Figure 1.
UR5 Robotic arm.
Figure 1.
UR5 Robotic arm.
Figure 2.
Type-2 triangular membership functions with 20% lower lag and 20% scale uncertainty.
Figure 2.
Type-2 triangular membership functions with 20% lower lag and 20% scale uncertainty.
Figure 3.
Structure of an IT2FLS.
Figure 3.
Structure of an IT2FLS.
Figure 4.
FSMC and T2FSMC with adaptive control gains of Γ.
Figure 4.
FSMC and T2FSMC with adaptive control gains of Γ.
Figure 5.
Input membership functions of the fuzzy type-2 systems with 20% lower lag uncertainty.
Figure 5.
Input membership functions of the fuzzy type-2 systems with 20% lower lag uncertainty.
Figure 6.
FSMC and T2FSMC with variable of α.
Figure 6.
FSMC and T2FSMC with variable of α.
Figure 7.
FSMC with α and Γ.
Figure 7.
FSMC with α and Γ.
Figure 8.
Predefined fuzzy type-2 output membership functions of the controller gains of Γ.
Figure 8.
Predefined fuzzy type-2 output membership functions of the controller gains of Γ.
Figure 9.
Tuned fuzzy type-2 output membership functions of gains of Γ.
Figure 9.
Tuned fuzzy type-2 output membership functions of gains of Γ.
Figure 10.
Predefined fuzzy type-2 output membership functions of the controller gains of α.
Figure 10.
Predefined fuzzy type-2 output membership functions of the controller gains of α.
Figure 11.
Tuned fuzzy type-2 output membership functions of the controller gains of α.
Figure 11.
Tuned fuzzy type-2 output membership functions of the controller gains of α.
Figure 12.
Best value of Γ fuzzy rule tuning.
Figure 12.
Best value of Γ fuzzy rule tuning.
Figure 13.
Best value of α fuzzy type 2 tuning.
Figure 13.
Best value of α fuzzy type 2 tuning.
Figure 14.
Best value of α fuzzy type-1 tuning.
Figure 14.
Best value of α fuzzy type-1 tuning.
Figure 15.
Best value of α fuzzy type-2 tuning.
Figure 15.
Best value of α fuzzy type-2 tuning.
Figure 16.
Surface of tuned Γ fuzzy type-1 system.
Figure 16.
Surface of tuned Γ fuzzy type-1 system.
Figure 17.
Surface of tuned Γ fuzzy type-2 system.
Figure 17.
Surface of tuned Γ fuzzy type-2 system.
Figure 18.
Surface of tuned α fuzzy type-1 system.
Figure 18.
Surface of tuned α fuzzy type-1 system.
Figure 19.
Surface of tuned α fuzzy type-2 system.
Figure 19.
Surface of tuned α fuzzy type-2 system.
Figure 20.
Applied input disturbances.
Figure 20.
Applied input disturbances.
Figure 21.
Trajectory tracking in first joint using Γ fuzzy systems.
Figure 21.
Trajectory tracking in first joint using Γ fuzzy systems.
Figure 22.
Trajectory tracking in second joint using Γ fuzzy systems.
Figure 22.
Trajectory tracking in second joint using Γ fuzzy systems.
Figure 23.
Trajectory tracking in third joint using Γ fuzzy systems.
Figure 23.
Trajectory tracking in third joint using Γ fuzzy systems.
Figure 24.
Trajectory tracking in fourth joint using Γ fuzzy systems.
Figure 24.
Trajectory tracking in fourth joint using Γ fuzzy systems.
Figure 25.
Trajectory tracking in fifth joint using Γ fuzzy systems.
Figure 25.
Trajectory tracking in fifth joint using Γ fuzzy systems.
Figure 26.
Trajectory tracking in sixth joint using Γ fuzzy systems.
Figure 26.
Trajectory tracking in sixth joint using Γ fuzzy systems.
Figure 27.
Trajectory tracking in first joint using α fuzzy systems.
Figure 27.
Trajectory tracking in first joint using α fuzzy systems.
Figure 28.
Trajectory tracking in second joint using α fuzzy systems.
Figure 28.
Trajectory tracking in second joint using α fuzzy systems.
Figure 29.
Trajectory tracking in third joint using α fuzzy systems.
