Gravity Compensation and Compliance Based Force Control for

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Transcript Gravity Compensation and Compliance Based Force Control for

Gravity Compensation and Compliance
Based Force Control for
Auxiliarily Easiness in Manipulating Robot
Student ID : MA020213
Student : 莊沛語
Teacher :謝銘原
A. System structure
B. Denavit - hartenberg’ form
D. Auxiliary torque compensator
The objective of this paper is to present the gravity compensation
and compliance based force control for auxiliarily easiness in
manipulating robot arm.
Haptical application of the safety-priority robot arm technique which
interacts with people must reduce the ear ratio and design
necessary algorithm which can provide auxiliarily easiness in
moving the robot arm especially during the teach and learning mode.
In this study, discuss the effects of two aspects and propose a
control algorithm to improve efficiency of carrying heavy item. Firstly,
the gear ratio of motor is bounded so that robot can be more flexibly
compliant while user take grip on it.
To solve this problem of gravity compensation, we propose a
method that based on the concept of vector projection to calculate a
general solution which can construct a gravity model of multi-DOF
robot arm.
Furthermore, we define a virtual mode that is proposed to
compensate the deficiency of inertia’s physical phenomenon.
Secondly, propose an approach which call it force counterbalance
control (FCC) that not only balances external load variation in
addition to robot weight itself, but also keeps the property of
dexterous easiness in manipulating the multi DOF robot arm.
The FCC algorithm can be applied on several applications such as
carrying heavy item or being auxiliarily easinese in manipulating
robot arm.
Robot arm is widely used in different fields of application, from
industrial automation to domestic service. In past time, traditional
robot arm have been focused on stiff transmission, rapid movement
and high accuracy. Recently, researchers begin to put more
emphasis on the robot arm’s safety and reliability .
The actuators are often used to drive the hardware of the robots.
actuator control is one of the most important issues, and actuators
are always used by motor, hydraulic, Pneumatic and so on.
In the part of control, a lot of control methods are proposed by
robotics researchers, like Impedance Control , Admittance Control
(position based control), Force Control, Stiffness Control,
force/position Control and even Hybrid control.
The control algorithms that are mentioned above always suffer in
some physical disturbance, such as gravity, Coriolis force and
friction force.
The gravity compensator is an indispensable issue; some
researchers use special control algorithm that takes into account the
maximum admissible payload to reduce the disturbance of gravity ,
or use the concept of energy , or use Lyapunov control theorem to
compensate .
The gravity compensator is based on dynamics. Vector projection is
fully utilized to accurately compute the torque value that each joint
have to be compensated. Thus the gravity compensator can be real
time compensated in any position. If the gravity compensator is
correct, the robot manipulator can stop in any position after it is
moved to any position.
Beside of adding gravity compensator, we also add a new method,
auxiliary torque compensation, to compensate the deficiency that is
caused by gear ratio. Contributed by the compensation, the robot
manipulator can be moved freely and lightly.
A. System structure
In structure of the control
system which is based on 6DOF arm, use PCI base
motion control card that
provide the powerful real time
calculating capability to
program the self design control
algorithm .
Fig. 1. Control Structure
The motion control card
provides 1ms servo interrupt
time for the routine of the
control, and sends out the
control command to the servo
driver through the D/A
converter. The servo driver is
configured to the mode which
receives the torque command.
The test platform of arm is
actuated by servo motor with
50 ratio harmonic drives which
is in between the arm and
servo motor. So, use torque
mode to drive motor, and gave
robot manipulator some force
Fig. 2 .6 DOF Robot arm model
All of the physical model parameters of the system show in the
Table , and the Fig. show the each link and each axis of robot
manipulator, such as Link1, link2, kink3, axis1, axis2, axis3, axis4,
axis5, axis6.
B. Denavit- hartenberg’ form
The robot arm is designed with
6-DOF to reach attempted
point in 3D space. In order to
understand the dynamic state
of the robot, every joint space
relationship must be
established from base to end
Fig. 3. (a) 6 DOF Robot arm model.
Relationship between every
link coordinate systems of the
6- DOF arm using the Denavit
- Hartenberg convention. The
values of the kinematic
parameters are listed in Table ,
where d1, d3 and d5 are the
link lengths of base to shoulder,
shoulder to elbow and elbow to
wrist respectively.
