A General Framework for Open-loop Pivoting Anne Holladay and Robert Paolini and Matthew T. Mason The Robotics Institute — Carnegie Mellon University {ahollday, rpaolini}@cmu.edu, {matt.mason}@cs.cmu.edu Abstract— Pivoting is the rotation of an object between two fingers using gravity and inertial forces to impart angular momentum. We present an analysis of the mechanics of piv- oting and a framework for planning and execution. Extrinsic dexterity was defined by Chavan-Dafle et al. [1] as the use of external forces, such as gravity and inertial forces in post grasp manipulation. We analyze one such regrasp termed “pivoting” by Rao et al. [2]. We find a grasp and arm trajectory which can rotate an object between stable poses, if any. We demonstrate an implementation of pivoting with an ABB industrial arm and a two fingered gripper. I. INTRODUCTION Humans have a huge repertoire of regrasps. Some regrasps employ coordinated motions of many hand freedoms, dubbed ‘intrinsic motions’ of the hand. However humans also use the environment, like gravity or momentum, as an additional resource. For example, we find it quite natural to roll an object from our fingertips to our palm or to reorient chop- sticks in our hand by pressing them against the table. Chavan- Dafle referred to these actions as “extrinsic dexterity”. Much robotics research has focused on how to manipulate an object with the hand, using only the hand: intrinsic dexterity. But robots, lacking the dexterity of humans, should use the strategies provided by extrinsic dexterity, if anything, more often than humans. Chavan-Dafle describes several examples of extrinsic regrasps. This paper will explore, in detail, one of those regrasps: extrinsic pivoting. Pivoting is defined to be the rotation of an object about an axis determined by two contacts between the effector and object. The most common approach to manipulation is the “pick- and-place” paradigm, where an object is rigidly grasped and placed in the goal position. Pick-and-place provides an alternative to regrasping with pivoting. However, pick- and-place regrasps take more time and space to execute. In practice, industrial work cells commonly try to minimize the free space the arm motions require. Pick-and-place requires much more joint rotation compared to pivoting. Additionally, we will show that pivoting is faster than pick-and-place regrasps. Philosophically, the goal of manipulation is to understand the interactions between a robot and the world and use that understanding to accomplish tasks. Thoroughly understand- ing and exploiting the environment is long-range, very chal- This work was supported by National Science Foundation [NSF-IIS- 0916557] and Army Research Laboratory [W911NF-10-2-0016]. This work does not necessarily reflect the position or the policy of the U.S. Government or ARL. No official endorsement should be inferred. Fig. 1: Pivoting with a contact surface lenging goal. Current practice largely proceeds without this capability. For example, manufacturing automation engineers the environment for the task. However, we can make progress on smaller, more manageable aspects of this challenge. In the case of pivoting, we gain a deeper understanding of how an object can move when it is not rigidly grasped. Traditionally, to rigidly grasp an object, one must consider the form/force closure of the object by a certain grasp. To rotate the object, this consideration is no longer required. One can grasp objects with two fingers. By grasping with only two fingers, the grasp can not achieve form closure since the part can rotate about the contact axis. This is the exact freedom we will exploit. If the fingertips approximate point contacts with friction, we can rotate the object without slipping. With this motivation, we present a study of how environmental forces can be exploited through extrinsic dexterity to easily and effectively increase the dexterity of a multi-fingered hand. II. RELATED WORK This paper explores a type of extrinsic regrasping. In general in robotic manipulation, regrasping is avoided. This is particularly true in manufacturing where the gripper and workspace can be engineered for the task [3]. Pivoting is a simple and reliable way to increase the dexterity of a gripper without augmentation of the workspace. The importance of manipulation beyond pick-and-place has been noted in robotics research in the past. The Instant
A General Framework for Open-loop Pivoting
Anne Holladay and Robert Paolini and Matthew T. Mason The Robotics
Institute — Carnegie Mellon University
{ahollday, rpaolini}@cmu.edu, {matt.mason}@cs.cmu.edu
Abstract— Pivoting is the rotation of an object between two fingers
using gravity and inertial forces to impart angular momentum. We
present an analysis of the mechanics of piv- oting and a framework
for planning and execution. Extrinsic dexterity was defined by
Chavan-Dafle et al. [1] as the use of external forces, such as
gravity and inertial forces in post grasp manipulation. We analyze
one such regrasp termed “pivoting” by Rao et al. [2]. We find a
grasp and arm trajectory which can rotate an object between stable
poses, if any. We demonstrate an implementation of pivoting with an
ABB industrial arm and a two fingered gripper.
