300599 Advanced Robotics

Project I

Independent Joint Controller of a PUMA robot

Due date: 12 noon Friday 1st May 2015

Hard copy submission of the report with an assignment coversheet to Building X Reception, Kingswood – retain a copy of your

work and a receipt. Late submission will be penalised by 10% per calendar day.

Figure 1 shows a PUMA robot. This is a computer controlled six-joint robot, driven by six DC servomotors.

In Figure 2, coordinate systems have been established using Denavit-Hartenberg (DH) representation for the

first three degree-of-freedom of the robot. The geometrical parameters of the PUMA and other dynamical parameters

are given in table 1.

Figure 1. A PUMA robot. (a) A photo of the PUMA robot1

. (b) a sketch of the PUMA robot2

In this project students are required to work in a group of two to three students to design a controller for the

robot to move along predefined trajectories.

The aim of the project is to design suitable controllers and trajectory planners, for the first three joints of the

PUMA robot. The system developed should be implemented in SIMULINK and should allow the user to specify

the following:

1. Desired initial and final locations of the end-effector in Cartesian space (either in metres or in millimetres).

2. Robot speed as a percentage of the nominal maximum linear speed (It is assumed that the maximum

linear speed of the robot is 0.3 m/s).

3. Plots are required: i.e., actual and desired joint positions and the wrist centre positions in Cartesian

space vs. time, and tracking errors (in both joint and Cartesian space) vs. time.

The robot controller should be designed based on the parameters of the robot given in Table 1. Assume that

the inertial properties provided for link 3 incorporates those for links 4-6. Controllers designed should provide

satisfactory performance for the robot with up to 1.0kg of payloads.

A SIMULINK model of the robot will be provided to test your controllers. The model accepts voltages to

drive the power amplifiers for motors of joints 1 ~ 3. It also provides the positions and velocities of the motors

and the joints.

You are required to work in groups of two to three students each. Group members should be familiar with all

aspects of the project. The assessment will be based on the following aspects:

1 http://iel.ucdavis.edu/projects/robot/Puma560.html

2 http://www.ece.gatech.edu/academic/courses/ece4007/12spring/ece4007L02/tm2/

• Individual performance of each student towards the project during tutorial sessions according to the schedules

provided (30%).

• Individual demonstration of the MATLAB/SIMULINK programs (20%).

• Written GROUP report (50%).

Please note that all group members will also be asked to allocate their estimate of the percentage contribution

of each member of the group towards the project – the individual mark to the report will be given as (group

report mark × your percentage contribution / maximum percentage contribution in the group).

Groups will be assessed on their progress based on the following schedule. Group members present on the

dates mentioned in the schedule will be given a mark according to their progresses related to the schedule.

ZERO mark will be given to the student who is absent at the scheduled assessment time unless prior written

permission has been granted by the lecturer.

Assessment Schedule and Requirements:

1. Calculate the controller gains for the independent joint controllers for joints 1-3 (using the parameters given

in Table 1). Using the calculated gains to design the feedback controllers for the PUMA and implement

the controllers in SIMULINK.

Assessment time – tutorials in Week 7.

2. Develop and incorporate a Cartesian space trajectory planner into the controller developed in Step 1. Assuming

that the moving range for joints 1 – 3 is [-p, p]. The planner should accept user specified initial

and final wrist centre positions, and speed (as percentages of the nominal maximum values – assumed to

be 0.3 m/s) and plan a straight-line path for the robot to follow (generate the path every 0.1 second). The

joint information will be calculated using inverse kinematics of the robot.

Assessment time – tutorial in Week 10.

The final demonstrations of the completed projects are to be held during tutorials in Week 10 in XBG02. A

group report is to be submitted by each group by no later than 12noon, 1st May 2015.

The group report should contain at least the following aspects:

• Aim of the project.

• Methodologies, detailed equations and calculations used in designing the controllers and trajectory

planners.

• MATLAB/SIMULINK programs used in the project.

