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An Evaluation of Closed-Loop Control Options for Continuum
Manipulators
Ryan S. Penning, Jinwoo Jung, Nicola J. Ferrier, and Michael R. Zinn, Member, IEEE

Abstract—Continuum manipulators are gaining widespread
acceptance in commercial robotics, particularly in the medical
field, where their compliance allows a large benefit for patient
safety. However, this compliance also makes precise position
control of these manipulators quite difficult. This paper
presents two closed-loop control implementations applied to a
small scale continuum manipulator. These implementations
are both based on manipulator tip position feedback from an
electromagnetic sensor.
The command tracking and
disturbance rejection properties of the two control
implementations are shown to be approximately equivalent,
and provide improved position control when compared to
open-loop control, without sacrificing system stability.
I. INTRODUCTION
I
N recent years, there have been significant advancements
in minimally invasive medical telerobotic systems,
resulting in a number of commercially available systems
[1,2,3,4]. As the efficacy of these systems has been
demonstrated, researchers have begun to investigate
interventional systems in areas beyond more traditional
robotic surgery – where access is more challenging due to
size or other anatomical or clinical constraints. Examples of
such systems include small continuum robotic systems for
vascular or neurological interventions [1,2,3].
These systems often possess undesirable characteristics
which adversely affect performance, including device
friction and hysteresis, actuation and drive-train
nonlinearities, and lack of accurate sensors. As a result,
reduced positioning accuracy and dexterity, as compared to
traditional rigid robotic systems, is common. To improve
system performance while enabling more autonomous
capabilities, a number of researchers have focused on the use
of in-vivo feedback control [1,3,5,6,7,8,9,10]. In-vivo
feedback is the use of position, orientation, shape or other
data collected while the manipulator is at work inside the
patient collected via radiographic, electromagnetic and other
Manuscript received September 16, 2011. This work was supported in
part by the Wisconsin Alumni Research Foundation under Grant
MSN106564 and MSN136217.
R. S. Penning is a graduate student with the Mechanical Engineering
Department, University of Wisconsin – Madison, Madison, WI 53706 USA
(e-mail:rpenning@wisc.edu)
J. Jung is a graduate student with the Mechanical Engineering
Department, University of Wisconsin – Madison, Madison, WI 53706 USA
(e-mail:jjung22@wisc.edu)
N. J. Ferrier is with the Mechanical Engineering Department, University
of Wisconsin – Madison, Madison, WI 53706 USA (e-mail:
ferrier@engr.wisc.edu)
M. R. Zinn is with the Mechanical Engineering Department, University
of Wisconsin – Madison, Madison, WI 53706 USA (phone: 608-263-2893;
fax: 608-265-2316 e-mail: mzinn@wisc.edu)
methods. Advancements in sensor and actuator technology
and feedback control strategies for in-vivo use have
demonstrated marked improvements in performance and
efficacy [7,11,12,13,14,15]. This paper represents the first
direct comparison of different control architectures for use
with continuum manipulators. Others have utilized the
control to alter and improve the dynamics of the manipulator
in a 3D space [8,16,17,18,19]. In [7], the authors utilized a
configuration space controller to control the shape of a
multi-segment continuum manipulator.
One field that suffers from the difficulties of flexible
catheter manipulators is interventional electrophysiology, in
which radiofrequency ablation within the atria of the heart is
used to correct abnormal heart rhythms. The open volume
of the atria presents unique challenges in manipulating a
flexible catheter, and may benefit from closed loop control
of the catheter tip position.
In a previous paper, [22], we investigated the feasibility of
closed loop control of a continuum manipulator in a threedimensional open volume. This paper expands on the
exploration and details two closed-loop control options for
continuum manipulators: joint space and task space control.
The following sections detail our control implementations,
explore the dynamic properties of the catheter, and compare
the command tracking and disturbance rejection
performance of both closed loop control implementations.
II. SYSTEM OVERVIEW
Fig. 1 Overall system configuration. The catheter can be driven either
through direct operator input, or a pre-programmed trajectory, with the
latter option allowing for repeatable experimentation.
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utilizing a trakSTAR electromagnetic location system
(Ascension Technologies, Burlington, VT). This system
allows us to feed a small receiver (approximately 1.8mm in
diameter) down the center lumen of the catheter. This
sensor is fixed in place at the catheter tip, and provides full
position and orientation feedback, with an accuracy of
approximately 1.4mm. Since this sensor operates on
electromagnetic principles, it is sensitive to distortion
induced by nearby metallic objects and electrical noise. All
efforts have been made to reduce EM noise in the testing
environment, and the catheter and testing area are composed
entirely of non-metallic materials.