I. INTRODUCTION
Humans have a huge repertoire of regrasps. Some regrasps employ
coordinated motions of many hand freedoms, dubbed ‘intrinsic
motions’ of the hand. However humans also use the environment, like
gravity or momentum, as an additional resource. For example, we
find it quite natural to roll an object from our fingertips to our
palm or to reorient chop- sticks in our hand by pressing them
against the table. Chavan- Dafle referred to these actions as
“extrinsic dexterity”. Much robotics research has focused on how to
manipulate an object with the hand, using only the hand: intrinsic
dexterity. But robots, lacking the dexterity of humans, should use
the strategies provided by extrinsic dexterity, if anything, more
often than humans. Chavan-Dafle describes several examples of
extrinsic regrasps. This paper will explore, in detail, one of
those regrasps: extrinsic pivoting. Pivoting is defined to be the
rotation of an object about an axis determined by two contacts
between the effector and object.
The most common approach to manipulation is the “pick- and-place”
paradigm, where an object is rigidly grasped and placed in the goal
position. Pick-and-place provides an alternative to regrasping with
pivoting. However, pick- and-place regrasps take more time and
space to execute. In practice, industrial work cells commonly try
to minimize the free space the arm motions require. Pick-and-place
requires much more joint rotation compared to pivoting.
Additionally, we will show that pivoting is faster than
pick-and-place regrasps.
Philosophically, the goal of manipulation is to understand the
interactions between a robot and the world and use that
understanding to accomplish tasks. Thoroughly understand- ing and
exploiting the environment is long-range, very chal-
This work was supported by National Science Foundation [NSF-IIS-
0916557] and Army Research Laboratory [W911NF-10-2-0016]. This work
does not necessarily reflect the position or the policy of the U.S.
Government or ARL. No official endorsement should be
inferred.
Fig. 1: Pivoting with a contact surface
lenging goal. Current practice largely proceeds without this
capability. For example, manufacturing automation engineers the
environment for the task. However, we can make progress on smaller,
more manageable aspects of this challenge. In the case of pivoting,
we gain a deeper understanding of how an object can move when it is
not rigidly grasped.
Traditionally, to rigidly grasp an object, one must consider the
form/force closure of the object by a certain grasp. To rotate the
object, this consideration is no longer required. One can grasp
objects with two fingers. By grasping with only two fingers, the
grasp can not achieve form closure since the part can rotate about
the contact axis. This is the exact freedom we will exploit. If the
fingertips approximate point contacts with friction, we can rotate
the object without slipping. With this motivation, we present a
study of how environmental forces can be exploited through
extrinsic dexterity to easily and effectively increase the
dexterity of a multi-fingered hand.
II. RELATED WORK
This paper explores a type of extrinsic regrasping. In general in
robotic manipulation, regrasping is avoided. This is particularly
true in manufacturing where the gripper and workspace can be
engineered for the task [3]. Pivoting is a simple and reliable way
to increase the dexterity of a gripper without augmentation of the
workspace.
The importance of manipulation beyond pick-and-place has been noted
in robotics research in the past. The Instant
Insanity demonstration [4], [5] and the Handey project [6], [7]
both recognize the limitations of the “pick-and-place” formulation.
Here, pick-and-place was used to ‘regrasp’ ob- jects by simply
performing several pick-and-place operations in a row.
Regrasping, as it was originally formulated, relies on the
application of continuous controlled forces to the object through
the fingertips. A hand capable of this form of dexterity is often
referred to as a dexterous hand [8], [9], [10]. Much work has been
done along this vein, including rolling [11], sliding [12], and
finger gaiting [13], [14], [15], [16], [17], [18].
However, this paper concerns regrasping using external resources.
This form of regrasping was proposed by Chavan- Dafle et al. [1] as
“extrinsic dexterity”. A general use of external forces was
suggested by Lynch and Mason [19]. The external forces can be
categorized as either quasi-static, passive dynamic, or active
dynamic.
Quasi-static actions include motions like pushing or squeezing.
Nilsson [20] implemented pushing and squeezing on Shakey the robot.
Mason [21], [22] analyzed pushing an object under frictional
contact with a flat surface. Brock and Salisbury [23] proposed
using controlled slippage to regrasp object by identifying possible
slipping motions and selecting a grasp force that would produce a
desired slipping motion.