• Plots/outputs that demonstrate the effectiveness of the controller/planner.

• Conclusions

The final written report should be no more than 18 A4 pages (inclusive of MATLAB codes). Pages exceeding

the page limit will be penalised by 10% of full mark per page. The fonts used should not be smaller than 12

pts Times New Roman with margin of no less than 2cm on all sides. Marking criteria of the report can be

found in the unit Learning Guide.

x0

z0

y0

x1

z1

y1

d2

z2

x2

y2

a2

y3

z3

x3

a3

Shoulder

Elbow

Waist

d4 + d6

Figure 2. PUMA robot and its coordinate systems

Table 1. Parameters of the PUMA robot

Parameters Values

d1 (m) 0.0

d2 (m) 0.1491

d3 (m) 0.0

d4(m) 0.43307

d6(m) 0.05625

a1 (m) 0.0

a2 (m) 0.4318

a3 (m) -0.0203

Mass of the first link M1 (kg) 12.96

Mass of the second link M2 (kg) 22.34

Mass of the third link (including the 4th and 5th link) M3

(kg) 6.97

Center of mass for the 1st link along x (x1 m) 0.0

Center of mass for the 1st link along y (y1 m) 0.3088

Center of mass for the 1st link along z (z1 m) 0.0389

Center of mass for the 2nd link along x (x2 m) -0.3289

Center of mass for the 2nd link along y (y2 m) 0.005

Center of mass for the 2nd link along z (z2 m) 0.2038

Center of mass for the 3rd link along x (x3 m) 0.0204

Center of mass for the 3rd link along y (y3 m) 0.0137

Center of mass for the 3rd link along z (z3 m) 0.1244

Moment of inertia for the 1st link along x (I1xx kg m2

) 2.35

Moment of inertia for the 1st link along y (I1yy kg m2

) 0.2

Moment of inertia for the 1st link along z (I1zz kg m2

) 2.35

Moment of inertia for the 2nd link along x (I2xx kg m2

) 1.33

Moment of inertia for the 2nd link along y (I2yy kg m2

) 3.03

Moment of inertia for the 2nd link along z (I2zz kg m2

) 3.38

Moment of inertia for the 3rd link along x (I3xx kg m2

) 0.3148

Moment of inertia for the 3rd link along y (I3yy kg m2

) 0.3128

Moment of inertia for the 3rd link along z (I3zz kg m2

) 0.01

Gear ratio of the 1st link drive chain (n1) 1/(55+(Group No.)×2)

Gear ratio of the 2nd link drive chain (n2) 1/107.82

Gear ratio of the 3rd link drive chain (n3) 1/53.71

Moment of inertia of the motor armature driving the 1st joint (Im1) kg/m2

) 0.0002

Moment of inertia of the motor armature driving the 2nd joint (Im2) kg/m2

) 0.0002

Moment of inertia of the motor armature driving the 3rd joint (Im3) kg/m2

) 0.0002

Rated voltage of the motor driving the 1st joint (Vm1 V) 40

Rated voltage of the motor driving the 2nd joint (Vm2 V) 40

Rated voltage of the motor driving the 3rd joint (Vm3 V) 40

Rated torque of the motor driving the 1st joint (T1max N-m) 1.2

Rated torque of the motor driving the 2nd joint (T2max N-m) 1.2

Rated torque of the motor driving the 3rd joint (T3max N-m) 1.2

Effective viscous friction coefficient of the 1st joint feff1 (v1 N-s) 0.01

Effective viscous friction coefficient of the 2nd joint feff2 (v2 N-s) 0.005

Effective viscous friction coefficient of the 3rd joint feff3 (v3 N-s) 0.003

Motor armature resistance Ra (O) (joint 1-3) 1.6

Motor torque constant Ka (N-m/A) Joint (1-3) (same as Kb) 0.2531

Structural resonant frequency of the robot fr 10 (Hz)

The groups are formed as:

Group Number Student ID & Name

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

Project I

Independent Joint Controller of a PUMA robot

Due date: 12 noon Friday 1st May 2015

Hard copy submission of the report with an assignment coversheet to Building X Reception, Kingswood – retain a copy of your

work and a receipt. Late submission will be penalised by 10% per calendar day.

