Cognitive Robotics Final Project:
Cooperative Form Closure and Manipulation
of Large Objects
Felix Duvallet, Nicholas Heckman
The Robotics Institute
Carnegie Mellon University
5000 Forbes Ave
Problem Description and Introduction
Manipulating large objects with a single mobile robot is a difficult
task. The object is too large to push in a given direction or to rotate
accurately. A single mobile base would have to accurately find the
center of mass of a large object to push it, or find the end of the
object to rotate it. Any error can lead to unintended results. Using
multiple mobile bases to enclose and manipulate an object eliminates
any need to determine the exact center of mass or endpoints of the
object for pushing or rotation. This project demonstrates cooperative
form closure and manipulation of large objects using two mobile bases.
Cooperative form closure is the ability to secure an object from moving
by using the object's geometry and the form of the manipulators. This
differs from force closure, where force applied on the object by manipulators
and friction are used to secure the object, without utilizing the
object geometry. In this project, we use several robots to manipulate
a large object by achieving form closure.
Figure 1: Form closure vs.
Figure 2: Two Sony Aibo ERS-7
robots moving a large object
We use two Sony Aibo ERS-7 robots as a developmental
testbed for our solution. The object that we manipulate is a
Styrofoam block 19 inches long, 3 inches high, and 5 inches
wide. A 4”x1.5”x5” section block is cut away from the larger
Styrofoam block to allow the robots to achieve form closure.
The top face of the Styrofoam block had a strip of pink tape
running across the long axis, and two pieces of green tape running
across the short axis of the top face. These pieces of tape
are used for robot localization.
We will create the localization system that will allow the
dogs to determine its position and orientation relative to the
block. By default the dogs attempt to maintain a constant distance
from the end of the block and a constant orientation with respect
to the long axis of the block. Distance is determined by looking
at the green piece of tape on the block through the robot's
camera. The robot computes the length of the tape in camSpace.
The longer the perceived length of the tape, the closer the
tape is to the robot. Using proportional control, the robot
attempts to keep the length of the tape a constant length. Orientation
is determined by viewing a pink piece of tape that is placed
along the long axis of the block. When viewed in cam space,
a pink line that is in alignment with the robot's X-axis runs
through the center column of the camera image. As the orientation
of the line deviates from the robot's X-axis, the centroid of
the line likewise deviate from the center. We use a proportional
control to maintain the pink centroid in the center of the image.
We have the robots maintain a pose with respect to the block
such that the robots can move their end of the block slightly
by strafing or pushing.
Figure 3: Top view of the block
and localization markers
Figure 4: Two dogs cooperatively grasping
and pushing the object
We achieve form closure by localizing the block with respect to the
robot. We manipulate the block by having the robots attempt maintain
different positions and orientations with the block. As one robot
moves the block to achieve its goal orientation, it changes the position
and orientation of the block that the second robot perceives. The
second robot then moves the block to achieve its goal orientation.
By using this approach, all manipulation coordination is implicitly
performed. No inter-robot communication occurs.
Figure 5: View from the Aibo's camera. Block
is aligned in this image
Figure 6: Aibo's view. Block is off-center
Figure 7: Lines extracted from
the camera image
These are demonstration videos of closure, pushing, and a more advanced
Approach and grasp closure of a
large rectangular block
Push of rectangular block
Push+Rotation of block (move around
IV. Summary and Future Work
We have shown a method to achieve form closure of a rectangular
block using two mobile robots. Localization is performed using simple
markers. Additionally, we have demonstrated coordinated manipulation
of the block by using push and rotate motion biases, using only implicit
robot-robot coordination. In the future, we plan on using global localization
to allow for exact positioning of the object.
© 2007 Felix Duvallet, Nicholas Heckman