Using dynamics to manipulate an object allows actions such as
throwing, catching, and juggling. In these cases, inertia is
imparted to the object through the dynamic motions of the driving
manipulator. Aboaf et al. [24], [25] and Burridge et. al [26]
developed learning and control strategies for these types of
actions. Lynch and Mason [27] introduced the concept of “dynamic
dexterity”, referring to the con- trollability and planning of
dynamic manipulation actions. Srinivasa et al. [28] proposed a
technique for trajectory planning of dynamic contact manipulation
which separated the path planning problem from the time-scaling
needed to satisfy the dynamic constraints.
The work most closely related to this work uses passive dynamics by
introducing an understanding of gravity. Several different
approaches have studied the motion of an object lying on a flat
surface, for example a movable tray or a robot palm which tilts.
Erdmann and Mason [29] manipulated a planar object from an
arbitrary location on a tray to a known final location through a
series of tray tilts. Erdmann [30] later presented a framework for
non-prehensile manipulation of an object which can slide and rotate
using two palms. Bai [31] studied the tumbling of objects on the
palm of a dexterous manipulator using the fingers to stop the
object.
Sawasaki and Inoue [32] recognized the usefulness of grasps which
do not hold an object firmly and need not support its whole weight.
They presented a physical analysis of tumbling objects using a
multi-fingered dexterous hand by calculating the forces necessary
to push objects about an edge contacting the table. Aiyama et al.
[33] continued this work on pivoting showing how heavy objects can
be manipulated by only lifting part of its weight and rotating
about a vertex or edge. Finally, Carlisle et al. [34] presented a
method of
parts feeding to rotate an object about an arbitrary axis. Here a
specialized gripper was designed to allow free rotation between the
fingers using a bearing. Rao et al. [2] developed an automatic
planner to identify stable poses of polyhedral objects and choose a
grasp such that the object would stably rotate due to gravity into
the desired goal position. This work expands on this by relaxing
the requirements of stability and introducing dynamics.
III. PROBLEM FORMULATION
We will formulate the problem of manipulating an object by
considering an idealized model of the manipulator. For a
two-fingered hand, let the manipulator be a set of two point
contacts p1, p2 in the workspace W ' R3, and let M =Wp1 ×Wp2 '
(R3)2 be the configuration space of the manipulator.
Let O ⊂ W be the object to manipulate. Let FP be the fixed
reference frame. The object is endowed with a task frame FO which
is rigidly attached to its center of mass. Let ρ = (ro, Ro) ∈ SE(3)
be the configuration of O where ro is the position vector and Ro is
the quaternion defining the rotation of the body-attached frame
w.r.t. FP .
A grasp g specifies two points on the object, which are coincident
with the two end effector points. The two end effector points
describe a configuration of the manipulator that constrain the
mobility of the object to rotation in SO(2) relative to the
effector. This plane is defined by the normal ng = (p2 − p1)/||p2 −
p1|| and the midpoint of the manipulator pg = (p1 + p2)/2. Let Rg ∈
SO(2) be the set of object configurations reachable under grasp
g.
The pivoting grasp is similar to the definition of a caging grasp
[35], [36] in that the object is not immobilized by a grasp.
However, in this paper, the point fingers p1 and p2 contact the
object and remain fixed with respect to the object throughout the
manipulation task. A pivoting grasp provides partial closure. A
pivoting grasp will not enforce full force-closure, specifically it
can not resist torques in the direction of ng . The grasp wrench
space (GWS) [37], [38], [39] defining the space of wrenches that
can be applied to an object by a grasp can be found by
approximating the contact normal force and friction cone at each
contact point. Each force representing the boundary of the friction
cone can be translated to the wrench space origin. The convex hull
of the union of these boundary wenches defines the GWS. A grasp is
in force closure when this convex hull contains the wrench space
origin. By definition, a rotational grasp is not in force closure.
The GWS will be a lower dimensional subspace of the full wrench
space, and, therefore, the wrench space origin can never be
enclosed in the convex hull.
This degree of freedom inherent in the grasp describesRg . An
object can pivot around the axis ng with an origin at the midpoint
of the manipulator pg . The direction of rotation will be the
defined by the torque about ng . Let θ be the object orientation
relative to the hand.
We will henceforth only consider rotations between stable poses of
the object, although our framework may be extended in the future to
accommodate arbitrary configurations in Rg
(a) (b) (c)
Fig. 2: (a) An example of a collision between the gripper and the
table. If the gripper tried to grasp the object at the corner,
there would be a collision with the table. (b) A collision between
the object and gripper during rotation. As the object rotates, the
corner would collide with the palm of the hand. (c) Infeasibility
due to object and hand dimensions. The hand cannot open wide enough
to grasp the object.