Fig. 2 Catheter Design and Mechanics The left image shows the robotic
catheter itself, while the right shows the splayer block which attaches to
the base of the catheter. This splayer provides both articulation motion
(via the 4 pulleys), and insertion motion.
To allow us to evaluate various control schemes for
continuum manipulators, we have constructed the
Continuum Robotics Electromechanical System Testbed
(CREST). This, in concert with our own 3-DOF catheter
prototype and a commercial electromagnetic localization
system, represents a complete system capable of closed loop
control (Fig. 1). A more thorough description of this system
is available in [22], but we present a brief overview here for
clarity.
A. CREST
The CREST system is an 11-DOF servomechanical
system capable of independently driving two catheters.
Each catheter is attached to a pulley block with four motors
to control each of the four pull-wires. Each pulley block can
also be moved independently to extend or retract the
catheter. In addition, the entire mechanism can be rotated
about its longitudinal axis. For the controls implemented in
this paper, we will only make use of a single pulley block
and its associated insertion motion, with no longitudinal
rotation.
B. Catheter and Tip Position Tracker
The catheter used here is identical to the design we
presented in [22]. It consists of a PTFE spine with machined
slots to increase its flexibility (Fig. 2). Four diametrically
opposed control wires run through channels machined along
the length of this spine, and are held in place using an
expandable plastic mesh. A central lumen allows sensors
and other instruments to be fed down the length of the
catheter. The catheter itself extends through a stiff, rigidly
mounted sheath. By altering the length of the catheter that
extends from this sheath, and pulling on the proper pull
wires, the catheter can be manipulated throughout a 3D
workspace.
In order to track the position of the catheter tip, we are
C. Catheter Joint and Task space Definition
In our investigations, we have focused solely on
positioning of the catheter tip. At present, we have made no
attempt to control either catheter shape or tip rotation. For
this paper, we have selected two different generalized
coordinate systems to define the configuration of the
catheter. These will be referred to as task space and joint
space. We define task space to be the (x,y,z) coordinates of
the tip of the catheter relative to the center point of the stiff
sheath exit. Positive y is defined to be in the direction of
catheter extension, and positive z to be upwards. This
allows for an intuitive description of the catheter tip
position. However, because this coordinate frame is not
based on the mechanics and kinematics of the catheter,
significant coupling exists among the actuated axes. That is,
a change along a single task space axis may require multiple
actuation actions. This motivates the use of joint space
coordinates. By defining tip position as a function of two
orthogonal articulations and total insertion length, this
coordinate space more closely matches the actuated axes,
and allows for decoupling of insertion and articulation
actuation coordinates. By assuming a constant curvature
along the length of the catheter, these coordinates can be
obtained via a closed form solution as defined in [20,21] and
illustrated in Fig. 3.
Fig. 3 Coordinate space definition. The joint space coordinate frame is
based on an assumption of constant curvature of the catheter. (That is, the
catheter always attains a shape that represents some portion of a circle.)
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Fig.4 Control architectures under investigation. A) Task space control implementation. B) Joint space control implementation
III. CONTROL ARCHITECTURE
Control of our catheter prototype presents several inherent
challenges. Chief among these is the non-linear behavior of
the catheter, which can arise due to internal friction, device
hysteresis and a host of other factors. In our previous work
[22], a joint space controller was implemented as a proof of
concept for closed loop control of a continuum manipulator
in an open volume. Since this previous publication, we have
more thoroughly evaluated both this joint space controller
and a task space controller. Both of these controllers were
formulated based on several assumptions. First, that both
the desired position and the measured position are available
only in task space. The desired position will typically be
provided by the human operator. Since task space allows for
a more intuitive specification of this position, this is what we
have chosen to implement in our workstation software.
Similarly, the feedback from the trakSTAR device is
provided in Cartesian coordinates.
Second, catheter
dynamics are assumed to be negligible. This assumption is
valid for the relatively low-speed movements specified by
the clinician. However, for higher speed movements, such
as compensating for the motion of a beating heart [8], it will
not hold. Finally, the inverse kinematics are based on an
assumption of constant curvature in the catheter. For this
work, this is assumed to be a reasonable approximation of
the true catheter behavior and is thus appropriate for
coordinate transformations.
A. Task Space
Our task space control implementation (Fig 4A) is based
on the error as calculated in the task space frame as defined
above. A simple integral controller is then applied on each
axis. The inverse Jacobian is utilized to transform the action
defined by this control into joint space, and from there, into
catheter actuation space via the CREST inverse kinematics.
