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Robotics Research
l^hnical Report


"Door Opening" Experiments
Using the Four Finger Manipulator


Gerardo Lafferriere
Deepak Mohan

Technical Report No. 280

Robotics Report No. 100

March, 1987

New York University
Institute of Mathematical Sciences

Computer Science Division

25 1 Mercer Street New York, NX 1 00 1 2

"Door Opening" Experiments
Using the Four Finger Manipulator


Gerardo Lafferriere
Deepak Mohan

Technical Report No. 280

Robotics Report No. 100

March, 1987

New York University

Dept. of Computer Science

Courant Institute of Mathematical Sciences

251 Mercer Street

New York, New York 10012

Work on this paper has been supported by Office of Naval Research Grant N00014-82-K-
0381, National Science Foundation CER Grant DCR-8320085, and by grants from the Digital
Equipment Corporation and the IBM Corporation.

"Door Opening" experiments using the
Four Finger Manipulator.


Gerardo Lafferriere
Deepak Mohan


Software has been developed that enables the Four Finger Manipulator to "open a
door". The axis of rotation of the door is unknown, and the robot uses force/position
feedback information to perform the task. Two variants of the problem have been
implemented. In the first case the robot "holds a knob and opens a door "(a simple
door with no external forces), and in the second case the robot "pushes open a spring
loaded door".

March 11th 1987


Most robots in use today use position control and hence have to be programmed very
accurately and in great detail to perform specific tasks. Such an approach has many draw-
backs, such as poor adaptability to changes in the environment and great sensitivity to model-
ing errors. Robots using force feedback control could in principle be more versatile, more
adaptable and safer. However, force feedback control strategies for real time robots arc not
well understood at the present time. (See [6] for a survey of such strategies.) The problems
associated with force control become particularly complex when several robots must
cooperate to perform a task, or in the case of dextrous manipulation by several fingers. The
NYU Four Finger Manipulator described in the next section is a device built to study control
edgorithms to deal with such situations.

In this report we focus on one specific type of task that robots may often have to per-
form. This task is to rotate an object about an unknown axis of rotation. Typical examples
of such a situation are:

a) Pulling a door knob to open a door.

b) Turning a crank.

c) Turning a wrench.

d) Pushing £■. door open.

In the absence of the knowledge of the axis of rotation, the robot must move depending
only on the feedback information that it can gather. This information depends on the sensors
available (force, vision, etc.). A control algorithm must then utilize this information effec-

We have developed software that enables our "Four Finger Manipulator" to perform the
above task using force/position feedback information. Two variants of this problem have
been considered.

1) Task 1: "Hold a knob and open a simple door". In this case there are no external
forces acting on the door, and initially an approximate starting direction has to be speci-

2) Task 2: "Push open a spring loaded door". In this case an external force acts on the



The Four Finger Manipulator (FFM) is a simple two dimensional robot designed and
fabricated at the NYU Robotics Laboratory to study dextrous manipulation and problems
associated with real time control of robots. Although the FFM is a two dimensional robot,
many of the ideas/algorithms developed for this system can be extended to a three dimen-
sional arrangement. A schematic representation of the system (top view) is shown in Fig. 1.

The FFM consists of four identical and independently controllable fingers (see Fig. 2)
mounted on the four sides of a square table. Each finger can be moved in the X-Y plane
with the aid of two stepper motors connected to the finger through a system of carriages and
links. In all the robot has eight degrees of freedom (2x4 fingers). Each finger is compli-
ant, and has two pairs of strain gauges that enable it to sense the X and Y component of the
force acting on the finger. The accuracy of the strain gauges is about 0.01 N. Each of the
eight stepper motors is controlled by an INTEL 8088 processor and has a position encoder
attached to it. These processors, along with the other precision components provide a posi-
tion accuracy of about 0.001 cm. Together, the strain gauges and motor encoders provide all
the information required for force/position control of the system.

The host computer for the FFM is a SUN workstation with a Motorola 68000 processor
running the UNIX operating system. This workstation serves as the primary system for
software development, data storage, controller and data analysis. The FFM also has a lower
level controller also with a 68000 processor running the NRTX operating system. NRTX is a
real time version of UNIX that provides several features for real time processing such as
preemptive scheduling, multitasking, host controller communication etc. The lower level
controller communicates with the finger motors and strain gauges.

The FFM software incorporates data analysis facilities. Information (forces, positions,
etc.) is stored in standard "frames" at each cycle of execution, and these frames can be
archived to the host computer. This archived data can then be interpreted using the "S" ([3] &
[4]) data analysis package for which several extensions have been written. The graphs
shown below were obtained using this package.

Details of the system software architecture are given in [2]. A complete description of
the FFM is given in [1].