(see Section VIII). Assuming a flat work surface, a configu- ration
is stable when the center of mass ocm lies above the face of the
convex hull that is in contact with the support surface. The space
Rg ∈ SO(2) can be represented by the unit sphere. We will partition
Rg based on the “capture regions” of the faces of the object. Each
face of the convex hull can be projected onto a unit sphere
centered on ocm. These projected faces define the set of
configurations which will converge to a representative stable
configuration under quasi-static conditions. We will henceforth
refer to the set of configurations within a capture region by their
representative stable configuration, recognizing that the object
will tumble due to gravity into the stable configuration.
Our goal is to find the rotation R : [ρs ⇒ ρf ] ∈ Rg where ρs and
ρf are representative stable poses. We will find a pivot grasp and
trajectory which will execute this rotation.
IV. QUASI-STATIC MANIPULATION
In some cases, the final configuration can be reached solely with
gravitational torque. This means the object would rotate into the
goal pose due to the grasp by simply lifting the object off the
table. For a given object, there may be a grasp point, pg which
could completely rotate the object into the goal, however this
grasp is often not a feasible grasp. First, we will describe this
ideal grasp, p∗. Then, we will define feasibility and a strategy
for adjusting the initial grasp to meet the feasibility
requirements.
From an arbitrary stable pose to any other, the rotation axis is
not necessarily horizontal. However, rotations about the vertical
axis can be trivially done by rotating the gripper. We are only
concerned with which face of the convex hull contacts the table. In
this case, the rotation axis is always horizontal, perpendicular to
gravity. Let the moment arm pr = (ocm−pg) be the vector from the
grasp midpoint to the center of mass ocm. The torque due to gravity
is τ = pr×G where G denotes gravity. When the object is lifted, the
torque due to gravity will cause the object to rotate such that pr
is parallel with gravity. If it is already parallel with the
gravity vector, as in the case where the ρs and ρf differ by a
180
rotation, dynamics will be necessary to complete the
rotation.
To find the grasp, we proceed in this step as if a face between ρs
and ρf is the goal face.
We must choose the moment arm pr such that it intersects the goal
face of the convex hull. For uniformly distributed objects, the
centroid of that face, oc, is stable (requires no tumbling into a
stable pose). Any alternative point on that face would produce a
valid grasp; we have chosen the centroid for simplicity. Therefore,
we can choose pg to be the point along the line from oc to ocm
where it intersects the boundary of the object. The grasp axis n
should be parallel to the cross product of ρs and ρf where the
configuration can be represented by a unit vector in that
coordinate frame.
A given grasp can be infeasible for any of four reasons, described
in the following paragraphs. In some cases, the grasp can be
adjusted to satisfy a constraint. When it can not be adjusted, a
pivot is not possible.
1) Collisions between the gripper and the environment: For example,
it is common for the gripper to collide with the work surface, see
Figure 2a. This happens when pg is on the face which is in contact
with the table. This can also occur in an environment with clutter
or a limited workspace. To account for these collisions, we move
the grasp directly away until there is no collision. The contact
normal of the collision provides the direction to move. So in the
case of a collision with the table, if we move the grasp in the +z
direction, we can avoid the collision.
2) Collisions between the gripper and the object during rotation:
By definition pg will be within the object. We are specifically
concerned with collisions other than the grasp contact points. This
includes collisions caused by the rotation of the object, as shown
in Figure 2b. These collisions can be detected using the model of
the object and the depth of the hand (the distance from fingertips
to palm). In general, we must sweep the volume of the object
throughout its rotation and check for collisions with the gripper.
For the wooden blocks in our test set, the problem can be solved
using a planar projection. We only need to check whether the worst
point on the object collides with the hand. The worst point is the
point on the object farthest from the line pr in the direction of
rotation. When these collisions occur, the grasp
Fig. 3: Diagram of Swaying Motion.
should be moved closer to this worst point. 3) Instability due to
slippage: If the grasp is too close
the object’s edge, slippage could occur causing the gripper to
prematurely drop the object. In fact, every initial grasp is at an
object edge by definition, since it is found by intersecting the
line through the goal face centroid and the center of mass with an
edge. Therefore, the grasp must be adjusted by moving closer to the
interior of the object along a line to the center of mass.
4) Object dimensions: Finally, the most restrictive con- straint
comes from the shape of the object. The object must fit inside the
gripper. If this is impossible, the grasp can not be adjusted to be
usable. The object must have two parallel faces with a width
smaller than the width of the hand. These faces must be
perpendicular to n surrounding pg . Figure 2c shows an example
where the object can not be rotated.
Once a grasp is determined, simply lifting the object straight up
will cause a rotation. This motion can be done at any speed and
does not require any minimum acceleration of the arm.
