1995 IEEE International Conference on Robotics and Automation
Experiments in Adaptive Model-Based Force Control
Louis Whitcomb∗, Suguru Arimoto,
Tomohide Naniwa
Department of Mathematical Engineering
and Information Physics
University of Tokyo
Bunkyo-ku, Tokyo 113, Japan
Email: [email protected]
Fumio Ozaki
Energy and Mechanical Research Laboratory
Research and Development Center
Toshiba Corporation
4-1 Ukishima-cho, Kawasaki-ku
Kawasaki 210, Japan.
Email: [email protected]
Abstract
This paper reports comparative experiments with a provably correct model-based adaptive robot control algorithm
for simultaneous position and force trajectory tracking of a
robot arm whose gripper is in point contact with a smooth
surface. The experiments show the new adaptive modelbased offers performance superior to that of its non-modelbased counterpart over a wide variety of operating conditions.
1
DIRECT
2 DRIVE
JOINTS
3
FORCE
SENSOR
RIGID
SURFACE
1. Introduction
This paper reports recent experiments with a new class
of model-based adaptive force control algorithms for robot
arms [3]. The problem addressed in this paper is the control of robots whose motion is constrained by point contact
between the robot tool and a smooth rigid environment
or workpiece. Manufacturing applications for force control include a great variety of commonplace tasks, such as
grinding, polishing, buffing, deburring, and assembly operations currently performed either manually or by fixed
automation equipment.
Figure 1. The Toshiba Direct Drive Arm.
algorithm under a variety of conditions in actual working
implementations.
The new force control algorithm provides asymptotically
exact tracking of both end-effector position and contactforce [3]. This force control algorithm utilizes a slidingmode control technique of a type first espoused for the
case of free (non-contact) robot motion [12]. The stability of the new force control algorithm can be proven with
respect to the commonly accepted nonlinear rigid body
dynamical equations of motion. Moreover, its adaptive
extension can be shown to adaptively compensate for unknown plant parameters such as link and payload inertia,
joint friction, and friction arising at the contact point between the tool tip and the surface. In [8] the authors report
satisfactory performance of this force control algorithm in
numerical simulation studies. This paper demonstrates the
comparative advantages and disadvantages of this control
2. Three Force Controllers
We adopt the commonly accepted plant model for a robot
arm in rigid contact with a smooth frictionless surface
τ
=
M (q)q̈ + C(q, q̇)q̇ + g(q) + v(q)f
(1)
where q, q̇, and q̈ are the joint position, velocity, and acceleration vectors, τ is the joint torque vector, M and C are
the standard inertial and coriolis matrices, respectively,
g is the gravity vector, f is the tool-tip force normal to
the surface (a scalar), and v(q) is a vector normal to the
jointspace surface. We adopt the standard notation to factor (1) as τ = W (q̈, q̇, q̇, q)θ, the product of a matrix valued
function, W , and a vector of plant parameters, θ.
2.1. IDCF: Model-Based Force Control
∗ We
gratefully acknowledge the support of the Japan Society
for the Promotion of Science, a Japanese Governmental agency,
under a post-doctoral fellowship awarded to the first author.
First author is presently at the Department of Mechanical Engineering, Johns Hopkins University, 123 Latrobe Hall, 3400
North Charles Street, Batimore, MD 21218, email:[email protected].
In [2, 8] the authors prove the stability of a new
model-based force controller, which we will call “IDCF”
(Acronym for “Inverse Dynamics Critically Damped
Force”), as follows:
τidcf =
1
W (r̈ − η̇, ṙ − η, q̇, q)θ − K2 ē + v(q)fr
(2)
=
W (r̈ − η̇, ṙ − η, q̇, q)θ − K2 Q(q)e2 − K2 Q(q)Λe1
|
{z
}
model
based
f eedf orward
|
{z
}
derivative
position
f eedback
− γv̄∆F +
|
{z
feeds forward the desired surface normal force in the onedimensional joint space subspace normal to the surface,
and (iii) feeds back the integral of the force error in the
one-dimensional joint space subspace normal to the surface. The difference between the IDCF and the PDF controller is that the PDF controller omits all model-based
plant compensation. The IDCF and PDF controller are
identical when the IDCF parameter vector θ has value zero
1
.