Figure 29.
Trajectory tracking in third joint using α fuzzy systems.
Figure 30.
Trajectory tracking in fourth joint using α fuzzy systems.
Figure 30.
Trajectory tracking in fourth joint using α fuzzy systems.
Figure 31.
Trajectory tracking in fifth joint using α fuzzy systems.
Figure 31.
Trajectory tracking in fifth joint using α fuzzy systems.
Figure 32.
Trajectory tracking in sixth joint using α fuzzy systems.
Figure 32.
Trajectory tracking in sixth joint using α fuzzy systems.
Figure 33.
Trajectory tracking in first joint using αΓ fuzzy systems.
Figure 33.
Trajectory tracking in first joint using αΓ fuzzy systems.
Figure 34.
Trajectory tracking in second joint using αΓ fuzzy systems.
Figure 34.
Trajectory tracking in second joint using αΓ fuzzy systems.
Figure 35.
Trajectory tracking in third joint using αΓ fuzzy systems.
Figure 35.
Trajectory tracking in third joint using αΓ fuzzy systems.
Figure 36.
Trajectory tracking in fourth joint using αΓ fuzzy systems.
Figure 36.
Trajectory tracking in fourth joint using αΓ fuzzy systems.
Figure 37.
Trajectory tracking in fifth joint using αΓ fuzzy systems.
Figure 37.
Trajectory tracking in fifth joint using αΓ fuzzy systems.
Figure 38.
Trajectory tracking in sixth joint using αΓ fuzzy systems.
Figure 38.
Trajectory tracking in sixth joint using αΓ fuzzy systems.
Figure 39.
Velocity tracking in first joint using Γ fuzzy systems.
Figure 39.
Velocity tracking in first joint using Γ fuzzy systems.
Figure 40.
Velocity tracking in second joint using Γ fuzzy systems.
Figure 40.
Velocity tracking in second joint using Γ fuzzy systems.
Figure 41.
Velocity tracking in third joint using Γ fuzzy systems.
Figure 41.
Velocity tracking in third joint using Γ fuzzy systems.
Figure 42.
Velocity tracking in fourth joint using Γ fuzzy systems.
Figure 42.
Velocity tracking in fourth joint using Γ fuzzy systems.
Figure 43.
Velocity tracking in fifth joint using Γ fuzzy systems.
Figure 43.
Velocity tracking in fifth joint using Γ fuzzy systems.
Figure 44.
Velocity tracking in sixth joint using Γ fuzzy systems.
Figure 44.
Velocity tracking in sixth joint using Γ fuzzy systems.
Figure 45.
Velocity tracking in first joint using α fuzzy systems.
Figure 45.
Velocity tracking in first joint using α fuzzy systems.
Figure 46.
Velocity tracking in second joint using α fuzzy systems.
Figure 46.
Velocity tracking in second joint using α fuzzy systems.
Figure 47.
Velocity tracking in third joint using α fuzzy systems.
Figure 47.
Velocity tracking in third joint using α fuzzy systems.
Figure 48.
Velocity tracking in fourth joint using α fuzzy systems.
Figure 48.
Velocity tracking in fourth joint using α fuzzy systems.
Figure 49.
Velocity tracking in fifth joint using α fuzzy systems.
Figure 49.
Velocity tracking in fifth joint using α fuzzy systems.
Figure 50.
Velocity tracking in sixth joint using α fuzzy systems.
Figure 50.
Velocity tracking in sixth joint using α fuzzy systems.
Figure 51.
Velocity tracking in first joint using αΓ fuzzy systems.
Figure 51.
Velocity tracking in first joint using αΓ fuzzy systems.
Figure 52.
Velocity tracking in second joint using αΓ fuzzy systems.
Figure 52.
Velocity tracking in second joint using αΓ fuzzy systems.
Figure 53.
Velocity tracking in third joint using αΓ fuzzy systems.
Figure 53.
Velocity tracking in third joint using αΓ fuzzy systems.
Figure 54.
Velocity tracking in fourth joint using αΓ fuzzy systems.
Figure 54.
Velocity tracking in fourth joint using αΓ fuzzy systems.
Figure 55.
Velocity tracking in fifth joint using αΓ fuzzy systems.
