13-02-2013, 04:03 PM
Dynamic Simulation of an Improved Passive Haptic Display
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Introduction
The Haptic Display
The word haptic is one unfamiliar to most. It comes from the Greek haptesthai,
meaning \to touch," dened as relating to or based on the sense of touch. A haptic
display is a device that interacts with a user through his or her sense of touch. Just
as a computer monitor is a visual display and a set of headphones is an aural display,
a haptic device is a touch display. There are many uses for such displays in the elds
of teleoperation, articial environments (virtual reality), and ergonomics.
One of the rst applications of haptic displays was in teleoperation. Tactile feedback
can improve the performance of a local operator manipulating a remote system.
Such a system relies on the user projecting his dexterity into the remote environment.
Although humans rely highly on visual cues to perform tasks, we also depend
on tactile cues for object identication and manipulation. [10] In situations where
visual sensing is impaired it can actually be replaced by tactile sensation. [8] Also, a
more accurate representation of the remote environment will instill a greater sense of
presence in the user, which may improve his or her performance. [20]
Passive Haptic Displays
Most existing haptic displays are active, comprised of actuators that can do positive
or negative work on the interfaced system. However, some current research involves
the study of passive haptics. [7] [14] [15] [18] A passive haptic display has no actuators
that can add energy to the system. That is, all energy added to such a device must
come from the user. Such a device has a primary advantage of safety over a similar
active device. Uncommanded movement is less probable in passive devices and is in
general easier to prevent. This makes passive haptics ideal for applications where
safety has high priority, such as assisted surgery and situations where high contact
forces are possible.
Passive haptic displays are a challenge to control, since arbitrary control actions
are not possible. A control action which adds energy to the system is not achievable.
An eective controller must determine whether or not desired control actions are
unachievable, and if so, dene an achievable set of command inputs which act as a
compromise between system performance and realizability.
Organization of This Work
This work explores the enhancement of a simulation of a passive haptic display and its
subsequent use in the evaluation of control concepts that may increase system performance.
This chapter has provided some introductory information on haptic displays.
Chapter 2 reviews previous work done in the design and manufacture of a two degreeof-
freedom passive haptic testbed, the Passive Trajectory Enhancing Robot (PTER).
Chapter 3 explains the enhancement of a dynamic simulation of PTER through modeling
of stick-slip friction and actuator dynamics. Chapter 4 deals with the design
and manufacture of an actuator testbed used to perform system identication tests
on one of PTER's four actuators, with the intent of building an actuator model for
use in the dynamic simulation. Chapter 5 addresses the implementation and simulated
performance of two new control concepts. Experimental results for one of these
control concepts are also presented. Finally, Chapter 6 contains closing comments
about the contribution of this work and some ideas for further research.
Development of PTER
PTER - Physical Description
An experimental passive haptic testbed has been built and used by previous students
for the purpose of studying the behavior of such a device and to evaluate control
techniques. [6] [11] This device has been named PTER| the Passive Trajectory
Enhancing Robot. Figure 1 is a diagram of PTER. It is a planar robotic arm in a
ve-bar parallel linkage arrangement.
PTER's purpose is to exert forces on the hand of a user, who grips the handle at
the endpoint of link D. It does this by providing torques to links A and B through
its network of four actuators. The actuators are controllable friction clutches. The
clutches are passive devices, only serving to remove energy from the system, hence
the passivity of the entire device. Clutch 1 and clutch 2 connect links A and B,
respectively, to ground. Clutch 3 couples the velocities of links A and B together.
Clutch 4 inversely couples links A and B together through the gears located in the
middle of the device. Since PTER has more clutches than degrees of freedom, the
robot is overactuated. This conguration was selected in order to provide greater
freedom in providing arbitrary torques to each of the main links A and B.
PTER - Kinematic and Dynamic Equations
Kinematic and dynamic analysis of PTER have been suciently addressed by Charles
[4], Davis [6], and Gomes [11]. The pertinent equations will be summarized here and
the reader is referred to their work for the full derivations. These equations were used
in the development of the dynamic simulation of PTER later in this work. Figure
2 is a schematic diagram of PTER, showing the applicable coordinate systems and
parameter terminology.
Control Methods
Since its inception, several controllers have been implemented on PTER. PTER's
control needs can be separated into three parts. One controller must identify a set
of desired link torques given the instantaneous state of the system and its desired
behavior. The second controller must transform the desired link torques into a set
of achievable clutch torques, taking into account the system state and the clutches'
passivity constraint. Finally, the third controller must provide command signals to the
physical hardware in order to produce the torques desired by the second controller.
Most of the previous work in controlling PTER has concentrated on the rst two
concepts. The latter task of generating control signals has been solved open-loop
through the use of a lookup table.
The initial controller as suggested by Charles [4] and implemented by Davis [6] is
an impedance controller, which computes desired tip forces through the simulation
of spring and damper elements between the endpoint of the robot and the desired
path. An algorithm named the \torque translator" was developed by Davis in order
to select a set of achievable clutch torques which match the desired link torques as
closely as possible. The signs of the clutch velocities are used to determine whether
or not a desired output torque is achievable.
Gomes looked into several dierent controllers with the aim of both improving
path following performance and minimizing tip acceleration [11]. He implemented a
simplied version of the torque translator, which considered desired tip forces rather
than desired clutch torques. High levels of tip acceleration due to rapid application
and release of clutches was evident. In light of this, Gomes implemented a blending
algorithm, which gradually applied and released clutches. This algorithm did not
signicantly improve the tip acceleration prole. A controller using the tip velocity
rather than the position error was also investigated with promising results, though
the implementation was very basic.
Dynamic Simulation
A dynamic simulation of PTER was written in MATLAB by Charles [4]. In the
simulation the controller attempts to constrain the endpoint of the device to a circular
path. A force along the circle and a periodic normal disturbance force are applied to
the endpoint. The simulation computes net torque on links A and B by combining
required clutch torques with the user input force translated into link torques through
the Jacobian. The equations of motion are inverted and used to compute the link
accelerations from the net torques.