V. DYNAMICS
Rotation using quasi-static manipulation can reach some goal
rotations. However, we can reach larger angles by intro- ducing
dynamics. First, we must have a better understanding of the motion
of the object. The object can be in one of two modes: swaying
motion or pendulous motion.
A. Swaying Motion
When the object is being lifted off the table, part of the object
is free to slide, with friction, along the surface of the table. We
will consider the planar projection of this motion in the Y Z
plane. Any motion in the direction of ng will not affect the
rotation. Therefore, a point pA will represent the sliding edge in
contact with the table. The grasp point pg can be moved in the Y Z
plane by the arm.
Let position of pg be given by u(t) = (ux(t), uy(t)) T .
Then the motion of pA is given by AX = √ l2 − uy(t)2 +
ux(t) where l is the length of the support face. This ap-
proximates pg at the edge of the block, which is actually
infeasible. However, it is sufficient for this analysis. AY = 0
while uy(t) <= l. This condition insures contact with the table.
This is shown in Figure 3.
Under the quasi-static assumption, u(t) will be slow enough that
there is no angular momentum when pA loses contact. We will break
this assumption and allow u(t) to have a non-zero acceleration. Let
θ be the object orientation relative to the hand. Then the angle is
given by
θ = cos−1( uy(t)
l )
From the object model, we know the initial θ and the θ where pA
loses contact. We can discretize our angular velocity ω using
waypoints of u(t) described in Section VI.
B. Pendulous Motion
When pA loses contact with the table, the object is now free to
rotate about ng . There are many factors affecting the motion of
the object which are difficult to model, especially the friction
between the fingertips and the object. However, we can approximate
this system as a simple pendulum. We will model the contact area as
point contact with friction. This treats the object like an
additional linkage attached to the hand with a rotational joint.
The resulting inaccuracies of the model will be insignificant
compared with the size of the capture regions in many cases. We can
analyze the dynamics of this system, but we can not control it
using strategies like those used on inverted pendulum or cart-pole
problems since our system is open-loop.
Thus, our system has three degrees of freedom, x, y, and φ, where x
is the horizontal position ux(t) of the hand, and y is the vertical
position uy(t), and φ denotes the counter- clockwise angle between
the moment arm, pr = (ocm−pg), and the vertical. lcm denotes the
length from pg to ocm. The position of the point mass ocm is given
by
ocm =
) (1)
T = 1
1
The Lagrangian yields the equations of motion:
(mh+mo)x+molcmφ cos(φ)−molcmφ 2 sin(φ) = fx (4)
(mh+mo)y+molcmφ sin(φ)+molcmφ 2 cos(φ)−mg = fy
(5) molcmx cos(φ) +molcmy sin(φ)
+mol 2 cmφ+moglcm sin(φ) = −bφ (6)
where mo is the mass of the object, mc is the mass of the hand, g
is gravity, b is a constant for friction at the fingertips, and fx
and fy are the forces applied by the hand in x and y
respectively.
VI. PLANNING
We can now formulate our problem: given a model of an object and
its center of mass and a goal orientation, find the pivoting action
which will rotate the object from the current orientation. We will
use the vision system described
by Paolini [40] to detect the object’s current pose, plan an
open-loop trajectory for the arm, and execute this trajectory. Our
algorithm consists of three steps:
1) Choosing a feasible grasp: We will choose a grasp as described
above, finding the initial, ideal grasp and adjusting it until it
is feasible.
2) Initialize an arm trajectory: Let ξk be our trajectory at
iteration k. The trajectory is parameterized by a series of
waypoints ξk = (xk1 , ..., x
k n). Each waypoint is a 2D point,
thus the space of possible trajectories T ∈ R2n . Let ~x = (x1,
...xn) be our waypoints. Then a trajectory is expressed as ξk~x ∈ T
.
We will initialize our trajectory as a quasi-static motion. This
means the waypoints will simply trace a straight line in the +z
direction with zero acceleration.
3) Optimize the arm trajectory: We model the cost of a trajectory
using three terms: the δφξ error of the object’s final pose, the
final angular velocity ωξ of the object, and the sum of the
euclidean distances between the waypoints dξ. Our objective can be
written
U(ξ) = αδφξ + β|ωξ|+ γdξ (7) where α, β, γ are weights. This cost
function minimizes the final error in φ. This determines the
success of the rotation. We would also like to minimize the final
angular velocity for two reasons: to minimize the object “banging”
on the table when the velocity is into the table, and to stop
over-swinging in the opposite case. Finally we would like to
minimize the overall distance the hand must travel.
