Towards Postural Synergies for Caging Grasps
Johannes A. Stork, Florian T. Pokorny and Danica Kragic
Abstract—Postural synergies have in recent years been successfully used as a low-dimensional representation for the controlof robotic hands and in particular for the synthesis of forceclosed grasps. This work proposes to study caging grasps usingsynergies and reports on an initial analysis of postural synergies
for such grasps. Caging grasps, which have originally only been
analyzed for simple planar objects, have recently been shown to
be useful for certain manipulation tasks and are now starting to
be investigated also for complicated object geometries. In thisworkshop contribution, we investigate a synthetic data-set ofcaging grasps of four robotic hands on several every-day objects
and report on an analysis of synergies for this data-set.

I. INTRODUCTION
Robots that can grasp unknown objects in the presence ofnoise are still not the state of the art. However, to enable
future service, household or companionship robots to operatein unstructured environments and to perform useful tasks,
such robots need to interact with and manipulate previously
unknown objects reliably. While a large amount of effort in
the robot grasping community has focused on the automaticsynthesis and evaluation of grasps that establish contact withan object [1], the benefits of caging grasps have recently
been rediscovered and exploited for manipulation planning[2]. Caging grasps constrain the object’s freedom of motion
by preventing it from escaping arbitrarily far [3]. However,they do not necessarily establish contacts. In fact, the related
concept of maximal caging [4, 5] has been proposed tomaximize the freedom of motion for the object while keeping
it trapped in a bounded set. The particular advantage of caging
grasps in applications of manipulation planning is that rigidity
constraints between an object and the robot can be neglected
in planning when the object is caged. The relative pose of
the robot hand and object is not fixed and therefore allows
for more flexibility. Humans often employ caging rather thanforce-closed grasps e.g. when holding on to hand-rails, when
opening doors etc.
The problem of dexterous grasp planning is highdimensional and has been approached by randomized searchin a low-dimensional hand posture subspace under the notionof eigengrasps [6, 7]. A low-dimensional topology-based
object representation and a matching posture evaluation for thegeneration of caging grasps on objects with holes is proposedin our current work at this conference [8]. There we represent
fundamental loops in an object using approximated shortest
homology generators and devise a method for generating
caging grasps on such objects.
This is a submission to the IEEE/ICRA workshop ”Hand synergies - how
to tame the complexity of grasping”. The authors are with the Computer
Vision and Active Perception Lab, Centre for Autonomous Systems, School ofComputer Science and Communication, KTH Royal Institute of Technology,
Stockholm, Sweden, {jastork,fpokorny,dani}@kth.se

Fig. 1: Objects and hands from the data-set. From left to right:
Objects Chair, Purse, Bag, Lawn Mower, Travel Bag and robot
hands Armar III (right hand), DLR 1, Schunk SDH, iCub (righthand).

To explore the prospect of applying the eigengrasp approachto caging grasps, we will here consider a data-set of secure
caging grasps which we generated on a collection of objects
with holes. Example postures of four hands on five every-day
objects are investigated for the existence of postural synergies,
and the relation of a ‘grasp target volume’ and these synergies
is studied in this work.
Our evaluation shows that postural synergies exist in suchkind of caging grasps, and that postures highly depend on
the local shape and extent of the caged object part, and inparticular namely on the local volume.
II. RELATED WORK
Postural hand synergies and eigengraps can both be justified
based on the well-known results of [9], where principal
component analysis (PCA) of grasp joint space data is used
to show that the two first principal components (PCs) accountfor more than 80% of the total variance. There, grasp data is
acquired from human subjects shaping their hand as if theygrasped a displayed object. The frequently drawn conclusionof these results is that the digits of a human hand are notcontrolled on an individual level, but rather are commonly
actuated by a control that involves few postural synergies forforming general postures. Since the found synergies do notnecessarily coincide with a standard grasp taxonomy, it isbelieved that the hand’s shape is controlled independently fromthe applied forces. So called force synergies are subsequently
studied by [10] for lifting, holding and re-placing using agripper apparatus grasped by human subjects. The findings
include that the normal forces of all digits covary linearly
and that fluctuations in force are highly synchronized duringholding. The temporal aspects of the entire act of graspingis investigated from the perspective of synergies in [11]. Fivesubjects perform reach-to-grasp experiments with three classesof shapes that are systematically varied in size. Two common
patterns in the temporal sequence of marker positions arefound: opening and closing of the hand in general, as wellas thumb and long finger flexing. The synergies in grasp-toreach are shown to be different from the postural synergies as
the first PC accounts for 99.5% of the total variance and is irrespective of object shape, grasp or subject. Another approach
towards grasp synthesis using synergies is given in [6, 7].
Transferring the results for the human hand in [9], eigengrasps
for artificial hands are defined. As a result, a stochastic search
can be conducted in the highly reduced dimensionality of theeigengrasp space – instead of the full joint space – to generateenveloping pre-grasps. In [7], synergies are used in an on-line
interactive manner. A soft synergy model of hands is proposedin [12] to investigate the conjecture that humans learn a series
of inner hand representations of increasing complexity. In thatapproach, the synergetic hand displacement does not directly
determine joint angles but instead yields reference points.
Mechanical compliance is described as a dynamic equilibrium
between attraction towards the synergy-driven reference pointsof the pose and repulsive contact forces, joint stiffness andbody deformation.
In contrast to force-closed grasps, caging grasps, only boundan object’s mobility to prevent it from escaping arbitrarily
far from the manipulator. A caging grasp provides a way
to control an object without immobilizing it completely sothat the object will follow the manipulator. Early researchon caging has focused on analysis and efficient algorithms
for simple hand mechanisms with few degrees of freedoms[13, 14], and considered only simple objects in a plane.
Concavity of objects has been exploited for caging to findfinger position far away from the object [4]. Later, the studyof three-dimensional caging by multi-fingered hands led tothe definition of sufficient conditions and resulted in a cageplanning system [15]. The notion of stretching and squeezing
cages has been introduced for the analysis of caging mobile
rigid bodies in a Euclidean space of arbitrary dimension[16, 3]. Caging configurations have been considered as a
waypoint towards a full contact establishing grasp [3] and as amethod to deal with uncertainty in grasping [17]. Applications
in manipulation planning have also recently been found [2],making caging grasps a highly interesting set of postures toinvestigate.
III. METHODOLOGY AND DATA-SET
To investigate postural synergies in caging grasps we perform principal component analysis of joint space data. Here,
we work with a synthetic data-set containing 9142 distinct
caging grasps of four robot hands. Five real-sized every-day
objects are each caged by the hands. We shall not elaborate
here on the generation procedure for these caging grasps,
which is based on our work in [8] and which uses topologicalfeatures of the objects which are extracted from point-clouddata. The grasps in our data-set have been confirmed as caging
grasps by a rigid body simulation where a series of randomtranslations and rotations was applied and was not able to pull
the hand away from the object.