}
proportional
position
f eedback
v(q)fr
| {z }
| {z }
integral
f orce
f eedback
f orce
f eedf orward
Where r and ṙ are the reference position and velocity vectors, e1 = q − r, e2 = q̇ − ṙ, e = [e1T , e2T ]T , ē =
2
Q(q)(e2 + Λe1 ) + γv̄(q)∆F , Λ = ΛT > 0, v̄ = v/kvk
, γ is
Rt
the integral force feedback error gain, ∆F (t) = 0 ∆f (t)dt,
and ∆f (t) = f (t) − fr (t). η = P (q)ṙ + Q(q)Λe1 + γv̄(q)∆F
where P (q)is an n × n rank 1 matrix function whose image
is the surface normal at point q and whose kernel is the
surface tangent at q, and Q(q) = I − P (q). The reader is
referred to [3, 15] for a complete derivation.
3. Force Control Experiments
The arm used for these experiments (Figure 1) is a
three degree of freedom direct-drive arm developed at the
Toshiba Corporation for advanced robot control research
[5, 9]. Each joint is equipped with a direct-drive DC brush
motor, and high resolution 106 count laser optical encoder.
The control algorithms were executed on a 40Mhz Motorola 96002 DSP at a frequency of 333Hz. The IDCFA
adaptive parameters were initialized to zero at the beginning of each run. Coulomb and viscous friction model
terms were included in the implementation of IDCF and
IDCFA, though omitted from the derivation of Section 2
for clarity [15].
This controller has three distinct components. First, it
uses a rigid-body model to precisely feed forward jointtorques required to obtain the desired trajectory, and to
feedforward the desired tool-tip force. Second, in the joint
space subspace tangent to the rigid surface, the controller
uses a version of simple PD feedback. Third, in the onedimensional joint space subspace normal to the surface, the
controller uses feedforward of the desired surface normal
force, as well as feedback of the integral of the force error.
2.2. IDCFA:
Control
Adaptive
Model-Based
3.1. The effect of model-based rigid-body feedforward
Recent experimental studies, e.g. [16], have shown modelbased control algorithms for trajectory tracking to offer
performance superior to their non model-based counterparts over a wide range of operating conditions. This
is in contrast to several early experimental studies of
model-based robot trajectory tracking algorithms which
concluded that model-based controllers provided poorer
performance than their non model-based counterparts. In
these earlier studies, suggested explanations for their poor
performance include low controller sampling rates (e.g., [1]
pp. 107, [4] pp. 82) and unmodeled plant dynamics (e.g.,
[13] and [7]).
Force
Given the stability proof for (2), it is easy to show the
stability of its adaptive extension, which we will call “IDCFA” (Acronym for “Inverse Dynamics Critically Damped
Force Adaptive”) [2, 8]. This controller can be written
τidcf a =
W (r̈ − η̇, ṙ − η, q̇, q)θ̂ − K2 ē + v(q)fr
(3)
where θ̂ is the controller’s estimate of the plant parameter vector. The parameter update law is
˙
θ̂ =
−αW (r̈ − η̇, ṙ − η, q̇, q)T ē
Given this diversity of experimental results for unconstrained robot motion, in the present context of force
control it seems essential to investigate the comparative
performance of model-based versus non model-based force
controllers. The purpose of this section is to compare the
performance of the non model-based PDF controller, Section 2.3, with the fully adaptive model-based IDCFA controller of Section 2.2.
(4)
where α is a positive adaptation gain.
2.3. PDF: Proportional-Derivative
and Force Control
Position
As a standard of comparison, we selected a simple force
controller, which we will be call “PDF” (for proportionalderivative force controller). It takes the form
τpdf =
=
−K2 ē + v(q)fr .