To optimize, we want to minimize our cost with respect to the
waypoints ~x.
ξk+1 = argmin ~x∈R2n
U(ξk~x) (8)
We first used gradient descent. Next we perform a line search in
that direction to find the maxima and iterate until
convergence.
VII. IMPLEMENTATION
Fig. 5: Square prism. (Top) Pick-and-place. (Bottom) Pivot-
ing.
We have implemented this framework on a 6-DOF indus- trial
manipulator (ABB IRB140) with a maximum speed of 2.5 m/sec and
maximum acceleration of 20 m/sec2 (∼ 2g). Attached to this
manipulator, we used a two-fingered parallel jaw industrial gripper
(Robotiq) with modified fingertips. Attached to the end of the
fingertips were acorn nuts (see Figure 2) which would contact the
object with minimal surface area. Conforming with the current
capabilities of our vision system, we used wooden polyhedral blocks
as our objects.
We found it easiest to interface to ABB’s RAPID language if we used
only five waypoints, on average. This was due to the way the arm
interpolates velocities between points, by stopping or slowing at
each point. ABB interpolates between the waypoints using parabolic
interpolation. We found the use of five waypoints had several
advantages. Firstly, the computation time to find the gradient of
the trajectory was extremely quick. Secondly, the
trajectories
Fig. 6: Rectangular prism. (Top) Pick-and-place. (Bottom)
Pivoting
TABLE I: Execution Times (sec)
Pick & Place Pivoting Mean Stand. Dev. Mean Stand. Dev.
Tri. 90 7.23 0.24 5.31 0.97 Tri. 315 12.79 0.47 5.46 0.05 Squ. 90
8.45 0.86 5.94 0.15 Squ. ∗180 17.37 0.47 4.50 0.43 Rect. 90 7.75
0.16 6.13 0.91 Rect. ∗180 14.66 0.53 4.43 0.90 Rect. ∗180 17.33
0.56 5.48 0.52
were extremely simple, making them robust to noise and different
objects. Finally, these simple trajectories were in fact 100%
successful in our trials, implying an arbitrarily more complex
trajectory is unnecessary.
We tested our system on three types of wooden blocks: a right
triangular prism, a rectangular prism, and a square prism. With
each of these blocks we found a grasp and trajec- tory for several
possible rotations between two given sides, without specifying the
object position. For the rectangular and square prism, we
implemented a 90 rotation from the longest side to the adjacent
smaller side. This pivot with the rectangular prism can be seen in
Figure 6. The pivot did not require dynamics. The trajectory was
simply lifting the grasp point straight up. In fact, dynamics
caused a failure where the block would over rotate and tip over
when released. Therefore, the arm had to move slowly enough to not
violate the quasi-static assumption. These relatively slow times
can be seen in Table I. We also pivoted the rectangular and square
prisms 180 degrees from the longer faces to the opposite longer
faces. These pivots required dynamics: the grasp point should be
lifted quickly then jerked backwards and down. Finally, we
implemented a pivot between the symmetric sides of the triangular
prism, requiring no dynamics, and the hypotenuse and leg sides,
requiring dynamics.
As a baseline, we compared the pivot actions to a pick-and-place
sequence accomplishing the same rotation. These sequences were hand
coded. Several examples of the pivot and pick-and-place
trajectories can be seen in Figures 4, 5, and 6. To test
repeatability, we implemented each pivot action 25 times.
Additionally, we timed the pivot and pick-and-place actions.
Although these actions are open- loop, small variations in the time
occurred due to system stochasticity. These times and the variation
can be seen in Table I.
Several things should be noted about these times. Namely, the
pick-and-place actions are remarkably slow. Several factors explain
this. The Robotiq gripper is in fact quite slow relative to many
industrial grippers. On average, to open and then close the hand
fully takes 4.84 seconds with 0.05 variation. In several
pick-and-place operations, two pick-and- places were required
(denoted by ∗ in Table I). Additionally, these actions are, by
nature, rotations. This industrial arm can translate its end
effector quite quickly, but rotating the wrist is much slower. The
pivot actions required no wrist rotation and are extremely fast
(almost all of the time accounted for
with the gripper). However, the pick-and-place operations required
the wrist to rotate 90 or 180 which is quite slow. Also, such large
rotations are quite clumsy and require a lot of free space around
the object for the arm to move in.
Additionally many of the pick and place operations were quite
difficult to accomplish without causing the wrist of the robot arm
to collide with the table. A simple solution is to use a fixture in
the workspace to lift smaller objects, like these blocks, off the
table. A fixture was required for the triangular prism 315
rotation.
