Research ArticleHUMAN-ROBOT INTERACTION

Ergodicity reveals assistance and learning from physical human-robot interaction

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Science Robotics  17 Apr 2019:
Vol. 4, Issue 29, eaav6079
DOI: 10.1126/scirobotics.aav6079
  • Fig. 1 Illustration of motion signals and statistics using the center of mass in walking.

    For the task of walking on a line, we can distinguish between two hypothetical cases—a high-quality execution (A) and a low-quality execution (B) by tracking the vertical and mediolateral displacement of the person’s center of mass. These displacements can be characterized as motion signals (C) with a reference or desired trajectory that is based on typical gait patterns. As a trajectory, the high-quality execution does not exactly track the reference trajectory in time, but when we look at the Fourier reconstruction of the trajectory statistics (D), we can see that the high-quality execution is very similar to the reference distribution. In contrast, the low-quality execution has spatial statistics that are very different from the reference distribution.

  • Fig. 2 Target-reaching trials of a stroke participant.

    A patient with stroke was asked to reach to one of three targets (EE, elbow extension; SF, shoulder flexion; RF, reach forward) in different areas of their workspace. The ergodic measure (left) provides clear distinctions between the level of full-arm support and partial-arm or no-arm support in the case of both EE and RF (as indicated by the circled data). The error measure (right) provides little distinction between the fully supported case and the partially supported. Each marker represents a trial from the same individual.

  • Fig. 3 Experimental system.

    Participants directly controlled the cart position xc and indirectly controlled the angle θ and angular velocity θ. of the cart-pendulum system (left). The goal state used to calculate the RMS error was (θ,θ.)=(0,0), and the distribution used as the task definition for the information measure was a Dirac delta function at (θ,θ.)=(0,0) (right).

  • Fig. 4 Assistance adds information.

    The histogram of unassisted trajectories (left) has its highest density at θ = ±π, which is the farthest point from the goal state. The rest of the distribution is diffuse over the state space. Although the histogram of the assisted trajectories (right) also has a high density at θ = ±π, the distribution is not as diffuse as that of the unassisted trajectories. There are bands of high density spreading outward from the goal state (θ,θ.)=(0,0). The spatial statistics of the assisted trajectories are more similar to the reference distribution in Fig. 3, because there is a high density at and around the goal state. This suggests that assistance increased the task information encoded in the movement. This outcome is captured by measuring the ergodicity of the trajectories in each group with respect to the reference distribution. The mean ergodicity of the unassisted trajectories is 0.739, and the mean ergodicity with assistance is 0.631. This lower number indicates that less information is lost in the assisted motion than the unassisted motion.

  • Fig. 5 Learning increases information.

    The histogram of week 2 control trajectories (left) has its highest density at θ = ±π, which is the farthest angle from the goal state at (θ,θ.)=(0,0). The control trajectories also spend time near the goal state, but to a lesser extent. The histogram of trained trajectories (right) also has high density near θ = ±π, but there are large bands of high density in the region −1.5 ≤ θ ≤ 1.5 and 4θ.4. These bands make the statistics of the trained group closer to the spatial statistics of the reference distribution in Fig. 3. We quantified how well these statistics match that of the reference by calculating the ergodicity. The trained trajectories are on average more ergodic (μ = 0.705) than the controls (μ = 0.751). In other words, the trained motions communicate information about the task goal more effectively than the control motions.

  • Fig. 6 Comparison of the control and trained group performance progress over training.

    The statistical comparisons of the trained and control groups excluded the data from the first session (gray) to avoid including the effects of the assistance algorithm itself. For the task-specific measures (top row), there was no difference between the two groups, and block had no significant effect on performance. For the error and ergodic metrics, block has a significant effect, especially in the control group. Under both measures, the control group performance was worse at the beginning of the second session (the first two blocks in white) but by the end of the session performed as well as the trained group. Ergodicity enables one to see the difference between the treated and untreated group, and both error and ergodicity allow one to see learning as a function of block. Error bars indicate standard error.

  • Fig. 7 The new arm coordination training 3D.

    Device provides haptic feedback in three dimensions to simulate a specified inertial model via admittance control. A force-torque sensor at the end effector provides input to the admittance control loop. During this experiment, high-stiffness virtual springs were used to restrict user motion to a straight line corresponding to the path of the cart in the virtual display (bottom left). The display provided real-time visual state feedback about the cart-pendulum system that the user was attempting to invert.

  • Table 1 Paired two-sample t tests comparing unassisted and assisted trials.

    Hypothesis testing was performed in R (43) by subtracting the unassisted condition from the assisted condition, showing improvement due to assistance in all five measures. Both the task-specific measures and ergodicity—measured as the distance from ergodicity—capture the effect of the assistance. Note that the df for success rate is 39 because there is only one rate per participant.

    No
    assistance
    n = 20
    Assistance
    n = 20
    MeasureμSDμSDtdfP
    Success
    rate
    0.34750.1630.7920.18212.314395.162 × 10−15
    Balance
    time
    0.1910.4111.6611.91326.51911992.541 × 10−122
    Time to
    success
    25.3337.64820.0687.824−17.20211991.926 × 10−59
    Error0.6320.0620.6260.102−1.67411999.433 × 10−2
    Ergodicity0.7390.1910.6310.283−11.26111994.954 × 10−28
  • Table 2 Two-sample t tests of week 2 control trials and week 2 trained trials.

    Hypothesis testing was performed in R (43) by comparing the means of the control group with the means of the trained group. Error and ergodicity—measured as the distance from ergodicity—were the only measures that revealed a significant improvement in the mean between the trained group and the control group. Note that the df for success rate is 31 because there is only one rate per participant.

    Control
    n = 13
    After
    training
    n = 20
    MeasureμSDμSDtdfP
    Success
    rate
    0.4380.2110.3800.200−0.8032310.4280
    Balance
    time
    0.2950.5700.2430.5021.3789880.1687
    Time to
    success
    24.3197.84424.9817.7941.3019880.1935
    Error0.6290.0610.6210.058−1.9639880.0499
    Ergodicity0.7510.2070.7050.177−3.7019882.266 × 10−4

Supplementary Materials

  • robotics.sciencemag.org/cgi/content/full/4/29/eaav6079/DC1

    Data file S1. Performance metrics calculated for each trial and participant session.

    Data file S2. An example of trajectories collected from a single participant in their first session without assistance.

    Data file S3. An example of trajectories collected from a single participant in their second session with assistance.

  • Supplementary Materials

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    Other Supplementary Material for this manuscript includes the following:

    • Data file S1 (.csv format). Performance metrics calculated for each trial and participant session.
    • Data file S2 (.csv format). An example of trajectories collected from a single participant in their first session without assistance.
    • Data file S3 (.csv format). An example of trajectories collected from a single participant in their second session with assistance.

    Files in this Data Supplement:

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