In this experiment, we employed a reference trajectory
in which the robot tool-tip describes a circle on the surface
1 The well known “Craig/Raibert hybrid controller” first reported in [10] is similar in many respects to the “PDF” controller described in Section 2.2. The controllers differ in two
respects. First, the system dynamics in [10] are formulated in
workspace coordinates, rather than jointspace coordinates. Second, the controller presented in [10] is presented ad-hoc — without a proof of stability. To the best of our knowledge, an experimental comparison between the similar force controllers which
differ only in the coordinate system (workspace or jointspace)
has not been performed.
(5)
− K2 Q(q)e2 − K2 ΛQ(q)e1 − γv̄∆F + v(q)fr .
|
{z
}
derivative
position
f eedback
|
{z
}
proportional
position
f eedback
| {z }
| {z }
integral
f orce
f eedback
f orce
f eed
f orward
The PDF controller (i) uses simple PD feedback in
the joint space subspace tangent to the rigid surface, (ii)
2
operation was limited by a variety of defects inherent in
conventional industrial arms including, highly geared joint
actuators, limited sensor and actuator I/O bandwidth, and
limited computational power. This section investigates the
stability and performance of the force control algorithms
of Section 3.1 at higher reference velocities.
of the rigid, flat, aluminum plate (as pictured in Figure 1).
The reference trajectory circle diameter was 0.2 meters.
The reference trajectory speed was a constant 0.0628 meters/second. The robot tool-tip thus completes a complete
traversal of the circle in 10 seconds. The initial robot position error was about 0.05 meters. The initial robot velocity
error was 0.0628 meters/second.
Figure 3 shows the tracking performance of both the IDCFA (left) and PDF (right) for a fast reference trajectory.
The reference trajectory speed was 0.628 meters/second,
ten times faster than that of Figure 2. The robot tooltip thus completes a complete traversal of the 0.2 meter
diameter circle in 1 second. The reference normal force
was 40 Newtons, the initial robot position error was about
0.05 meters, and the initial robot velocity error was 0.628
meters/second.
Figure 2a (left) shows three graphs of actual IDCFA
controller performance. The top graph shows the outline
of the robot tool-tip actual and reference position trajectories in the plane of the rigid surface. The middle graph
shows the tracking errors in X and Y (in the plane) as
well as Z (normal to the plane) as a function of time. The
units are meters. These two graphs confirm that under
the IDCFA controller, the robot state quickly converges
to steady-state tracking errors of well under 0.005 meters.
The bottom graph shows the actual and reference tool-tip
surface normal force. The reference force was a constant
40 Newtons (about 4 Kg-F). The actual steady-state force
tracking error under the IDCFA controller can be seen to
remain within 10% of the reference.
These graphs show the IDCFA controller to exhibit
start-up tracking transients which converge after a few
seconds to near steady-state performance. These startup transients are typical of adaptive control systems for
which the adaptive parameter values are initialized to zero
[16]. The top and middle graphs show the steady-state
force tracking error under the IDCFA controller to be under 1 centimeter, while that for PDF is over 4 cm. The
PDF position tracking error is four times worse than for
IDCFA.
Figure 2b (right) shows the corresponding three graphs
for the PDF controller performance for the same reference
trajectory. The top graph and middle graph show PDF
position tracking performance which is dramatically different from that of the IDCFA controller. At steady-state,
the PDF controller provides tracking errors of 0.025 meters
- approximately five times worse than that of the IDCFA
controller. The bottom graph shows the actual and reference tool-tip surface normal force. Again, the reference
force was a constant 40 Newtons. The actual PDF steadystate force can be seen to remain within about 20% of the
reference — about 200% of the error of the IDCFA controller.
The bottom graphs show the actual and reference tooltip surface normal force for IDCFA (left) and PDF (right).
The reference force was a constant 40 Newtons. Here we
see the force tracking performance controllers of both controllers to be poor. The PDF steady-state force errors are
about two times worse than for IDCFA.
