Author Contributions
Conceptualization, H.J.Y, S.Y.C., and M.J.H.; Methodology, H.J.Y, S.Y.C., and M.J.H.; Experiment, H.S.K.; Analysis, S.Y.C. and H.S.K.; Writing-Original Draft Preparation and Revision, H.J.Y and M.J.H.; Supervision, S.Y.C. and M.J.H.; Funding Acquisition, M.J.H.
Figure 1.
Comparison of trapezoidal motion profile and 3rd-order polynomial trajectory with the same maximum velocity and acceleration.
Figure 1.
Comparison of trapezoidal motion profile and 3rd-order polynomial trajectory with the same maximum velocity and acceleration.
Figure 2.
Comparison of trapezoidal motion profile, 3rd-order polynomial trajectory, and 5th-order polynomial trajectory with the same duration of motion.
Figure 2.
Comparison of trapezoidal motion profile, 3rd-order polynomial trajectory, and 5th-order polynomial trajectory with the same duration of motion.
Figure 3.
Trapezoidal motion profile.
Figure 3.
Trapezoidal motion profile.
Figure 4.
Three sections of trapezoidal motion profile.
Figure 4.
Three sections of trapezoidal motion profile.
Figure 5.
Short-pitch trapezoidal motion profile.
Figure 5.
Short-pitch trapezoidal motion profile.
Figure 6.
The case where residual vibrations caused by two jerks are amplified: (a) in acceleration phase; (b) in deceleration phase.
Figure 6.
The case where residual vibrations caused by two jerks are amplified: (a) in acceleration phase; (b) in deceleration phase.
Figure 7.
The case where the residual vibrations caused by two jerks are eliminated: (a) in acceleration phase; (b) in deceleration phase.
Figure 7.
The case where the residual vibrations caused by two jerks are eliminated: (a) in acceleration phase; (b) in deceleration phase.
Figure 8.
Experimental setup.
Figure 8.
Experimental setup.
Figure 9.
The experiment in which the robot moved with a constant configuration: (a) initial position; (b) final position.
Figure 9.
The experiment in which the robot moved with a constant configuration: (a) initial position; (b) final position.
Figure 10.
The velocity profiles when the robot moved 500 mm with a maximum velocity of 1000 mm/s.
Figure 10.
The velocity profiles when the robot moved 500 mm with a maximum velocity of 1000 mm/s.
Figure 11.
Position deviations at target point: (a) when ; (b) when .
Figure 11.
Position deviations at target point: (a) when ; (b) when .
Figure 12.
The velocity profiles when moving 500 mm over 0.8 s.
Figure 12.
The velocity profiles when moving 500 mm over 0.8 s.
Figure 13.
Position deviations at target: (a) when ; (b) when .
Figure 13.
Position deviations at target: (a) when ; (b) when .
Figure 14.
The velocity profiles when moving a short distance with a maximum velocity of 1000 mm/s.
Figure 14.
The velocity profiles when moving a short distance with a maximum velocity of 1000 mm/s.
Figure 15.
Position deviations at target: (a) when ; (b) when .
Figure 15.
Position deviations at target: (a) when ; (b) when .
Figure 16.
The experiment where the robot linearly moved while the configuration changed: (a) initial position; (b) final position.
Figure 16.
The experiment where the robot linearly moved while the configuration changed: (a) initial position; (b) final position.
Figure 17.
The velocity profiles when moving 425 mm with a maximum velocity of 1000 mm/s.
Figure 17.
The velocity profiles when moving 425 mm with a maximum velocity of 1000 mm/s.
Figure 18.
Position deviations at target: (a) when ; (b) when .
Figure 18.
Position deviations at target: (a) when ; (b) when .
Figure 19.
The velocity profiles when moving 425 mm over 0.8 s.
Figure 19.
The velocity profiles when moving 425 mm over 0.8 s.
Figure 20.
Position deviations at target: (a) when ; (b) when .
Figure 20.
Position deviations at target: (a) when ; (b) when .
Figure 21.
The velocity profiles when moving a short distance with a maximum velocity of 1000 mm/s.
