-In the present paper it was developed and programmed a simple 6 DoF tele-operated slave system that can track in real-time a master system. The arm's length parameters were calculated using a database of 196 male and female students from 18 to 22 years old. A classic control scheme were used in the slave system for the position tracking. The master system movement modifies the end effector's Euclidean position of the slave system. Experimental results of the system are provided including the desired trajectory and the robot behavior, showing the trajectory error.
T person can perform tasks remotely, these systems avoid
ELEOPERATION is a set of technologies through which a
the exposure of people to dangerous and / or inaccessible
sites [
Nowadays, robot arms have much attention in different
fields [
In [
Another application for robotic arms is for the industrial
field, In [
In 2013, a humanoid robot for upper limbs was
performed using a motion tracking system to execute tasks
in search and rescue missions, such cutting through walls,
tasks that involved manual labor or require the use of power
tools. It was named HUBO and had six degrees of freedom
[
Tele-operated robot arms have been used in the surgery
field too to perform a variety of invasive procedures, in
2014, there was an study with a robot focusing on the
movement of surgeons’ hands and arms, employing theories
and methods from the study of human motor control [
Robotic arms are currently enabling people with upper
extremity disabilities to perform daily activities on their
own [
A representative sample size was calculated for finite and known populations, according to the total number of students enrolled in the University, with 95% of confidence. This sample was formed by 198 subjects, 46 women and 153 men who were invited to be part of the study.
Twelve anthropometric dimensions were taken for
every participant (as shown in figure 1), upper limb
length, clavicle-shoulder length, shoulder-elbow length, and
shoulder-wrist length. This anthropometric data was taken
according to standard methods [
These mentioned dimensions were taken with the
purpose of simulating the main movements of the upper limb
[
Shoulder: Flexion/extension, abduction/adduction. Elbow: Flexion/extension.
Forearm: Pronation/supination.
Wrist: Flexion/extension, radial/cubital deviation.
Subjects were measured wearing light clothes, as light as possible in order to have more reliable and accurate data, this procedure lasted ten minutes approximately for each person. After the anthropometric information was collected, these data were captured in Microsoft Excel and then migrated to the statistical software Minitab in order to obtain measures of central tendency and percentiles. We used (eq. 1) to calculate the percentiles of the anthropometric data (depicted in Table 1). These data helped us estimate the links’ length for the master robot.
P = µ ± Z (1)
µ: Sample mean.
: Standard deviation of the sample.
Z: Standard value from normal distribution. • • • • • • • •
The basic movements of the human arm can be simplified in three dual rotational articulations plus the end effector (depicted in figure 2):
In this work a 6 DoF manipulator with rigid rotational joints is considered and it is depicted in (figure 3).
From (eq. 3) we can extract the end effector’s pose. Looking at the block matrix t in A0 n we can determine the Euclidean position, and looking at the block matrix R in A0 n we can derive the rotation. For this to happen we need to transform a rotation matrix to a vectorial representation. The most natural would be Yaw, Pitch and Roll, depicted in (fig. 4).
Meaning that the pose is defined as: (2) (3) (4)
Where: • • • • • • • •
4
As only the position was intended to be controlled, (eq. 4) changed to (eq. 5). The control scheme used for the robot’s end effector to converge in a desired position (regardless of the orientation) was a simple PID Controller (eq. 6).
It is important to notice that the robot will only converge if it exists in the manipulator’s work zone (defined by eq. 7) u(t) = ~q˙.
Kp: Proportional gain diagonal matrix.
Ki: Integrative gain diagonal matrix.
Kd: Derivative gain diagonal matrix. e(t): error defined by ~xd(t) ~x(t) x ! xr8 xr9
R3|xr 31 ⇡ Pin=1 li: Manipulator work zone.
In order to control the system we need the inverse kinematics given by (eq. 8).
(eq. 8) can be re-written in a more appropriate form as (eq. 9)
~q = f (~x) ~q =
Z
~q˙dt = Jv+~e(t) ~q˙ is the articular velocities vector.
Jv+ is the sub-matrix of linear velocities of the geometric Jacobian’s psuedo-inverse. Which is a matrix that maps the linear velocities to articular velocities.
The geometric Jacobian was calculated using (eq. 10) J = z1 ⇥ (on z1 o1) z2 ⇥ (on z2 o2) . . . zn ⇥ (on . . . zn
on) (10)
Where zi is the product between the rotation matrix i and the vector kˆ ⇥ 0 0 1 ⇤T , and oi is the translation of the frame i.
In this case, the end effector’s orientation it’s not needed, hence, the geometric Jacobian is restricted to use only linear velocities. 5
The algorithm was developed in Matlab/Arduino trying to make the real-time bidirectional communication as real as it can be. We used the tic and toc Matlab’s functions to establish an adaptive delay that match a fixed integration step for the control.
The adaptive delay was calculated using the algorithm’s execution time and a fixed desired step for the integrator (depicted in figure 5).
The master system consisted in using an Arduino MEGA (figure 6) and three potentiometers as input for the desired position in real time. (5) (6) (7) (8) (9)
~xd(t) was modified in each iteration moving the potentiometer’ position (figure 7)
In (figure 8) can be seen the position error between ~xd(t) and ~x(t). In the same way, the articular values stabilize at a certain value depicted in (figure 9). It can be seen that the control scheme proposed works as expected controlling the end effector’s euclidean position. Also, the bidirectional communication between Arduino and Matlab using a Serial protocol is fast enough to control in real-time te system. In the future, we might change the code from Matlab to C++ or ROS to speed up the communication and make h smaller. From this work we established that the next step will be the orientation control and then we will need to build the robot arm and apply the control scheme.
Once we prove the control scheme works, we then need to build the master system which will include a 6 DoF IMU (depicted in figure 11) to obtain the complete pose.