We conclude that IDCFA offers tracking performance
superior to PDF. We attribute the superior force and position tracking performance of the IDCFA controller to its
feedforward compensation of rigid-body dynamics such as,
inertial, coriolis, gravity, and friction terms. The PDF
controller, in contrast, does not compensate for rigid-body
dynamics. It is worth noting that we observed stable performance of the IDCFA controller for a variety of high
speed trajectories (in excess of 1 meter/second) for which
the PDF controller was unstable.
These plots dramatically demonstrate the performance
advantage of the model-based IDCFA controller over PDF
control, and the ability of the adaptive controller to rapidly
“learn” the plant parameters within a few seconds. We
conclude that the poor performance obtained with the
PDF controller is due to its inability to compensate for
the robot’s dynamics. While the PDF controller is unable
to compensate for these plant dynamics, the IDCFA controller is largely able to cancel these effects, thus providing
superior tracking performance.
3.3. The effect of PD feedback gain
Is “high gain PDF” better than IDCFA? It is well known
that increasing the position and velocity error feedback
gains can be shown both analytically and experimentally to
result in smaller tracking errors. In digital motion control
systems, the upper limit of feedback gain is often limited
by a variety of defects including, (i) position and velocity
sensor resolution and noise, (ii) joint position and velocity
limits, (iii) actuator saturation limits, and (iv) controller
sampling rate and numerical accuracy.
3.2. The effect of “fast” trajectories
To the best of our knowledge, previous experimental investigations have all demonstrated stable force control only
in the case of robot motion at low (or zero) velocity. For
example, [17] employs an exact linearization algorithm to
analyze and experimentally demonstrate force control at
slow velocities and [14] employs a linearized plant approximation to analyze and experimentally demonstrate force
control at zero reference velocity. The omission of highspeed experimentation may be attributed to two factors.
First, the analytical results employing approximate plant
linearizations are difficult to extend to the case of high
speed robot motion. Second, we surmise that high speed
Given the strong dependence of tracking error on feedback gains, the following question arises: If the feedback
gains of a simple “PDF” type controller are increased, will
its performance improve to equal that of the corresponding
“IDCFA” controller? This section discusses the compara-
3
PDF: Actual and Desired Tool Tip Position. Speed = 0.062 m/s. File=f_25d.log.
-0.3
-0.35
-0.35
METERS
METERS
IDCFA: Actual and Desired Tool Tip Position. Speed = 0.062 m/s. File=f_25c.log.
-0.3
-0.4
-0.4
-0.45
-0.45
-0.1
-0.05
0
METERS
0.05
0.1
-0.1
IDCFA: Tool Tip XYZ Position Error. Speed = 0.062 m/s. File=f_25c.log.
0.03
0.03
0.02
0.02
0.01
0.01
METERS
0.04
METERS
0.05
0.04
0
-0.01
-0.02
-0.02
-0.03
-0.03
-0.04
0.1
-0.04
2
4
6
8
10
12
SECONDS
14
16
18
-0.05
0
20
IDCFA: Actual and Desired Tool Tip Surface Normal Force. Speed = 0.062 m/s. File=f_25c.log.
60
50
50
40
40
30
20
10
10
4
6
8
10
12
SECONDS
14
16
18
4
6
8
10
12
SECONDS
14
16
18
20
30
20
2
2
PDF: Actual and Desired Tool Tip Surface Normal Force. Speed = 0.062 m/s. File=f_25d.log.
60
NEWTONS
NEWTONS
0.05
0
-0.01
0
0
0
METERS
PDF: Tool Tip XYZ Position Error. Speed = 0.062 m/s. File=f_25d.log.