And then they correspond to
the position in the link
coordinate diagram of The D-H
convention allows the
construction of the forward
kinematics function by
composing the coordinate
transformations into one
homogeneous transformation
(b) 4 axis Coordinate systems of the robot.
C. Gravity compensator
The general control block
diagram is . All of robot
manipulator controls always
suffer in external disturbance
such as gravityG(q) , damping
and even CoriolisforceC(q, q )
that are caused by angular
velocity and linear velocity. ,
the damping can be reduced
by low gear ratio and the
Coriolis force is too small to be
eliminated in this system.
Fig. 4. Control block diagram
Because the gripper is too light to ignore,
just consider axis1 to axis 4. The
coordinate transformation shows in
Fig. Then, the dynamics is used to
compute the compensator of gravity.
Gravity has relationship with each joint,
so we base on the concept of
following with Fig.
1. Base coordinate bases on X0, Y0
and Z0.
2. Gravity always points to X0 of base
3. The torque that one joint sustains is
the moment projection that relatives
this joint.
In Fig. 6, F means a force vector in 3D space, r means nearest
distance vector of 3D space and e means the unit projection vector,
so the equation of the moment in 3D space is got form Fig.
• The moment size that projects along unit vector
computed with
by inner product in (4)
can be
means projection vector of torque.
Base on the concept of (4) and (5), expand the single axis to
multi-DOF axes and compute the torque of each axis that gravity
F is equivalent to each link weighting, R is equivalent to the center
of each link and e is equivalent to the unit vector of motor of each
joint. F, r and e of every joint can be computed form Fig.5 (b) and (6),
By (8), (9), (10), each joint torque that have to be
compensated by motor can be obtained with Fig.7.
Fig. 7. The physical features of every axis.
D. Auxiliary torque compensator
In the condition of senseless, the gear ratio make the robot
manipulator is manipulated difficultly on haptical control. Therefore,
the methods that are angular momentum and angular impulse
principle and parabolic curve are proposed to deal with this damper
Therefore, bring up a method of parabolic curve to solve above
problem, and the parabolic curve is shown in Fig.8.
Fig. 8. The parabolic curve that be looked on as auxiliary force
In a word, the dexterous gravity compensator is obtained by gravity
compensator, parabola function and angular momentum and
angular impulse principle shown in Fig.9.
Fig. 9. The parabolic curve that be looked on as auxiliary force
In order to measure the torque that is caused by external weight, we
use the closed loop system of impedance control. The definition of
impedance control is the relationship between position and torque,
and the concept of impedance control is introduced by Hogan and is
considered as a classical control in robotics. The closed loop of
impedance control is shown in Fig.10.
Fig. 10. Impedance control.
A lot of workmen always have to carry heavy object; it may cause
movement injury mindlessly because they have to make a power to
move heavy item. Therefore, the method that combines the gravity
compensator, auxiliary torque compensator and impedance control
is proposed to solve this question. The force counterbalance control
algorithm can increase force to arise heavy item, and user can also
freely move the manipulator that loads heavy item to some place
where user wants. The general block diagram of force
counterbalance control is shown in Fig.11.
Fig. 11. Force balance control.
First, impedance control is utilized to construct spring model. we
take the axis torques that above we can feel the movement of the
robot manipulator that holds the heavy object is light and handy. The
flow diagram is shown in Fig.12.
Fig. 12. Weight estimate algorithm.
Fig. 13. Force counterbalance control experiment.
(a) Moving robot manipulator freely and lightly by Auxiliary torque
(b) Halting robot manipulator by gravity compensator.
(c) Adding a 2.5Kgw heavy object.
(d) Computing the weight of object and robot self by FCC.
(e) Moving the robot and object freely and lightly after adding FCC.
(f) Halting the robot and
In this paper, dexterous gravity compensator
and FCC are proposed. Many advantages of the
algorithm are listed as follows:
1. Because of the dexterous gravity compensator,
robot arm has good performance in compliance.
2. The force counterbalance control (FCC) is
helpful for arm to load weight payload and help
people to move objects.
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