6 robotic systems control

7/29/2019 6 Robotic Systems Control

1/18

Robotic Systems(6)

Dr Richard Crowder

School of Electronics and Computer Science


2/18

Environment

Overview of the problem

Controller

Joints

End Effector

VisionDemand

Feedback


3/18

Robot Control

Control depends on the robots configuration and application

Conventional

Position Control

Speed Control Force Control

Biologically inspired

Behaviour based

Artificial Intelligence

.


4/18

Joint Control

This relies on the real time solution of the reverse kinematicequation (typically at 20-25Hz).

A number of problems are apparent,

Coupling of joint position and velocities with gravityand inertia terms


5/18

Trajectory generation

Trajectoryposition, velocity and acceleration of eachdegree of freedom

Path update rate is typically 60 to 2000 times per second

Typically we are aware of the initial and final points, needto program invia points

Need to blend in the via points into a single fluid

movement, using polynomials path generations


6/18

Trajectory generation

t


7/18

Resolved motion control

Used in teleoperation, the input is normally either speed orforce

Lift (turn)

Reach (twist)

Sweep (tilt)

Z

X

Y

Linear (rotary)


8/18

Jacobian Matrix(1)

Jacobian matrix generalises the notion of the ordinaryderivative of a scalar function

We have defined the [T] matrix, hence we can state:

P(t) [px(t) py(t) pz(t)]T V(t) [vx(t) vy(t) vz(t)]

T

(t)qJ=

(t)

V(t)

]q.....q(t)] = [q[T

n1 J is the Jacobian


9/18

Jacobian Matrix (2)

vx is the x component of the tool velocity as a function of an individual joint velocity

zis the Z component of the tools angular velocity

J11 is the partial derivative of the x component of the to0p position with respect to the variable J1

dq

dq

dq

dq

dq

dq

J.....

......

......

......

......

.....J

=

v

v

v

6

5

4

3

2

1

66

11

z

y

x

z

y

x


10/18

Jacobian Matrix (3)

pi-1 is the position of the (i-1)th frame relative to the origin

p is the position of the tool relative to the origin

zi-1 is the unit vector along the axis of rotation of the ith frame

intjolinearafor

Z

intjorotaryaforZ

)pp(Z

Ji

i

ii

i

0

1

1

11


11/18

Example

Consider a simple two link manipulator.

m

n

a d1 1 90 0 n

2 2

0 m 0

1000

mSn0CS

CmSCSSCS

CmCSSCCC

T222

2112121

2112121

2

0


12/18

Jacobian

0p

CmCp

CmSp

mSnpCmSpCmCp

1

y

21

1

y

21

1

x

2z21y21x

2

1

2

2121

2121

mC0

SmSCmC

SmCCmS

z

x

y

Note Joint 1 has no impact on the velocity in the Z direction

The velocities are a function of1and2, hence J needs to recomputed as the

manipulator moves


13/18

Transformations of forces

If we consider a 61 representation of the velocity of any body [v]T ora force [F M]T

As in previous cases a 66 transformation can be applied to map thesevalues from one frame to a second.

This can be achieved by considering an extension to the kinematics andJacobian analysis.

Considered the following example where the transformation a generalvelocity vector in frame A to a second frame B is required. Thisprocedure is only valid if the two frames are rigidly connected


14/18

Transformations of forces

Xw

Zw

Yw

XT

ZTYT

SensorApplied

force

Objective if a force is applied at the tip, what does the sensor measure


15/18

Solution(1)

We need to find TF (force at the sensor tip), knowing SF (the sensor output),

in addition we know the location of the tip with reference to the sensor, hence:

0=

=

RRP

RT

TTFTF

T

S

T

SSORG

T

T

ST

S

T

S

S

T

ST

S

T

)computedbecanknown,is(as

Xw

Zw

Yw

XT

ZTYTSensorSensor: SF Applied

Force: TF


16/18

Solution(2)

1000

5.25.086.00

3.486.05.00

0001

T

1000

55.087.00

087.05.00

0001

T

T

S

S

T

5086007323152

8605001214234

001000000508600

000860500

000001

=

.....

.....

..

..

TTS

Hence.


17/18

Solution(2)

5.2

3.4

2

0

0

1

0

0

2

0

0

1

5.086.007.323.15.2

86.05.001.214.23.4

001000

0005.086.00

00086.05.00

000001

Sensor readings Actual tip forces


18/18

Summary..

Considered the configuration of industrial manipulators

Determination of the DH matrix

Forward and inverse kinematics

Next step

Sensing Tactile, force and vision

Introduction to biologically inspired systems

6 robotic systems control

Documents