Figure 1.
A block diagram of the proposed LfTD system, which trains a robot with two degrees of freedom to perform rehabilitation exercises. These exercises are learned from therapist demonstrations using DMP
Figure 2.
Schematic diagram of a two-dimensional DMP. This diagram illustrates how learned weights (ω) model trajectories, adjusting the motion from the start (y0) to the goal (g) positions
Figure 3.
Conceptual block diagram of the MRAC illustrating the adaptive control strategy by highlighting the feedback loop that dynamically adjusts controller gains (K, ) to enhance disturbance robustness
Table 1.
Parameters for the LfTD Model
| Parameters | Description | Value |
|---|---|---|
| n | No. of gaussians | 60 |
| α | DMP parameter | 8.5 |
| β | DMP parameter | 4 |
| αx | Canonical system constant | 0.8 |
| τ | Time scaling constant | 0.218 |
| r | Controller adaptation rate | 100 |
| K | Adaptive controller gain | [10 16] |
| li | Robot link lengths | [50, 50] cm |
Figure 4.
Two distinct demonstrations performed by human subject, depicting variations in movement patterns traced during demonstrations. (a) S-shaped pattern; (b) ’3’-shaped pattern
Figure 5.
Sixty equally spaced Gaussian distributions illustrating the basis functions used
Figure 6.
Performance optimization using PSO
Figure 7.
Reproduced demonstrated trajectory using the proposed LfTD technique
Figure 8.
Total position reproduction error in DMP modeling
Figure 9.
Adaptation of the demonstrated trajectory to changes in starting Points and goals. Figure (a) shows the trajectory adapted to a new goal, maintaining the original starting point. Figure (b) demonstrates how both the starting point and goal are changed
Figure 10.
LfTD framework in trajectory tracking performance between desired and actual trajectories. (a) Tracking for each DOF. (b) Tracking for the demonstrated trajectory executed by the robot
Figure 11.
Tracking the generated trajectory with added disturbances mimicking patient deviation for (a) each DOF and (b) for the demonstrated trajectory as executed by the robot