IEEE Robotics & Automation Magazine - June 2020 - 84

compensation equations are directly programmed in HomeRehab's National Instruments (NI) MyRIO controller, which
runs at a sampling time of 1 ms. A local host Python server is
created as middleware between the PC that runs the ML algorithm and the HomeRehab controller. The input message for
the server is the actual position of the end effector (three
angles), and the output consists of the torques needed in the
three motors to compensate for the gravity force of the
mechatronic device. Communication between the computer
and the NI MyRIO controller is achieved by the User Datagram Protocol (UDP), sending end-effector positions from
the controller to the computer and receiving compensation
torques computed by the ML algorithm. The average computation time for ML prediction and UDP communication is
approximately 2-3 ms.
The validation experiment consists of moving the HomeRehab system to 120 points (84 points inside the limits of
the training cube and 36 points outside the training cube).
None of these points was previously used for the training
phase. These 120 points result from the combination of
x = [- 0.53, - 0.43, - 0.33, - 0.23, - 0.13, - 0.03, 0.03, 0.13,
0.23, 0.43], y = [0.07, 0.11, 0.15] and z = [0.29,0.33,0.37,
0.41] (m). Thirty-six of the 120 points are outside the training
cube (they do not satisfy - 0.4 1 x 1 0.4 m).
The validation test is carried out as follows: First, a PID
controller holds the device still at the selected point with a
position error lower than 0.1 mm. The torque values computed by the PID to hold the device still at each one of the points
are considered the ground-truth data for validation. Once the
system reaches each point, we replace the torques computed

2.8

0.4

1.4

2.6

0.2

1.2

Torque (N·m)

2.2

-0.2
-0.4
-0.6

1.8
1.6

2.4
Torque (N·m)

by the PID controller with the torques derived from the proposed two methods, and we evaluate whether the device
remains immobile in the same position or if it moves (either
falling or moving in other directions). The outcomes of this
experiment show that both methods behave properly, holding
the device at all 84 points that lie within the training workspace. However, the ML-based method fails to hold the device
still at 25 points outside the training workspace, while the
analytical method succeeds at all 36 points outside the training workspace.
Figure 6 shows an example of the torque values
computed by both methods along 10 validation points:
x = [- 0.53, - 0.43, - 0.33, - 0.23, - 0.13, - 0.03, 0.03, 0.13,
0.23, 0.43], y = 0.11, and z = 0.37 (m). It can be seen from
Figure 6 that the torque values for both methods, compared
with the PID torque values, are slightly different at each
point. However, HomeRehab remains still at most of them,
which is considered a good behavior. This fact is due to the
friction components of the mechanism that need to be overcome to start moving. In this particular set the analytical
equations are able to hold the system still at all 10 points.
However, the ML-based method fails at points 1 and 10,
which are outside the limits of the training cube (point 2 is
also outside the limits, but the method performs well). At
these two points, the robot does not hold still with the MLbased method.
Figure 7 illustrates the box plots of the error at all 120
points between the PID values and the values given by both
methods. For each joint and method, two sets of box plot figures are shown, one for the 84 points inside the limits of the

-1

PID

0.6
0.4
0.2

-0.8

1 2 3 4 5 6 7 8 9 10
Validation Point
(a)

0.8

0
1 2 3 4 5 6 7 8 9 10
Validation Point
(b)
Analytical Model

-0.2

1 2 3 4 5 6 7 8 9 10
Validation Point
(c)

ML Algorithm

Figure 6. The torque values computed by the PID controller and both methods (analytical model and ML algorithm) in a set of 10
validation points. (a) Torque x 1 . (b) Torque x 2 . (c) Torque x 3 .

IEEE ROBOTICS & AUTOMATION MAGAZINE

JUNE 2020

IEEE Robotics & Automation Magazine - June 2020

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