0.05
-0.05
0
-0.05
0
0
20
2
4
6
8
10
12
SECONDS
14
16
18
20
Figure 2. IDCFA vs PDF: Low Speed Tracking: IDCFA force control (left) and PDF force control (right). tool-tip
actual and reference surface trajectory (top). tool-tip X,Y, and Z tracking errors vs. time (middle). Actual and
reference tool-tip surface normal force vs. time (bottom). tool-tip speed = 0.0628 meters/second.
tive effect of varying feedback gains in the PDF and IDCFA
controllers.
diag[−10, −10, −10]; Λ = diag[5, 5, 5], thus maintaining
approximately the same “damping ratio” with a 50% decrease in velocity gain. The lower feedback gains result in
significantly poorer PDF performance, while the IDCFA
performance is degraded only slightly.
Figure 4 shows the reference and actual tool-tip positions for the IDCFA and PDF controllers for high and
low feedback gain settings. The reference trajectory was
a 0.2 meter diameter circle, with tip velocity 0.0628 meters/second, normal force 40 Newtons, and initial tip position error of 0.05 meters.
The bottom two graphs of Figure 4 show the tracking performance of the two controllers with K2 and Λ
gains increased by a factor of 50% from nominal to K2 =
diag[−30, −30, −30]; Λ = diag[15, 15, 15], thus maintaining approximately the same “damping ratio” with a 50%
increase in velocity gain. The higher feedback gains result
PDF and IDCFA performance which is slightly improved
over nominal. The IDCFA controller, however, is still seen
to outperform the PDF controller. Note that a slightly
higher feedback gain setting resulted in instability for both
controllers.
Figure 2a and 2b show the robot tool-tip trajectory under the IDCFA controller (top left) and the PDF controller (top right) with the feedback gains of K2 =
diag[−20, −20, −20]; Λ = diag[10, 10, 10]. Here the IDCFA
controller clearly outperforms the PDF controller.
The top two graphs of Figure 4 show the tracking performance of the two controllers with K2 and Λ gains
decreased by a factor of 50% from nominal to K2 =
We conclude that IDCFA is superior to “high gain
4
PDF: Actual and Desired Tool Tip Position. Speed = 0.61 m/s. File=f_25j.log.
-0.3
-0.35
-0.35
METERS
METERS
IDCFA: Actual and Desired Tool Tip Position. Speed = 0.61 m/s. File=f_25i.log.
-0.3
-0.4
-0.4
-0.45
-0.45
-0.1
-0.05
0
METERS
0.05
0.1
-0.1
IDCFA: Tool Tip XYZ Position Error. Speed = 0.61 m/s. File=f_25i.log.
0.03
0.03
0.02
0.02
0.01
0.01
METERS
0.04
METERS
0.05
0.04
0
-0.01
-0.02
-0.02
-0.03
-0.03
-0.04
0.1
-0.04
0.5
1
1.5
2
SECONDS
2.5
3
3.5
-0.05
0
4
IDCFA: Actual and Desired Tool Tip Surface Normal Force. Speed = 0.61 m/s. File=f_25i.log.
60
50
50
40
40
30
20
10
10
1
1.5
2
SECONDS
2.5
3
3.5
1
1.5
2
SECONDS
2.5
3
3.5
4
30
20
0.5
0.5
PDF: Actual and Desired Tool Tip Surface Normal Force. Speed = 0.61 m/s. File=f_25j.log.
60
NEWTONS
NEWTONS
0.05
0
-0.01
0
0
0
METERS
PDF: Tool Tip XYZ Position Error. Speed = 0.61 m/s. File=f_25j.log.
0.05
-0.05
0
-0.05
0
0
4
0.5
1
1.5
2
SECONDS
2.5
3
3.5
4
Figure 3. IDCFA vs PDF: High Speed Tracking. IDCFA force control (left) and PDF force control (right). tooltip actual and reference surface trajectory (top). tool-tip X,Y, and Z tracking errors vs. time (middle). Actual
and reference tool-tip surface normal force vs. time (bottom). tool-tip speed = 0.0628 meters/second.