This inverse Jacobian is calculated numerically based on the
inverse kinematics with an incremental disturbance in each
of the three task space directions is applied, and the resulting
change in position is determined. This necessitates solving
the (closed form) inverse kinematics a total of six times. At
present, this is easily accomplished within each major cycle
of the control. If a more complex form of inverse
kinematics/dynamics model is chosen in the future, this
could potentially exceed the allotted computation time, and
an approximated Jacobian may need to be used.
Our assumption of negligible catheter dynamics yields an
open-loop device transfer function with unity gain and no
phase lag. Thus, an integral controller will modify this
response with a -20dB per decade gain slope and a constant 90 degree phase lag. This yields a 90 degree phase margin,
and a cross-over frequency that can be adjusted by changing
the integral gain. As will be discussed in III.D, this allows
us to limit the bandwidth of our controller to be below the
natural frequencies of the catheter itself. An integral control
term also serves to eliminate the presence of an algebraic
loop in the closed-loop transfer function.
B. Joint Space
Unlike the task space control discussed above, our joint
space control implementation (Fig 4B) makes direct use of
the device inverse kinematics, rather than the inverse
Jacobian. These equations are solved to convert both
commanded and measured position to joint space. For the
same arguments presented above, a simple integral control is
used to generate the control action, which is then passed
through the inverse mechanics of the CREST to generate the
actuation space commands.
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C. Architecture Comparison
Although task and joint space control represent very
different control architectures, under a specific set of
assumptions, they can be shown to produce nearly identical
results. For this, we will assume that the inverse kinematics
of the device can be linearized about a given operating point.
Additionally, we will assume that the device will remain
within the local neighborhood of this operating point. These
assumptions allow us to manipulate the block diagrams of
the control architectures following classical linear system
rules. Bringing the two calculations of inverse kinematics in
the joint space system to the inside of the summing junction,
yields a system that is very similar in structure to the task
space controller (Fig. 5).
The inverse Jacobian is numerically calculated as:
(1)
Where ε is an incremental displacement along each axis
and
M-1 is the linearized inverse kinematics of the device,
evaluated at the selected operating point.
Under our linearized system approximation, (1) can be
simplified to:
(2)
Thus, for the narrow set of approximations described here,
and assuming the integral controller values are tuned
identically, both task and joint space control should yield
similar actuation commands (qe) for a given error, and thus
both systems should perform almost identically. Note that
for higher frequencies or large errors, these results will not
necessarily hold true.
D. System Identification
In order to experimentally verify our assumptions on
catheter dynamics, we have attempted to characterize the
frequency response of both the articulation and insertion
axes of our device. While these axes are powered by
identical motors, the mechanics of each results in differing
frequency responses. Thus, a control bandwidth that is
appropriate for one axis will not necessarily yield acceptable
performance on a different axis.
To evaluate the open loop frequency response of each
axis, a chirp position command was input to the system with
the catheter in its neutral position. The resulting position
was recorded (utilizing the trakSTAR sensor).
This
information was then analyzed using Matlab’s
tfestimate command. The results, shown in Fig 6, show
Fig. 5 Manipulation of the operating point model block diagram yields
very similar structures between task and joint space control.
Fig. 6 Catheter response to 0.1cm chirp command swept from 0.1 to
20Hz. Frequencies beyond 20Hz were not excited in order to protect
the CREST hardware.
the significantly different response between the insertion and
articulation axes. While both show similar bandwidths
(approximately 10-12 Hz), the articulation axis experiences
a natural frequency near 7 Hz, while the insertion axis shows
a natural frequency closer to 10Hz. In our investigations of
closed loop control, we make the assumption that the
dynamics of the catheter system are negligible. For this
assumption to hold, we must therefore limit our analysis to
frequencies well below these frequencies. As such, we will
assume for frequencies below 5 Hz, the dynamics of the
catheter are negligible.
These results also highlight the competing constraints
imposed by the safety requirements and performance
expectations of the system.
In general, the system
bandwidth must be high enough that the physician
experiences minimal time lag when commanding the
catheter. To increase the system bandwidth, it would be
necessary to increase the natural frequency of the
articulation axis by increasing the relative stiffness of the
catheter. This also benefits the system by reducing the
effects of internal friction. However, in medical applications
a stiffer catheter is more likely to injure nearby tissue,
raising the risk of serious complications. We have attempted
to compromise between these constraints by developing a
catheter that is relatively stiff, while still being within the
bounds of being medically reasonable.