Figure 21.
The velocity profiles when moving a short distance with a maximum velocity of 1000 mm/s.
Figure 22.
Position deviations at target: (a) when ; (b) when .
Figure 22.
Position deviations at target: (a) when ; (b) when .
Figure 23.
Comparison of residual vibration when the proposed method is applied and the IST is applied: (a) trajectory; (b) residual vibrations.
Figure 23.
Comparison of residual vibration when the proposed method is applied and the IST is applied: (a) trajectory; (b) residual vibrations.
Table 1.
Experimental results of maximum amplitude and settling time when the robot moved 500 mm with a maximum velocity of 1000 mm/s.
Table 1.
Experimental results of maximum amplitude and settling time when the robot moved 500 mm with a maximum velocity of 1000 mm/s.
| | | Max. Amplitude (mm) | Settling Time (s) |
---|
Case 1 | 0.063 | 0.439 | 37 | 7.75 |
Case 2 | 0.125 | 0.375 | 5 | 0.875 |
Case 3 | 0.187 | 0.313 | 16 | 4.375 |
Case 4 | 0.250 | 0.250 | 2 | 0 |
Table 2.
Experimental results of maximum amplitude and settling time when moving 500 mm over 0.8 s.
Table 2.
Experimental results of maximum amplitude and settling time when moving 500 mm over 0.8 s.
| | | Max. Amplitude (mm) | Settling Time (s) |
---|
Case 1 | 0.063 | 0.674 | 40 | 8.375 |
Case 2 | 0.125 | 0.550 | 2 | 0 |
Case 3 | 0.187 | 0.462 | 22 | 5.375 |
Case 4 | 0.250 | 0.300 | 2 | 0 |
Table 3.
Experimental results for maximum amplitude and settling time when moving a short distance with a maximum velocity of 1000 mm/s.
Table 3.
Experimental results for maximum amplitude and settling time when moving a short distance with a maximum velocity of 1000 mm/s.
| | Distance (mm) | Max. Amplitude (mm) | Settling Time (s) |
---|
Case 1 | 0.063 | 62.5 | 55 | 11.5 |
Case 2 | 0.125 | 125 | 3 | 0 |
Case 3 | 0.187 | 187.5 | 17 | 7.25 |
Case 4 | 0.250 | 250 | 5 | 1.875 |
Table 4.
Experimental results of maximum amplitude and settling time when moving 425 mm with a maximum velocity of 1000 mm/s.
Table 4.
Experimental results of maximum amplitude and settling time when moving 425 mm with a maximum velocity of 1000 mm/s.
| | | Max. Amplitude (mm) | Settling Time (s) |
---|
Case 1 | 0.063 | 0.362 | 26 | 7.625 |
Case 2 | 0.125 | 0.300 | 7 | 1.5 |
Case 3 | 0.187 | 0.238 | 10 | 5.25 |
Case 4 | 0.250 | 0.175 | 7 | 4.875 |
Table 5.
Experimental results of maximum amplitude and settling time when moving 425 mm over 0.8 s.
Table 5.
Experimental results of maximum amplitude and settling time when moving 425 mm over 0.8 s.
| | | Max. Amplitude (mm) | Settling Time (s) |
---|
Case 1 | 0.063 | 0.674 | 31 | 7.25 |
Case 2 | 0.125 | 0.550 | 3 | 0 |
Case 3 | 0.187 | 0.426 | 19 | 5.625 |
Case 4 | 0.250 | 0.300 | 6 | 2.625 |
Table 6.
Experimental results of maximum amplitude and settling time when moving a short distance with a maximum velocity of 1000 mm/s.
Table 6.
Experimental results of maximum amplitude and settling time when moving a short distance with a maximum velocity of 1000 mm/s.
| | Distance (mm) | Max. Amplitude (mm) | Settling Time (s) |
---|
Case 1 | 0.063 | 62.5 | 57 | 13 |
Case 2 | 0.125 | 125 | 3 | 0 |
Case 3 | 0.187 | 187.5 | 19 | 10.625 |
Case 4 | 0.250 | 250 | 5 | 5.5 |