It has been our experience that the upper bound on
adaptation gain varies strongly with reference trajectory
position and velocity. An adaptive gain matrix which is
“optimally” tuned for one reference trajectory, however,
is frequently unstable for a different trajectory. In our
experiments, the IDCFA adaptation gain was set to be as
large a multiple of I as possible while preserving stability
over a wide range of reference trajectories.
PDF”. For equal feedback gains, the comparative performance of IDCFA control is superior to that of PDF control. This is consistent with previous experimental observations which show model-based controllers to provide
performance superior to PD-type controllers over a wide
range of operating conditions, e.g. [16].
3.4. The effect of adaptive gain
Figure 5 shows the IDCFA tracking performance as α
varies over three orders of magnitude, kθk, for same reference trajectories employed in Section 3.1. Figure 6 shows
the corresponding adaptive parameter vector magnitude,
(kθ̂k), for these runs, plotted as a function of time.
The IDCFA controller adaptive update law (4) contains an
adaptation gain, α, whose value can theoretically be any
symmetric positive definite matrix. In practice, however,
the defects of the real world place an upper bound on this
parameter — beyond which the controller is unstable. Capable experimenters have reported the utility of setting α
to be a diagonal matrix whose values are set empirically,
e.g. [6], as well as using time varying adaptation gains,
e.g. [11].
This data confirms two points. First, that proper adaptation gain magnitude selection is essential for good performance. Second, it confirms previous experimental data
[16], demonstrating good adaptive controller performance
5
IDCFA: Actual and Desired Tool Tip Position. File=f_27a.log.
PDF: Actual and Desired Tool Tip Position. File=f_27b.log.
-0.3
-0.3
-0.35
METERS
METERS
-0.35
-0.4
-0.4
-0.45
-0.45
-0.1
-0.05
0
METERS
0.05
0.1
-0.1
0
METERS
0.05
0.1
PDF: Actual and Desired Tool Tip Position. File=f_27f.log.
-0.3
-0.3
-0.35
-0.35
METERS
METERS
IDCFA: Actual and Desired Tool Tip Position. File=f_27e.log.
-0.05
-0.4
-0.45
-0.4
-0.45
-0.1
-0.05
0
METERS
0.05
0.1
-0.1
-0.05
0
METERS
0.05
0.1
Figure 4. The effect of position feedback gains. IDCFA force control (left) and PDF force control (right). All
plots show tool-tip actual and reference surface trajectory. Feedback gains lowered by 50% (top), and feedback
gains increased by 50% (bottom).
to variations in γ.
with α set to a multiple of the identity matrix. Individual
tuning of the elements of α is not always a prerequisite
for good performance — a multiple of the identity matrix
works well in many cases.
4. Conclusion
The preliminary experiments presented in Section 3 are,
to the best of our knowledge, the first implementation of
a provably correct nonlinear adaptive force controller on
a high performance multi-axis direct-drive arm. The data
illustrate the following points:
3.5. The effect of force feedback gain
Like many of the previously reported experimental studies,
e.g. [14, 17], the three force control algorithms (5), (2), and
(3) incorporate feedback signals from a force sensing robot
ripper. While the integral feedback gain, γ in (2) and
(3), may theoretically take any positive value, in practice
the system is unstable beyond an (empirically determined)
upper limit. This section examines the effect of various γ
settings on tracking performance.
1. Position and force tracking performance of the IDCFA
controller was observed to be superior to that of a
conventional (non adaptive, non model-based) quasilinear force control feedback law.
2. The IDCFA controller was observed to provide stable
and accurate high-speed tracking in contrast to the
PDF controller’s poor performance.
Figure 7 shows the force tracking performance of the
IDCFA controller for four different values of integral force
feedback gain γ. The figure shows (from top to bottom)
γ = 0.0, γ = 0.001, γ = 0.005, γ = 0.01. The top
graph shows the poor force tracking performance when integral force feedback is disabled (γ = 0.0). The subsequent
graphs show improved force tracking performance as γ is
increased. The highest value shown, γ = 0.01 and was
used in all other experiments in this paper. Note that the
system was unstable for approximately γ ≥ 0.05.