IV. EXPERIMENTAL RESULTS
To compare the control architectures discussed in III, a
series of experiments was conducted to evaluate both the
command tracking and disturbance rejection properties of
each controller.
For each experiment, control wire
tensioning was performed via an automated routine,
ensuring repeatable results. In addition, the control wires
were allowed to completely slack prior to this tensioning
routine. This allowed the manipulator to begin from a
consistent configuration each time, minimizing the effects of
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the history-dependent behavior of the device. For all
evaluations the catheter was initialized to its home position:
an insertion length of 8cm, and no articulation, or (0,8,0)cm
in task space.
A. Command Tracking
Our primary focus in evaluating these control
architectures is on the ability of each to track a given input
command. This is critical for safe, efficient medical
operation. Improper positioning can result in injury to
cardiac tissue, or difficulty in positioning the catheter on the
problematic tissue. To explore the command tracking
capabilities of both the joint space and task space control
architectures, we utilized a pre-programmed trajectory. This
trajectory is a 10cm square normal to the longitudinal axis of
the catheter and centered about the catheter’s home position
(Fig. 7). A square trajectory was chosen so that all three
axes of manipulation (two articulation directions and the
insertion axis) would be involved. At the relatively low
articulations this trajectory required, control wire friction is
not a significant contributor to error, as control wire tension
is relatively low. This low tension also minimizes stretching
of the control wires. Figure 8 shows the results of our
control system evaluation. Overall, both architectures
perform similarly, and showed great improvement relative to
open loop control. However, the task space architecture
appears to have more difficulty tracking the corners of the
trajectory accurately, resulting in the catheter tip tracing
small loops. This could potentially be due to the different
maximum speed of each physical axis of the device. While
the pitch and yaw articulation axes are quite fast, the
insertion axis is much slower. Since each one of these axes
are entailed in the control of a given task-space direction,
these differing time constants cannot be compensated for.
Under joint space control however, these axes are under
separate control, and can thus be tuned more appropriately.
Fig. 8 Catheter command tracking performance. Task and Joint Space
controllers performed similarly to each other, and both show significant
improvement over open-loop performance.
B. Disturbance Rejection
The ability of each control architecture to respond to and
recover from disturbances is critical to safe and effective invivo operation of the catheter. A patient’s heartbeat and
respiration both impart significant disturbance forces to the
catheter. If this disturbance results in unstable behavior, or
is not adequately compensated for, serious complications
can arise. To evaluate the disturbance rejection capabilities
of our control implementations, the catheter was placed in
it’s a neutral position (8cm insertion, no articulation), and a
5g mass attached to the tip was dropped, resulting in a nearly
instantaneous loading of the catheter. For both control
architectures, a representative time history of tip position is
shown in Figure 9. One important note is that because the
force applied is impulsive and therefore exceeds the 5 Hz
maximum for our assumption of negligible dynamics. The
effects of this can be seen regardless of control architecture,
and manifests as the oscillations seen shortly after applying
the force. Overall, no significant difference was observed
between the two control architectures. Both were able to
recover from this rather substantial disturbance, with each
taking approximately 3 seconds to do so.
V. CONCLUSIONS AND FUTURE WORK
Fig. 7 Catheter command tracking test trajectory (shown to scale). Each
side of the square was traversed in 6 sec, following a sinusoidal velocity
profile.
Our evaluation of joint and task space control of
continuum manipulators shows that both control
architectures show very similar results. As supported by our
analysis, this is particularly true when errors are kept
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[6]
[7]
[8]
[9]
[10]
[11]
Fig. 9 Control reaction to a disturbance At time = 0, a .5g mass was
applied to the tip of the catheter (as illustrated in inset).
relatively small, and for trajectories that do not require
simultaneous articulation and insertion motion. In addition,
both architectures show a very similar ability to reject
disturbances of the catheter, with no indications of unstable
behavior.
Future development will focus on two key areas:
improving system kinematic/dynamic models, and
incorporating additional sensing modalities.
We are
currently developing a lumped parameter-based model that
incorporates control wire friction [23]. This provides a
much more accurate prediction of catheter behavior, and will
be incorporated into a model-based controller. We are also
developing a stereo vision system, intended to emulate the
fluoroscopy available in clinical procedures that will be used
as an additional estimate of 3-dimensional catheter position.
By combining this system with the electromagnetic sensing
system currently in use, we hope to leverage the strengths of
each measurement technique, to compensate for the
weakness of the other.
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
ACKNOWLEDGMENT
The authors would like to thank Cathryn Banach for her
design and construction of the catheter pulley block.
[21]
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