3 -


3.1. The Problem.

The "door" is shown in Fig. 3. It has a revolving knob and is hinged to a base and
placed arbitrarily in the robot workspace. It is assumed that no external forces act on the
system (springs, load, etc.). The center of rotation is unknown.

Given this situation, the task is to develop an algorithm that would enable the FFM to
"open the door".

3.2. Solution to Task 1.

The problem requires the robot to do the following :

a) Grasp the door knob.

b) Move the center of the knob along the arc of a circle, maintaining the grip.

To perform this task, each of the three fingers must have a different trajectory of
motion. Without force control this could be very complicated as the experimenter would
need to program each finger separately, yet with appropriate high-precision coordination.

We have developed and implemented an algorithm for the FFM that enables the experi-
menter to consider a grasped body and the fingers as a single unit. This exploits the fact that
once the gripping points are fixed, both the position (and orientation) of the body and the
external forces (and torques) exerted on it can be obtained by a linear transformation of the
positions and forces sensed at the fingers. In this strategy the experimenter chooses a refer-
ence point on the grasped body and issues target motion and force commands for this point.
The algorithm automatically calculates trajectories for finger movements. (Theoretical details
of this algorithm will appear in a separate report.) Thus the independent finger motions
(which must also account for the gripping forces) become invisible to the experimenter.

Our solution utilizes the above scheme. We take the reference point as the center of
the knob. The problem then simplifies to that of rotating the center of the knob about an
unknown axis of rotation. The problem can be viewed as follows (See fig. 4) : Line OT is
to be rotated about point O by the robot holding the knob at point T (reference point). The
robot has no information of the radius R or the coordinates of point O. However, the robot
can use force/position feedback information, and has an approximate idea of the direction in
which to move initially.

The algorithm uses an approach similar to that described in [7]. We want to move in the
direction tangent to the circle described by the knob and keep the forces in the normal direc-
tion to a minimum.


Fig. 5 shows the computed motion TQ and the actual motion TS after one control cycle
of a typical experiment. Errors create a normal force along OT which is absorbed by the
finger compliances. This force is detected by the strain gauges at the fingers and the robot
feels a net force pointing from the center of rotation. Hence if the robot moves perpendicu-
lar to this force in the desired direction it will be moving correctly. After calculating the tar-
get direction of motion, the robot adjusts its fingers to set this force equal to zero. Initially
we do not have any normal force; thus an approximate direction of initial motion must be
specified. This is justified, since when humans open doors, they do ordinarily have an idea
as to in which direction to move initially. Moreover, the algorithm could be extended to han-
dle the case when the robot has no idea of the direction of motion, by selecting a direction in
which the force buildup is minimum.

3.3. Te§t Results for Task 1.

This algorithm has been implemented successfully on the Four Finger Manipulator using
existing software and control structure. The modular nature of the system makes it easy to
incorporate additional top-level planning routines to the system. A new such "planner" was
written for this algorithm.

Several experiments were run to study the dependence of the algorithm on various
parameters. A step size greater than 0.03 cm sometimes causes excessive force buildup on
the fingers and sometimes causes the safety limits for motion to be exceeded. A step size of
0.02 cm was found to be appropriate. A smaller value slows down the motion needlessly.
Sensitivity to specified initial direction of motion was found to be low, so even a crude esti-
mate works.

Figures 6-8 give experimental data. Fig. 6 shows the forces on the reference point
along the trajectory. As soon as the force reaches the threshold value of 1 N the robot makes
a correction in the estimate of the tiingent. Fig. 7 shows the estimated t£mgent along the tra-
jectory at various points. It can be seen from Fig. 6 that once the forces build up past the
threshold, the robot moves in such a way as to make corrections in the estimated tangent as
well as to reduce the total forces on the reference point.

Figures 8 a,b,c show the forces on each finger. The system of three fingers adjusts
after each cycle to maintain the grip and sustain the normal forces exerted by the door. The
force sensed by each finger differs due to their different locations with respect to the door.
An inner control loop adjusts the fingers to give the desired end result. The forces on each
finger remain within safe limits of about 3 N. In fact values mostly stay between 0.5 and 1.5
N, which is the expected variation due to the force threshold value used.

5 -


4.1. The Problem.

In some cases a robot may need to push an object on which an external force acts. An
example of such a situation is a spring loaded door. As before, the center of rotation may
be unknown. This task can be handled by using just one finger, but here we consider the
more complex situation in which the robot needs to use a tool to push the door. This can be
the case when the door is beyond the reach of all the fingers, or if the orientation of the door
does not permit any of the fingers to touch it in the right direction, or in case when the door
surface is dangerous to the robot (hot, reactive, etc.). Use of a tool can also improve the
force sustaining capability of the robot, since the total force could be distributed on more
than one finger. For simplicity we assume here that the tool is a disk and the door is a
straight line segment. Fig. 9 shows the schematic arrangement of the door and the tool. We
assume also that the friction at the contact point between the tool and the door is negligible.