Figure 55.
Velocity tracking in fifth joint using αΓ fuzzy systems.
Figure 56.
Velocity tracking in sixth joint using αΓ fuzzy systems.
Figure 56.
Velocity tracking in sixth joint using αΓ fuzzy systems.
Figure 57.
Variation of Γ for Γ type-1 fuzzy system.
Figure 57.
Variation of Γ for Γ type-1 fuzzy system.
Figure 58.
Variation of Γ for Γ type-2 fuzzy system.
Figure 58.
Variation of Γ for Γ type-2 fuzzy system.
Figure 59.
Variation of α for α type-1 fuzzy system.
Figure 59.
Variation of α for α type-1 fuzzy system.
Figure 60.
Variation of α for α type-2 fuzzy system.
Figure 60.
Variation of α for α type-2 fuzzy system.
Figure 61.
Variation of Γ for αΓ type-1 fuzzy system.
Figure 61.
Variation of Γ for αΓ type-1 fuzzy system.
Figure 62.
Variation of Γ for αΓ type-2 fuzzy system.
Figure 62.
Variation of Γ for αΓ type-2 fuzzy system.
Figure 63.
Variation of α for αΓ type-1 fuzzy system.
Figure 63.
Variation of α for αΓ type-1 fuzzy system.
Figure 64.
Variation of α for αΓ type-2 fuzzy system.
Figure 64.
Variation of α for αΓ type-2 fuzzy system.
Figure 65.
Input torque in first joint using Γ fuzzy system.
Figure 65.
Input torque in first joint using Γ fuzzy system.
Figure 66.
Input torque in second joint using Γ fuzzy system.
Figure 66.
Input torque in second joint using Γ fuzzy system.
Figure 67.
Input torque in third joint using Γ fuzzy system.
Figure 67.
Input torque in third joint using Γ fuzzy system.
Figure 68.
Input torque in fourth joint using Γ fuzzy system.
Figure 68.
Input torque in fourth joint using Γ fuzzy system.
Figure 69.
Input torque in fifth joint using Γ fuzzy system.
Figure 69.
Input torque in fifth joint using Γ fuzzy system.
Figure 70.
Input torque in sixth joint using Γ fuzzy system.
Figure 70.
Input torque in sixth joint using Γ fuzzy system.
Figure 71.
Input torque in first joint using α fuzzy system.
Figure 71.
Input torque in first joint using α fuzzy system.
Figure 72.
Input torque in second joint using α fuzzy system.
Figure 72.
Input torque in second joint using α fuzzy system.
Figure 73.
Input torque in third joint using α fuzzy system.
Figure 73.
Input torque in third joint using α fuzzy system.
Figure 74.
Input torque in fourth joint using α fuzzy system.
Figure 74.
Input torque in fourth joint using α fuzzy system.
Figure 75.
Input torque in fifth joint using α fuzzy system.
Figure 75.
Input torque in fifth joint using α fuzzy system.
Figure 76.
Input torque in sixth joint using α fuzzy system.
Figure 76.
Input torque in sixth joint using α fuzzy system.
Figure 77.
Input torque in first joint using αΓ fuzzy system.
Figure 77.
Input torque in first joint using αΓ fuzzy system.
Figure 78.
Input torque in second joint using αΓ fuzzy system.
Figure 78.
Input torque in second joint using αΓ fuzzy system.
Figure 79.
Input torque in third joint using αΓ fuzzy system.
Figure 79.
Input torque in third joint using αΓ fuzzy system.
Figure 80.
Input torque in fourth joint using αΓ fuzzy system.
Figure 80.
Input torque in fourth joint using αΓ fuzzy system.
Figure 81.
Input torque in fifth joint using αΓ fuzzy system.
Figure 81.
Input torque in fifth joint using αΓ fuzzy system.
Figure 82.
Input torque in sixth joint using αΓ fuzzy system.
Figure 82.
Input torque in sixth joint using αΓ fuzzy system.
Figure 83.
Velocity tracking in first joint using Γ fuzzy systems.
Figure 83.
Velocity tracking in first joint using Γ fuzzy systems.
Figure 84.
Velocity tracking in second joint using Γ fuzzy systems.
Figure 84.
