Force-field compensation in a manual tracking task

Abstract

This study addresses force/movement control in a dynamic "hybrid" task: the master sub-task is continuous manual tracking of a target moving along an eight-shaped Lissajous figure, with the tracking error as the primary performance index; the slave sub-task is compensation of a disturbing curl viscous field, compatibly with the primary performance index. The two sub-tasks are correlated because the lateral force the subject must exert on the eight-shape must be proportional to the longitudinal movement speed in order to perform a good tracking. The results confirm that visuo-manual tracking is characterized by an intermittent control mechanism, in agreement with previous work; the novel finding is that the overall control patterns are not altered by the presence of a large deviating force field, if compared with the undisturbed condition. It is also found that the control of interaction-forces is achieved by a combination of arm stiffness properties and direct force control, as suggested by the systematic lateral deviation of the trajectories from the nominal path and the comparison between perturbed trials and catch trials. The coordination of the two sub-tasks is quickly learnt after the activation of the deviating force field and is achieved by a combination of force and the stiffness components (about 80% vs. 20%), which is a function of the implicit accuracy of the tracking task.

Conflict of interest statement

Competing Interests: The authors have declared that no competing interests exist.

Figures

Figure 1. Experimental setup.

A: Haptic manipulandum BdF used in the experiments. B: Dynamic visual display. The red circle identifies the position of the target and the white circle the position of the hand; both have a 2 cm diameter. The eight-shaped pathway is displayed in the background for one group of subject. For the other group the background is uniformly black. The ideal eight-shaped path is ±15.7 cm wide and ±9 cm high; total length is equal to 102 cm; the nominal circling period is 8 s. C: Real-time flow of information among the four main modules of the robotic manipulandum (BdF haptic manipulandum; Motion analysis and performance evaluation; Task controller; Force-field generator); : position vectors of the target and the hand, respectively; D = 6 cm: threshold for the tracking error e; : target speed modulating function; T = 8s: nominal circling time; b = 100 N/m/s: viscous coefficient of the curl field . D: Profile of the target speed modulating gain.

Figure 2. Characteristics of errorless trajectories.

A: Speed and curvature profiles of the target in the case of ideal, errorless tracking performance. The curvature scale (in m−1) is divided by 200. The correlation coefficient of the two curves is equal to 0.91. B: Pattern of force determined by the curl field, in the case of ideal, errorless tracking performance. The force vectors, perpendicular to the eight-shaped path and directed to the right of the instantaneous velocity vector, range between 8.3N and 18.3N.

Figure 3. Tracking error and lateral deviation.

A: Decomposition of the tracking error into a longitudinal and normal component. : position vectors of the target and the hand, respectively; : longitudinal and normal unit-vectors, respectively. B: Characterization of a catch trial in terms of the initial and final values of the lateral deviation (LDini and LDfin, respectively).

Figure 4. Response patterns of one subject at the end of the familiarization phase during two consecutive turns (FA2).

A: Trajectories of the subject (red) and trajectory of the target (blue) for the whole phase. B: Time course of the speed (blue for the target and red for the hand), curvature (blue for the target and red for the hand), and tracking error (green).

Figure 5. Learning curve of the tracking error δ for the whole population of subjects: mean ± standard error.

FA: familiarization phase (60 turns); FF: force-field phase (60 turns); WO: wash-out phase (30 turns).

Figure 6. Response patterns at the beginning of the force field phase during two consecutive turns (FF1).

A: Trajectories of the subject (red) and trajectory of the target (blue) for the whole phase. B: Time course of the speed (blue for the target and red for the hand), curvature (blue for the target and red for the hand), and tracking error (green).

Figure 7. Response patterns at the end of the force field phase during two consecutive turns (FF2).

A: Trajectories of the subject (red) and trajectory of the target (blue) for the whole phase. B: Time course of the speed (blue for the target and red for the hand), curvature (blue for the target and red for the hand), and tracking error (green).

Figure 8. Comparison of the tracking performance indicators between the end of the familiarization phase (FA2) and the end of the force field phase (FF2).

The data are averaged over the whole population. Each box shows the mean value (central line) and the mean±SE (lower and upper line). The lines extending from each end of the box represent the mean±SD. DUR (duration of each turn); NP (number of peaks for each turn of the hand speed profile); FE (figural error); CC (correlation coefficient between speed and curvature of the hand); (tracking error); (longitudinal component of the tracking error: negative means that the hand is lagging); (lateral or normal component of the tracking error: negative means that the hand is deviated on the right of the target direction). NP, FE, CC and exhibit significant differences between FA2 and FF2 at the p = 0.00000, p = 0.008340, p = 0.000028 and p = 0.000025 significance level, respectively.

Figure 9. Response patterns during rightward catch trials of FF2 phase.

Figure 10. Block diagram of the hybrid control task.