What is the Inverse Kinematics

• Kinematic analysis is one of the first steps in the design of most industrial robots. Kinematic analysis allows the designer to obtain information on the position of each component within the mechanical system

Analytical Inverse Kinematics with Body Posture Control 

What is solution

What does the paper do?

• This paper studies and implements the inverse kinematics.

• Moreover, the FPGA-implementation of inverse kinematics for two type’s robot manipulators is presented.

What is robot manipulator?• A robot manipulator is composed of a

serial chain of rigid links connected to each other revolute or prismatic joints.

• A revolute joint rotates about a motion axis

• A prismatic joint slide along a motion axis.

x0y0

z0

x0y0

z0

x1z1

y1x2z2

y2x3z3

y3 x4

z4y4

x5

z5y5

d1

d5

a3a2

2

1

3 4

5

IK formulations

1000

100

010

001

z

y

x

THR

1000

010

00

00

1

11

11

10

d

CS

SC

A

1000

0100

0

0

2222

2222

21 SaCS

CaSC

A

1000

0100

0

0

3333

3333

32 SaCS

CaSC

A

1000

0010

00

00

44

44

43 CS

SC

A

(1)

(2)

(4)

(5)

(6)

(7)

1000

A 54

43

32

21

10

50

zzzz

yyyy

xxxx

HR

paon

paon

paon

AAAAAT

The parameters of robot manipulator‘s

Table 2.The parameters robot manipulator‘s

The Implementation in FPGA

• The implementation of inverse kinematics, we use parallel processing method,

• it is resource consumption in FPGA. The FPGA chip adopts herein is an Altera DE2 Cyclone II EP2C35F672

The Implementation in FPGA• The implementation of inverse kinematic is

developed by VHDL; therefore, the finite state machine method is applied.

• In Fig.3, there are 42 steps to perform the inverse kinematics in (34)~(40).

• The circuit needs 3 multipliers, 2 dividers, 2 adders, 1 square root function, 1 component for arctangent function, 1 component for arccosine function, 1 look-up-table for sine function and some comparator for atan2 function.

Finite state machine

s1

+

x

21V

51 ,

-

s0

(228)

Z

Y

X2

xX

Y2

Y/X

M2

M1

D1

A1x

1V

M1

+22V

A1

+A1

+A2

(88100)

S1

D2

-

(80000)

3V

s2 s3 s4 s5

tan-1

s6

C1

s7

x

(160)

cos-1

C2

s8 s9

6V

(250)

+M3 A1

5V

s15

atan2

s16

3

2V

LUT for sin

t1

)(sin

V

3

4

s17

x

1/r3

M3

s18

*3

Table II

Y/X

21 dd

23

22 aa 32aa2

2a3a

(a)

s20

x

s19

x

M1

M3

s22 s23 s24 s29 s30 s39 s40 s41

4V

1V

5V

7V

2V

xM2

+-

A1

s21

x

x

M1

M2

7V

2V

5V

1V +A1

2S

2C

D1

22 C/S

x

1/r1

M1

*11

x

1/r5

M3

*55

s25

tan-1

C1

2atan2

Table II

s38

x

1/r2

M3

*2

+

3

-- 4

x

1/r4

M1

*4

2

(160)3a

(b)

Simulation results in Quartus II and Matlab