IEEE Robotics & Automation Magazine - June 2020 - 80

Gravity
Equations
Fitting
Process

Gravity Compensation Model
Using Fitted Parameters

Supervised
Learning

Gravity Compensation
Algorithm Using ML

Experimental
Torques

Figure 2. The gravity compensation strategies.

mechanism. In this model, the torques depend on the pose
and weight distribution of the links. The positions of the centers of mass and the weights of the links may be estimated
from the CAD model. However, these parameters must be
experimentally adjusted to take into account manufacturing
uncertainties and unmodeled components.
In the case of the rehabilitation robot presented in [9], the
authors focused on offsetting the gravity of the motors. The
mass of the rest of the mechanism is neglected compared to
the mass of the motors. This assumption is due to the fact that
the designed rehabilitation robot for the forearm and wrist is
relatively small. Instead of using the CAD parameters or the
known mass of the motors, some authors prefer to measure
the torques in a set of positions to estimate the parameters of
the gravity model without the need to identify the masses
[10]. Note that this approach also uses the system's static equilibrium equations.
Other methods do not use any system equation. For example, in [4], the authors define a working area where the compensation for the weight of the exoskeleton is to be applied,
and this volume is discretized into small cubes. In each cube,
the force is calculated at each vertex so that the gravity is compensated for and the robot is immobile. Once the force database is completed (and knowing in which cube the
exoskeleton is located during the rehabilitation exercise), a
weighted mean of the eight vertices of the cube gives the gravity compensation force value.
ML-Based Approaches
ML is a set of algorithms based on two main ideas: the acquisition of new knowledge from external sources and the
improvement of knowledge representations and structures
so that existing knowledge may be better exploited [11].
In ML, there are many possible techniques and approaches to achieve the same goal; some of them are more appropriate than others for a specific problem. Among the
existing approaches are neural networks, Bayesian classifiers, nearest neighbor classifiers, support vector machines,
and decision trees.
ML algorithms use computational methods to get information directly from data without relying on a predetermined
model. Thus, once a gravity force database is available, MLbased techniques can compute an estimation of the gravity
80

IEEE ROBOTICS & AUTOMATION MAGAZINE

JUNE 2020

components. In fact, ML has already
been used to solve some mechatronic
problems, such as the design of smart
laser-welding controllers [12] and
adaptive exoskeleton controllers for
optimal rehabilitation [13].

Materials and Methods
Based on the strategies found in the literature, this article analyzes and compares two different solutions to achieve
gravity compensation (Figure 2) and
tests them on the HomeRehab system. The first one, the analytical method, uses the device's
gravity equations with experimentally fitted parameters. The
second solution implements a novel strategy based on ML
to compensate for gravity without using the device's static
equations. The HomeRehab robotic system (Figure 3) is
used to train and test the proposed methods. Table 1 shows
its main technical specifications.
HomeRehab has the option to work in both the 2D and
3D workspaces. When working in 2D, the patient exercising with HomeRehab sits in a chair and trains with 2D
movements in a planar workspace. Once the patient is able
to control and hold the weight of its arm, our device lets
him or her exercise on virtual daily life activities in a 3D
workspace by standing up and holding the end effector as
a traditional haptic device. In this case, the proposed active
gravity compensation methods aim to overcome the
weight of the device so that the exercises are more realistic
and less tiring.
To derive the static-equilibrium equations of HomeRehab, it is assumed that the links' centers of gravity are placed
along their axis, but not necessarily at their geometric centers (unknown distances l b, l c, l d, and l e), and also at different heights with respect to the plane of rotation of the
pantograph (llb, llc, lld, and lle) . The lengths of the mechanism
are l 1 = 0.2 m, l 3 = 0.3 m, and l 3 = 0.4 m. Angle θ1 is the
rotation of the mechanism with the horizontal plane, while
angles θ2 and θ3 define the position of the pantograph links.
The handle is modeled as a punctual mass (point A), and the
gravity centers of the driving links (points D and E) are
located closer to the ends where the motors are anchored.
Note that the pulley of the mechanism rotates in solidarity
with the pantograph. Its center of gravity (point F) is not
over axis x, and it is also outside the pivoting plane of the
pantograph.
Using the scheme in Figure 3 and operating the static-equilibrium equations, the gravity components of the device are
x1 = - p1 s1 +

p 2 c 1 c 2 + p 3 c 1 s 3 - p 4 c 1 + p 5 c 1 c 3,

x 2 = - p 2 s 1 s 2,
x3 =

p 3 s 1 c 3 - p 5 s 1 s 3,

(1)

where s i = sin i i, and c i = cos i i . These components depend
on five parameters, p 1, p 2, p 3, p 4, and p 5, which, in turn,

IEEE Robotics & Automation Magazine - June 2020

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