Several examples showing pick-and-place actions com- pared to
pivoting actions are shown on our website1 and in the accompanying
video.
VIII. FUTURE WORK
We would like to incorporate sensor feedback correspond- ing to the
location of the object throughout the motion.This could be visual
feedback of the position of the block. This would give us more
accuracy in the final location of the object and allow us to more
thoroughly take advantage of the pendulum model. Through feedback
control, we could pivot the block to an arbitrary rotation if we
can close the gripper with enough accuracy. We could detect
slippaged with haptic feedback from the fingertips allowing us to
modulate the gripping force of the fingertips.
Further, we would like to continue to explore fingertip material
and shape and how it affects the rotation process. Soft or hard
fingertips and objects have a large effect on the success of a
pivot. The shape and regularity of the object need not be limited
to objects with parallel faces. We would like to explore a more
general class of pivotable objects.
REFERENCES
[1] N. Chavan-Dafle, A. Rodriguez, R. Paolini, B. Tang, S.
Srinivasa, M. Erdmann, M. T. Mason, I. Lundberg, H. Staab, and T.
Fuhlbrigge, “Extrinsic dexterity: In-hand manipulation with
external forces,” in IEEE International Conference on Robotics and
Automation (ICRA), May 2014.
[2] A. Rao, D. Kriegman, and K. Goldberg, “Complete algorithms for
feeding polyhedral parts using pivot grasps,” Robotics and
Automation, IEEE Transactions on, vol. 12, no. 2, pp. 331–342, Apr
1996.
[3] G. Monkman, S. Hesse, and R. Steinmann, Robot grippers. John
Wiley and Sons, 2007.
[4] R. Paul, K. Pingle, J. Feldman, and A. Kay, “Instant insanity,”
film, 1971.
[5] J. Feldman, G. Feldman, G. Falk, G. Grape, J. Pearlman, I.
Sobel, and J. Tenenbaum, “The Stanford hand-eye project,” in
Proceedings of the First International Joint Conference on
Artificial Intelligence. Citeseer, 1969, pp. 521–526.
[6] P. Tournassoud, T. Lozano-Perez, and E. Mazer, “Regrasping,” in
IEEE International Conference on Robotics and Automation, vol. 4,
1987, pp. 1924–1928.
[7] T. Lozano-Perez, J. Jones, E. Mazer, P. O’Donnell, W. Grimson,
P. Tournassoud, and A. Lanusse, “Handey: A robot system that
recognizes, plans, and manipulates,” in Robotics and Automation.
Proceedings. 1987 IEEE International Conference on, vol. 4, mar
1987, pp. 843 – 849.
[8] J. K. Salisbury Jr., “Kinematic and Force Analysis of
Articulated Hands,” PhD Dissertation, Stanford University,
1982.
[9] M. T. Mason and J. K. Salisbury, Jr., Robot Hands and the
Mechanics of Manipulation. The MIT Press, 1985.
[10] J. Salisbury and J. Craig, “Articulated hands: Force control
and kinematic issues,” The International Journal of Robotics
Research, vol. 1, no. 1, pp. 4–17, 1982.
[11] A. Bicchi and R. Sorrentino, “Dexterous manipulation through
rolling,” in IEEE Int. Conf. on Robotics and Automation, 1995, pp.
452–457.
[12] M. Cherif and K. Gupta, “Planning quasi-static fingertip
manipulations for reconfiguring objects,” in IEEE Transactions on
Robotics and Automation, vol. 15, 1999, pp. 837–848.
[13] R. Fearing, “Simplified grasping and manipulation with
dextrous robot hands,” IEEE Journal of Robotics and Automation,
vol. 2, no. 4, pp. 188–195, 1986.
[14] J. Hong, G. Lafferiere, B. Mishra, and X. Tan, “Fine
manipulation with multifinger hands,” in ICRA, Cincinnati, OH,
1990, pp. 1568–1573.
[15] T. Omata and K. Nagata, “Planning reorientation of an object
with a multifingered hand,” in Proceedings of the IEEE
International Conference on Robotics and Automation, 1994, pp.
3104–3110.
[16] L. Han and J. Trinkle, “Dextrous manipulation by rolling and
finger gaiting,” in Proceedings of the IEEE International
Conference on Robotics and Automation, 1998, pp. 730–735.
[17] D. Rus, “In-hand manipulation of piecewise-smooth 3d objects,”
in International Journal of Robotics Research, vol. 18, no. 4,
1997, pp. 355–381.