4.2. Solution to Task 2.

The algorithm for this task utilizes the system described above, but this time we exploit
the fact that there is a continuous tangential force on the tool. As was said before, this force
can be determined using the forces sensed by the fingers. To open the door in such a situa-
tion the target motion of the reference point should be in a direction opposite to the force
being sensed. However the external forces must now be overcome by the robot. It is impor-
tant in this task to obtain accurate estimates of the tangent to the trajectory to avoid excessive
slippage of the tool along the door. Slip can also be reduced by using a small step size.

The physical setup used is very similar to that of Task 1. The center of rotation is at O.


At a position T on the circumference the tangential force is in a direction TF . The direction
TP which is opposite to TF is the desired direction of motion. At another point T the


tangential force vector is 7" F and the target motion vector h T P . The robot senses the
forces at each point and then moves in a direction opposite to the direction of the force that it
senses. The magnitude of the force is not important as long as the fingers can sustain it.

The FFM grasps the tool using three fingers and brings it in contact with the door. The
door exerts a force on the tool which is tangential to the trajectory of the door. The robot
senses this force using its force sensors, calculates the direction opposite to this force, and
then moves a discrete amount in this direction. Then the direction of the sensed force
changes and the robot repeats this step, and thus keeps moving in the appropriate direction to
open the door, meanwhile overcoming the tangential force exerted on it by the door.

- 6 -

4.3. Test Results for Task 2.

This algorithm has also been implemented successfully on the FFM using the existing
software and control structure. A new top level "planner" was also written for this algo-

Tests were again conducted to study dependence of this algorithm on internal parame-
ters. Again a step size of 0.02 cm was found to be appropriate. Figures 11 -13 give experi-
mental data. Fig. 11 shows the trajectory of motion of the reference point. Fig. 12 shows the
estimated tangent at various points. Due to the small step size of 0.02 cm, the estimated
tangents lie nearly along the arc of a circle. Fig. 13 shows the forces on each finger. The
magnitudes are different on each finger due to varied distribution of the door spring force on
each finger. The position of finger 3 was such that it sustained the maximum force. Fingers
1 and 2 maintain the tool grip and sustain forces depending on their position.


The FFM is successfully able to open a "simple door" as well as a "spring loaded door"
using only force/position feedback information. In both the cases the force build up on the
fingers was kept to a minimum, and accurate estimates of the tangent directions were
obtained. The time taken in both the cases was about 40 seconds to move a distance of about
8 cm and a rotation angle of 40 degrees.

The speed of the system can readily be increased using a multiprocessor, such as the
NYU Ultracomputer [5], to distribute the various computational tasks involved. Implementa-
tion of this improvement is soon to begin.


The project depended criticeilly on extensive support provided by our colleagues at the
FFM project of the NYU Robotics Laboratory. In particular we would like to thank:

Mr. Fred Hansen : for providing excellent hardware support, fixtures and mechanical

Mr. Maw Kae Hor : for providing useful suggestions and permitting us to use parts of
his thesis for the FFM description section of this report.

Prof. James Demmel : for providing useful suggestions and ideas through various stages
of this project.

Mr. James Fehlinger : for software support.

Mr Dayton Clark : for software support.
Mr. Shidan Tavana : for hardware support.


1) Hor, Maw Kae, NYU dissertation (in preparation).

2) Fehlinger, James : Experimenter's Guide to the Four Finger Manipulator, Robotics
Report #102, Courant Institute, NYU, 1986.

3) Becker, R.A. and Chambers J.M. : S: An Interactive Environment for Data Analysis
and Graphics. Wadsworth Advanced Books and Software, Monterey, CA, 1984.

4) Becker, R.A. and Chambers J.M. : Extending the "S" System. Wadsworth Advanced
Books and Software, Monterey, CA, 1985.

5) Gottlieb, Allan: An Overview of the NYU Ultracomputer project, Ultracomputer Note
#100, Courant Institute, NYU July 1986.

6) Whitney, Daniel E.: Historical Perspective and State of the Art in Robot Force Control,
Proceedings of the IEEE Conference on Robotics and Automation , St. Louis, pp. 262-
268, 1985.

7) Raibert, M.H. and Craig, J.J.: Hybrid Position/Force Control of Manipulators, Transac-
tions of the ASME, Vol. 102, pp. 126-133, June 1981.

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(see fig. 2)







Encoder - Motor

Figure 1. Four Finger Manipulator ( overviev )








, Sirajn Gage Mounting Surface

. Force Sensing Finger

Figure 2. Four Finger Manipulator - Force Sensing Finger






.125 Dowel Pin Hole
(Typical of 6 Places)

Figure 3 Door Knob Fixture

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Figure 4

O 0^


Figure 5





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e K K


Id t/1 fe Vi



Axis of rotation

Figure 9


Figure 10


















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