3. “High gain PD” force controller performance is uniformly worse than that of IDCF and IDCFA.
4. Integral force error feedback was seen to be essential
for precise force tracking — corroborating previously
reported experimental data [14, 17].
5. The IDCFA controller’s parameter adaptation was
observed to be rapid — the model parameters were
seen to typically converge from a zero initial condition
to steady-state within several seconds.
We conclude that integral tool-tip force feedback is critical to good force tracking performance, thus corroborating
independently reported experimental results [14, 17]. Unsurprisingly, position tracking performance was insensitive
We note that the mathematically complicated problem
of transition from non-contact motion to contact motion
6
3
0.5
0.48
2.5
PARAMETER VECTOR MAGNITUDE
0.46
0.44
METERS
0.42
0.4
0.38
0.36
0.34
2
1.5
1
0.5
0.32
0.3
-0.1
-0.05
0
METERS
0.05
0
0
0.1
10
15
20
SECONDS
25
30
35
40
Figure 6. The effect of parameter adaptation gain on
IDCFA parameter vector magnitude, kθ̂k. The curves
are (from bottom to top) α = 0.001 (bottom curve),
α = 0.01, α = 0.1, α = 0.5, and α = 1.0 (top curve),
respectively.
0.5
0.48
0.46
0.44
0.42
METERS
5
0.4
0.38
(with resulting discontinuous change in the plant dynamical model structure) was observed not to be a problem in
this instance. The matter deserves careful attention. Finally, we have thus far observed the IDCFA controller to
provide reliable, stable tracking at tool-tip speeds in excess
of 1 meter/second. We believe that improvements in the
implementation (e.g., higher sample rate) will permit even
higher tool-tip speeds to be attained.
0.36
0.34
0.32
0.3
-0.1
-0.05
0
METERS
0.05
0.1
0.5
0.48
Acknowledgments
0.46
0.44
Professor K. Asano, of the Tohoku Institute of Technology,
has provided continued advice and encouragement. Dr.
K. Tatsuno’s inspired leadership at the Toshiba Corporation’s Energy and Mechanical Research Laboratory was
instrumental to this collaborative research project. Mr.
M. Obama of Toshiba Corporation’s Energy and Mechanical Research Laboratory provided invaluable expertise in
designing and instrumenting the new control system. Professor K. Osuka, presently at University of Osaka Prefecture, Japan, designed the original DD arm while with
the Toshiba Corporation Energy and Mechanical Research
Laboratory [5]. The authors are grateful for their generous
contributions.
METERS
0.42
0.4
0.38
0.36
0.34
0.32
0.3
-0.1
-0.05
0
METERS
0.05
0.1
0.5
0.48
0.46
0.44
References
METERS
0.42
0.4
[1] C. H. An, C. G. Atkeson, and J. M. Hollerbach.
Model-Based Control of a Robot Manipulator. MIT
Press, Cambridge, MA, USA, 1988.
[2] S. Arimoto, Y. Liu, and T. Naniwa. Model-based
adaptive hybrid control for geometrically constrained
robots. In Proc. IEEE Int. Conf. Robt. Aut., Atlanta,
GA, USA, 1993.
[3] S. Arimoto, T. Naniwa, and T. Tsubouchi. Principle
of orthogonalization for hybrid control of robot manipulators. In Proceedings of IMACS’92 (Int. Symp.
on Robotics, Mechatronics, and Manufacturing Systems ’92 Kobe), pages 1293–1300, Kobe, Japan, 1992.
0.38
0.36
0.34
0.32
0.3
-0.1
-0.05
0
METERS
0.05
0.1
Figure 5. The effect of parameter adaptation gain on
IDCFA position tracking. From top to bottom α =
0.01 (top), α = 0.1, α = 0.5, and α = 1.0 (bottom).