[18] T. Schlegl and M. Buss, “Hybrid closed-loop control of robotic
hand regrasping,” in Proceedings of the IEEE International
Conference on Robotics and Automation, 1998, pp. 3026–3031.
[19] K. M. Lynch and M. T. Mason, “Stable pushing: Mechanics, con-
trollability, and planning,” in The First Workshop on the
Algorithmic Foundations of Robotics (WAFR). A. K. Peters, Boston,
MA, 1994, pp. 239–262.
[20] N. J. Nilsson, “Shakey the robot,” SRI International, Tech.
Rep. 323, 1984.
[21] M. T. Mason, “Manipulator grasping and pushing operations,”
Ph.D. dissertation, Massachusetts Institute of Technology,
Department of Electrical Engineering and Computer Science,
1982.
[22] ——, “Mechanics and planning of manipulator pushing
operations,” IJRR, vol. 5, no. 3, pp. 53–71, Fall 1986.
[23] D. L. Brock, “Enhancing the dexterity of a robot hand using
controlled slip,” Master’s thesis, MIT, 1987.
[24] E. W. Aboaf, S. M. Drucker, and C. G. Atkeson, “Task-level
robot learning: Juggling a tennis ball more accurately,” in ICRA,
Scottsdale, AZ, 1989, pp. 1290–1295.
[25] E. W. Aboaf, C. G. Atkeson, and D. J. Reinkensmeyer,
“Task-level robot learning: Ball throwing,” MIT,” AI Memo 1006,
1987.
[26] R. R. Burridge, A. A. Rizzi, and D. E. Koditschek, “Toward a
dynamical pick and place,” in IROS, 1995, pp. 2: 292–297.
[27] K. M. Lynch and M. T. Mason, “Dynamic nonprehensile
manipulation: Controllability, planning and experiments,”
International Journal of Robotics Research, vol. 18, no. 1, pp.
64–92, January 1999.
[28] S. Srinivasa, M. Erdmann, and M. Mason, “Control synthesis for
dynamic contact manipulation,” in IEEE International Conference on
Robotics and Automation. IEEE, April 2005.
[29] M. Erdmann and M. Mason, “An exploration of sensorless manipu-
lation,” IEEE Journal of Robotics and Automation, vol. 4, no. 4,
pp. 369–379, 1988.
[30] M. A. Erdmann, “An exploration of nonprehensile two-palm
manipu- lation: Planning and execution,” in ISRR, 1995.
[31] Y. Bai and C. K. Liu, “Dexterous manipulation using both palm
and fingers,” in IEEE international conference on robotics and
automation, 2014.
[32] N. Sawasaki, M. Inaba, and H. Inoue, “Tumbling objects using a
multi- fingered robot,” in Proceedings of the 20th International
Symposium on Industrial Robots and Robot Exhibition, 1989, pp.
609–616.
[33] Y. Aiyama, M. Inaba, and H. Inoue, “Pivoting: A new method of
gras- pless manipulation of object by robot fingers,” in IEEE
International Conference on Intelligent Robots and Systems (IROS),
Yokohama, Japan, 1993, pp. 136–143.
[34] B. Carlisle, K. Goldberg, A. Rao, and J. Wiegley, “A pivoting
gripper for feeding industrial parts,” in IEEE Int. Conf. on
Robotics and Automation, 1994.
[35] A. Rodriguez, M. T. Mason, and S. Ferry, “From caging to
grasping,” The International Journal of Robotics Research, vol. 31,
no. 7, pp. 886–900, 2012.
[36] R. Diankov, S. Srinivasa, D. Ferguson, and J. Kuffner,
“Manipulation planning with caging grasps,” in IEEE International
Conference on Humanoid Robots, 2008.
[37] M. A. Erdmann, “A configuration space friction cone,” in IROS,
Osaka, Japan, 1991, pp. 455–460.
[38] B. Mishra, J. T. Schwartz, and M. Sharir, “On the existence
and synthesis of multifinger positive grips,” Algorithmica, vol. 2,
no. 4, pp. 541–558, 1987.
[39] A. Miller and P. Allen, “Graspit! A versatile simulator for
robotic grasping,” Robotics & Automation Magazine, IEEE, vol.
11, no. 4, pp. 110–122, 2004.
[40] R. Paolini, A. Holladay, A. Rodriguez, S. Srinivasa, and M.
Mason, “Robust and accurate object pose estimation for robotic
manipulation using colorless point clouds,” 2015, submitted to IEEE
International
Conference on Robotics and Automation (ICRA).
INTRODUCTION
Collisions between the gripper and the object during rotation
Instability due to slippage