD + -

Straight

Profile gen

xError xSpeed left

Figure : rotational and translation control loop

PD + -

Curve turn

Profile gen

wError wSpeed right

(R-L)/2 or gyro

+ -

+ +

(R+L)/2

L

R

alignSpeed

leftSpeed = xSpeed wSpeed; rightSpeed = xSpeed + wSpeed;

xSpeed = (rightSpeed+leftSpeed)/2

wSpeed = (rightSpeed-leftSpeed)/2


Gyro is fast in response

Accurate for fast curve turn (not for very slow turn) / opposite of optical encoder

Need to calibrate before run due to DC drift ?

Not affected by tires size change


4.0 DC motor sizing

Step 1 : Calculate maximum power required

Force(N) = mass(kg) acceleration(m/s2) =

o Desired acceleration = 7 m/s2 // experience required

Time(s)

Speed (m/s)

7 m/s2

3

7 m/s2

Maximum power


Force = 0.12kg 7m/s2 = 0.84N

Power (W) = force(N) speed(m/s) ( = )

Maximum power is required when robot is accelerating at 7 m/s2 near top

speed = 3m/s.

Max power required = 0.84N3 m/s = 2.52 watt.

Since there are 2 motors, power required per motor = 1.26 W.

Step 2 : Select motor (Faulhaber 1717SR)

Choose a motor with maximum Power 1.5 times to 2 times 1.26W = 1.89W

to 2.52 W,

Which is less than the Pmax of 1.96 W (Faulhaber 1717SR).


Note that I also overdrive the motor. 2x Lithium Polymer = 8.4V. Average

around 7.8 volts

Maximum power out at 7.8 V = (7.8/6)2 1.96 = 3.3 watts

Step 3 : Select gear ratio

Calculate torque and speed

o Tires diameter is 24mm

o Torque required = Forceradius ( = )


= 0.84N 12mm = 10.08 mNm

o Torque required per motor = 5.04mNm.

o Wheel circumference = Pidiameter = 0.0754m

o At 3m/s, wheel revolution = speed/circumference

= 3/0.0754m = 39.8 rps = 2387 rpm

Therefore, near top speed, motor must be able to provide torque output of

5.04mNm at speed of 2387 rpm.


Speed rpm

Torque mNm 5 10 15

14000

Figure : DC motor speed-torque characteristic

Accelerating

5.04mNm

Top speed

2387 rpm

Max power 1.96W Speed (m/s)

7 m/s2 7 m/s2


Speed rpm

Torque mNm 5 10 15

14000

7000

4667

1:1

3:1

Figure : DC motor speed-torque characteristic

12

32

Gear ratio 2:1

Accelerating

5.04mNm

Top speed

2387 rpm

Max power 1.96W


There is a range of gear ratio to select from

The higher the gear ratio, the more energy efficient the motor is.

Allows spare power for alignment

Prefer long & slim motors to short and fat motor. Lower c.g.


4.1 DC motor driver

MOSFET driver motor driver

Pull up

Figure : Min5 motor driver circuit

-Choose low turn-On resistance MOSFET

-Pull up input to prevent conduction


User interface Need feedback to tell what the mouse is doing

LED lights

Sound

Menu driven (dotmatrix display & input switch)

Websites Visit my website at www.np.edu.sg/alpha/nbk

(A* Pathfinding ) http://www.policyalmanac.org/games/aStarTutorial.htm

(Nakashima website) http://homepage1.nifty.com/hfd01577/index.html

(Pete Harrison) http://micromouse.cannock.ac.uk

Good Luck!

micromouse presentation

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