Figure 1 shows a PUMA robot. This is a computer controlled six-joint robot, driven by six DC servomotors.

In Figure 2, coordinate systems have been established using Denavit-Hartenberg (DH) representation for the

first three degree-of-freedom of the robot. The geometrical parameters of the PUMA and other dynamical parameters

are given in table 1.

Figure 1. A PUMA robot. (a) A photo of the PUMA robot1

. (b) a sketch of the PUMA robot2

In this project students are required to work in a group of two to three students to design a controller for the

robot to move along predefined trajectories.

The aim of the project is to design suitable controllers and trajectory planners, for the first three joints of the

PUMA robot. The system developed should be implemented in SIMULINK and should allow the user to specify

the following:

1. Desired initial and final locations of the end-effector in Cartesian space (either in metres or in millimetres).

2. Robot speed as a percentage of the nominal maximum linear speed (It is assumed that the maximum

linear speed of the robot is 0.3 m/s).

3. Plots are required: i.e., actual and desired joint positions and the wrist centre positions in Cartesian

space vs. time, and tracking errors (in both joint and Cartesian space) vs. time.

The robot controller should be designed based on the parameters of the robot given in Table 1. Assume that

the inertial properties provided for link 3 incorporates those for links 4-6. Controllers designed should provide

satisfactory performance for the robot with up to 1.0kg of payloads.

A SIMULINK model of the robot will be provided to test your controllers. The model accepts voltages to

drive the power amplifiers for motors of joints 1 ~ 3. It also provides the positions and velocities of the motors

and the joints.

You are required to work in groups of two to three students each. Group members should be familiar with all

aspects of the project. The assessment will be based on the following aspects:

1 http://iel.ucdavis.edu/projects/robot/Puma560.html

2 http://www.ece.gatech.edu/academic/courses/ece4007/12spring/ece4007L02/tm2/

• Individual performance of each student towards the project during tutorial sessions according to the schedules

provided (30%).

• Individual demonstration of the MATLAB/SIMULINK programs (20%).

• Written GROUP report (50%).

Please note that all group members will also be asked to allocate their estimate of the percentage contribution

of each member of the group towards the project – the individual mark to the report will be given as (group

report mark × your percentage contribution / maximum percentage contribution in the group).

Groups will be assessed on their progress based on the following schedule. Group members present on the

dates mentioned in the schedule will be given a mark according to their progresses related to the schedule.

ZERO mark will be given to the student who is absent at the scheduled assessment time unless prior written

permission has been granted by the lecturer.

Assessment Schedule and Requirements:

1. Calculate the controller gains for the independent joint controllers for joints 1-3 (using the parameters given

in Table 1). Using the calculated gains to design the feedback controllers for the PUMA and implement

the controllers in SIMULINK.

Assessment time – tutorials in Week 7.

2. Develop and incorporate a Cartesian space trajectory planner into the controller developed in Step 1. Assuming

that the moving range for joints 1 – 3 is [-p, p]. The planner should accept user specified initial

and final wrist centre positions, and speed (as percentages of the nominal maximum values – assumed to

be 0.3 m/s) and plan a straight-line path for the robot to follow (generate the path every 0.1 second). The

joint information will be calculated using inverse kinematics of the robot.

Assessment time – tutorial in Week 10.

The final demonstrations of the completed projects are to be held during tutorials in Week 10 in XBG02. A

group report is to be submitted by each group by no later than 12noon, 1st May 2015.

The group report should contain at least the following aspects:

• Aim of the project.

• Methodologies, detailed equations and calculations used in designing the controllers and trajectory

planners.

• MATLAB/SIMULINK programs used in the project.