7
[4] J. J. Craig. Adaptive Control of Mechanical Manipulators. Addison-Wesley, Reading, MA, 1988.
[5] H. Hashimoto, F. Ozaki, K. Asano, and K. Osuka. Development of a pingpong playing robot system using
7 degrees of freedom direct drive arm. In Proceedings
of IECON’87, pages 608–615, Cambridge, MA, USA,
1987.
[6] M. A. Johnson and M. B. Leahy Jr. Adaptive modelbased neural network control. In Proc. IEEE Int.
Conf. Robt. Aut., pages 1704–1709, Cincinnati, Ohio,
USA, May 1990.
[7] M. B. Leahy Jr., D. E. Bossert, and P. V. Whalen.
Robust model-based control: An experimental case
study. In Proc. IEEE Int. Conf. Robt. Aut., pages
1982–1987, Cincinnati, Ohio, USA, May 1990.
[8] T. Naniwa, S. Arimoto, L. L. Whitcomb, Y. H. Liu,
and J. Fujiki. Model-based adaptive control for geometrically constrained manipulators. In Proceedings
of the Robotics Society of Japan Third Robot Symposium, pages 339–344, Osaka, Japan, June 1993. RSJ.
(In Japanese).
[9] F. Ozaki, H. Hashimoto, M. Muruyama, and
H. Mayeda. Identification for a direct drive manipulator. In Proceedings of IECON’90, pages 421–426,
Pacific Grove, CA, USA, 1990. IEEE.
[10] W. Raibert and J. Craig. Hybrid position / force
control of manipulators. ASME Journal of Dynamic
Systems, Measurement, and Control, 103(2):126–133,
1981.
[11] J.-J. E. Slotine and W. Li. Composite adaptive control of robot manipulators. Automatica, 25(4).
[12] J.-J. E. Slotine and W. Li. On the adaptive control
of robot manipulators. The International Journal of
Robotics Research, 6(3):49–59, Fall 1987.
[13] L. M. Sweet and M. C. Good. Redefinition of the
robot motion-control problem. IEEE Control Systems
Magazine, 5(3):18–25, Aug 1985.
[14] R. Volpe and P. Khosla. An experimental evaluation
and comparison of explicit force control strategies for
robotic manipulators. In Proc. IEEE Int. Conf. Robt.
Aut., pages 1387–1393, Nice, France, 1992.
[15] L. L. Whitcomb, S. Arimoto, T. Naniwa, and
F. Ozaki. Adaptive model-based robot force control. IEEE Transactions on Robotics and Automation,
1995. (Submitted for Review).
[16] L. L. Whitcomb, A. Rizzi, and D. E. Koditschek.
Comparative experiments with a new adaptive controller for robot arms. IEEE Transactions on Robotics
and Automation, 9(1):59–70, 1993.
[17] T. Yoshikawa and A. Sudou. Dynamic hybrid position/force control of robot manipulators — on-line
estimation of unknown constraints. IEEE Transactions on Robotics and Automation, 9(2):220–226,
April 1993.
IDCFA: Surface Normal Force. Gamma = 0.0 File=f_28a.log.
60
50
NEWTONS
40
30
20
10
0
0
5
10
15
20
SECONDS
25
30
35
40
IDCFA: Surface Normal Force. Gamma = 0.001 File=f_28b.log.
60
50
NEWTONS
40
30
20
10
0
0
5
10
15
20
SECONDS
25
30
35
40
IDCFA: Surface Normal Force. Gamma = 0.005 File=f_28e.log.
60
50
NEWTONS
40
30
20
10
0
0
5
10
15
20
SECONDS
25
30
35
40
IDCFA: Surface Normal Force. Gamma = 0.01 File=f_28c.log.
60
50
NEWTONS
40
30
20
10
0
0
5
10
15
20
SECONDS
25
30
35
40
Figure 7. Integral force feedback and IDCFA force
tracking. γ = 0.0 (top), γ = 0.001, γ = 0.005, γ =
0.01 (bottom).
8