Velocity tracking in second joint using Γ fuzzy systems.
Figure 85.
Velocity tracking in third joint using Γ fuzzy systems.
Figure 85.
Velocity tracking in third joint using Γ fuzzy systems.
Figure 86.
Velocity tracking in fourth joint using Γ fuzzy systems.
Figure 86.
Velocity tracking in fourth joint using Γ fuzzy systems.
Figure 87.
Velocity tracking in fifth joint using Γ fuzzy systems.
Figure 87.
Velocity tracking in fifth joint using Γ fuzzy systems.
Figure 88.
Velocity tracking in sixth joint using Γ fuzzy systems.
Figure 88.
Velocity tracking in sixth joint using Γ fuzzy systems.
Figure 89.
Input torque in first joint using αΓ fuzzy system.
Figure 89.
Input torque in first joint using αΓ fuzzy system.
Figure 90.
Input torque in second joint using αΓ fuzzy system.
Figure 90.
Input torque in second joint using αΓ fuzzy system.
Figure 91.
Input torque in third joint using αΓ fuzzy system.
Figure 91.
Input torque in third joint using αΓ fuzzy system.
Figure 92.
Input torque in fifth joint using αΓ fuzzy system.
Figure 92.
Input torque in fifth joint using αΓ fuzzy system.
Figure 93.
Input torque in sixth joint using αΓ fuzzy system.
Figure 93.
Input torque in sixth joint using αΓ fuzzy system.
Table 1.
Fuzzy type-1 tuned rules for .
Table 1.
Fuzzy type-1 tuned rules for .
| |
---|
NB | NS | Z | PS | PB |
---|
| NB | VB | VS | B | B | B |
NS | S | M | VS | VB | B |
Z | S | B | VB | B | B |
PS | M | VS | VS | S | M |
PB | VB | M | B | VS | M |
Table 2.
Fuzzy type-2 tuned rules for .
Table 2.
Fuzzy type-2 tuned rules for .
| |
---|
NB | NS | Z | PS | PB |
---|
| NB | S | M | VB | S | M |
NS | M | M | M | B | B |
Z | VS | B | VB | VS | S |
PS | B | M | M | B | S |
PB | B | B | VB | B | S |
Table 3.
Fuzzy type-1 tuned rules for .
Table 3.
Fuzzy type-1 tuned rules for .
| |
---|
NB | NS | Z | PS | PB |
---|
| NB | VS | B | S | S | M |
NS | B | VS | S | S | VB |
Z | VB | VS | S | B | M |
PS | VB | B | B | M | B |
PB | B | M | M | VB | M |
Table 4.
Fuzzy type-2 tuned rules for .
Table 4.
Fuzzy type-2 tuned rules for .
| |
---|
NB | NS | Z | PS | PB |
---|
| NB | B | S | B | VB | S |
NS | M | VS | VS | VS | B |
Z | S | M | VS | B | VS |
PS | S | B | B | VS | S |
PB | S | VB | S | S | M |
Table 5.
Fuzzy type-2 tuned output MF parameters for .
Table 5.
Fuzzy type-2 tuned output MF parameters for .
MF | Scale | Lower Lag |
---|
Initial Value | Tunned Value | Initial Value | Tunned Value |
---|
NB | 0.8 | 0.8000 | 0.2 | 0.2399 |
NS | 0.8 | 0.9133 | 0.2 | 0.2691 |
Z | 0.8 | 0.4076 | 0.2 | 0.1971 |
PS | 0.8 | 0.5358 | 0.2 | 0.8950 |
PB | 0.8 | 0.7689 | 0.2 | 0.1536 |
Table 6.
Fuzzy type-2 tuned output MF parameters for .
Table 6.
Fuzzy type-2 tuned output MF parameters for .
MF | Scale | Lower Lag |
---|
Initial Value | Tunned Value | Initial Value | Tunned Value |
---|
NB | 0.8 | 0.8003 | 0.2 | 0.9133 |
NS | 0.8 | 0.0377 | 0.2 | 0.0527 |
Z | 0.8 | 0.4714 | 0.2 | 0.8419 |
PS | 0.8 | 0.5737 | 0.2 | 0.3308 |
PB | 0.8 | 0.3288 | 0.2 | 0.6841 |