• Plots/outputs that demonstrate the effectiveness of the controller/planner.

• Conclusions

The final written report should be no more than 18 A4 pages (inclusive of MATLAB codes). Pages exceeding

the page limit will be penalised by 10% of full mark per page. The fonts used should not be smaller than 12

pts Times New Roman with margin of no less than 2cm on all sides. Marking criteria of the report can be

found in the unit Learning Guide.

x0

z0

y0

x1

z1

y1

d2

z2

x2

y2

a2

y3

z3

x3

a3

Shoulder

Elbow

Waist

d4 + d6

Figure 2. PUMA robot and its coordinate systems

Table 1. Parameters of the PUMA robot

Parameters Values

d1 (m) 0.0

d2 (m) 0.1491

d3 (m) 0.0

d4(m) 0.43307

d6(m) 0.05625

a1 (m) 0.0

a2 (m) 0.4318

a3 (m) -0.0203

Mass of the first link M1 (kg) 12.96

Mass of the second link M2 (kg) 22.34

Mass of the third link (including the 4th and 5th link) M3

(kg) 6.97

Center of mass for the 1st link along x (x1 m) 0.0

Center of mass for the 1st link along y (y1 m) 0.3088

Center of mass for the 1st link along z (z1 m) 0.0389

Center of mass for the 2nd link along x (x2 m) -0.3289

Center of mass for the 2nd link along y (y2 m) 0.005

Center of mass for the 2nd link along z (z2 m) 0.2038

Center of mass for the 3rd link along x (x3 m) 0.0204

Center of mass for the 3rd link along y (y3 m) 0.0137

Center of mass for the 3rd link along z (z3 m) 0.1244

Moment of inertia for the 1st link along x (I1xx kg m2

) 2.35

Moment of inertia for the 1st link along y (I1yy kg m2

) 0.2

Moment of inertia for the 1st link along z (I1zz kg m2

) 2.35

Moment of inertia for the 2nd link along x (I2xx kg m2

) 1.33

Moment of inertia for the 2nd link along y (I2yy kg m2

) 3.03

Moment of inertia for the 2nd link along z (I2zz kg m2

) 3.38

Moment of inertia for the 3rd link along x (I3xx kg m2

) 0.3148

Moment of inertia for the 3rd link along y (I3yy kg m2

) 0.3128

Moment of inertia for the 3rd link along z (I3zz kg m2

) 0.01

Gear ratio of the 1st link drive chain (n1) 1/(55+(Group No.)×2)

Gear ratio of the 2nd link drive chain (n2) 1/107.82

Gear ratio of the 3rd link drive chain (n3) 1/53.71

Moment of inertia of the motor armature driving the 1st joint (Im1) kg/m2

) 0.0002

Moment of inertia of the motor armature driving the 2nd joint (Im2) kg/m2

) 0.0002

Moment of inertia of the motor armature driving the 3rd joint (Im3) kg/m2

) 0.0002

Rated voltage of the motor driving the 1st joint (Vm1 V) 40

Rated voltage of the motor driving the 2nd joint (Vm2 V) 40

Rated voltage of the motor driving the 3rd joint (Vm3 V) 40

Rated torque of the motor driving the 1st joint (T1max N-m) 1.2

Rated torque of the motor driving the 2nd joint (T2max N-m) 1.2

Rated torque of the motor driving the 3rd joint (T3max N-m) 1.2

Effective viscous friction coefficient of the 1st joint feff1 (v1 N-s) 0.01

Effective viscous friction coefficient of the 2nd joint feff2 (v2 N-s) 0.005

Effective viscous friction coefficient of the 3rd joint feff3 (v3 N-s) 0.003

Motor armature resistance Ra (O) (joint 1-3) 1.6

Motor torque constant Ka (N-m/A) Joint (1-3) (same as Kb) 0.2531

Structural resonant frequency of the robot fr 10 (Hz)

The groups are formed as:

Group Number Student ID & Name

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

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