IEEE Robotics & Automation Magazine - June 2020 - 85

training cube (in black) and the other for the remaining
points outside the limits (in blue). It can be seen that, while
the ML-method computes similar values to the analytical
method inside the training cube (except for joint 1), outside
the cube the joint 2 and 3 torque values are different.

Conclusions
Gravity compensation is a mandatory feature of mechatronic
devices used for rehabilitation. People with limited mobility
cannot manipulate bulky apparatus and should be able to perform rehabilitation tasks without extra impediments, as if
they were moving their limbs freely.
In this article, we describe the use of ML methods to ease
the complex task of developing proper active gravity compensation control algorithms for robotic rehabilitation. Gravity
compensation is of paramount importance to achieve
transparent haptic interactions, especially for medium- and
large-size mechatronic devices where the inertia of the system
is not negligible in free motion. Traditional control methods for active gravity compensation require deriving the

1.5

1
Torque Difference (N·m)

Torque Difference (N·m)

Discussion
From the outcomes of the validation experiment, it is difficult
to determine which of the two methods provides better gravity compensation torque values. There is a range of torques
where the results can be considered valid; that is, the system
holds still. This range of torques directly depends on the friction of the system. Even the PID torque values, used as
ground truth, are affected by the friction. Nevertheless, the
qualitative result (whether the system holds still or not) is a
valid outcome when the aim is to compensate for the device's
gravity forces.
Training data are obtained relatively fast (2.5 h) for a medium-size workspace used in upper-limb rehabilitation. The
analytical method seems to behave better, as it can give proper
results even outside the workspace covered by the training
data. However, deriving the gravity-equilibrium equations
may not always be possible or easy (e.g., for some parallel
mechanisms). The ML-based method enables the implementation of an algorithm that overcomes this drawback, as it
does not require the analytical equations of equilibrium, but it
does not perform very well outside the workspace considered
in the training data.
The drawback of the ML method may not be relevant if
the training data cover the entire workspace of the mechanism. However, this circumstance should be considered for

large and complex workspaces. The fact that the ML method
performs poorly outside the area of the training data sounds
like overfitting. We performed several experiments with different parameters (estimators, seeds, the train/test split, and
so forth) to further analyze the issue, and we discovered that
it was not overfitting but a lack of precision of the method.
Therefore, we think that using deep-learning methods may
lead to better results. The goal of this article was to focus specifically on traditional ML methods, but future work will
evaluate the performance of deep-learning methods as a
solution to the poor performance of the ML method outside
the workspace considered with the training data. A video
showing the behavior of the system using the compensation
methods is available as a supplement to this article. The MLbased method code and training data set are also available to
the public.

0.5

-0.5

0.5

-0.5

-1

-1.5

-1.5
Torque 1

Torque 2
(a)

Torque 3

Torque 1

Torque 2
(b)

Torque 3

Figure 7. The box plots of the torque difference between (a) the PID analytical-model values and (b) the values given by the PID-ML
methods (points within the training cube are in black, and points outside the training cube are in blue), with mean values (asterisks).

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IEEE Robotics & Automation Magazine - June 2020

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