A subset of of our caging grasp data-set is displayed inFig. 2. A brake-down of the numbers of grasps per handand object is given in Fig. 3. We used four simulated robotic
hands, namely the DLR, iCup, ARMAR III and Schunk hand.
The DLR Hand [18] (12 DOF) is a four-fingered articulated
robotic hand, about 50% larger that an average human hand.
The iCub child-sized humanoid robot hand [19] has nine
DOF. The five-fingered IAI-HAND-12 (10 DOF) for the
ARMAR III platform [20] is a symmetric three-fingered hand.
The Schunk SDH [21] (9 DOF) is a 3-fingered fully actuatedindustrial robot gripper. The object geometry data was takenfrom [22, 23]. All robot hands and objects are depicted inFig. 1.
IV. RESULTS
A principal component analysis (PCA) of the joint spacedata was conducted separately for each robot hand. The firstprincipal component PC1 on average captures about 72%of the overall variance and the 2nd PC never accounts formore than 10%. Lower-order principal components accountfor increasingly less variance. While, for the Armar III, iCuband Schunk hand, the captured variance of PC1 is about 70%,
it is 76% for the DLR 1 hand. The distribution of variance isgiven in Fig. 4. This quantitative results suggest the existenceof postural synergies in the caging grasps of each hand.
The plots for each robot hand in Fig. 5 show for eachcaging grasps the first two coordinates in principal component
space (red) as well as the first two coordinates of the principal
components themselves. For the Armar III and DLR 1 hands
the points form one dominant cluster with comparably little
scatter. For the Schunk SDH the points are concentrated on an
arc at the top side of a scattered field. The iCub hand produces
multiple clusters. To investigate the described clustering in
the plots, we color and scale the data points for each postureaccording to a convex volume approximation of the caged local
object part. The resulting plots, displayed in Fig. 6, indicatethat the clusters are based on the grasp target volume. For
the Armar III and iCub hands, the volume clearly separates
two individual clusters. In case of the DLR 1 hand the large
volume postures are surrounded by lower volume postures.
The lower volume postures themselves are clearly split into
two distinct segments. A similar structure can be seen for the
Schunk hand, where the large volume postures do, in contrast
to the other hands, not form a concentrated blob, but rather awedge-like connected shape.
Finally, we are interested in the distribution of the principal
components on the object shapes. For easy analysis, we color
the grasp target positions using a synergy-based RGB color
scheme. The 1st coordinate fades from blue to red whilethe 2nd coordinate determines the amount of green. In thisway, we can inspect the distribution of the first two PC’s
influence on the postures. Fig. 7 shows the resulting maps.
Different types of postures are apparently used for vertical andhorizontal parts of the chair by the iCub and the Armar III
hand. The DLR 1 hand uses a different posture for the middle
backrest since the long fingers are obstructed from closing duea) Purseb) Bagc) Chaird) Lawn Mowere) Travel Bag
1) Armar III (right hand)

2) DLR 1

3) Schunk SDH4) iCub (right hand)Fig. 2: Randomly selected examples of grasps from the caging data-set. The different sizes of the robot hands can clearly beseen in relation to the objects. While some areas cannot be reached by the large hands because of obstruction, some smaller
hands cannot reach around large volumes.

Endeffector

Armar III (2586)

DLR 1 (1971)

Schunk SDH (2249)

iCub (2336)

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Purse
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Travel Bag

Fig. 3: The data-set contains 9142 caging grasps of four robot hands on five objects. The table above shows how the grasps
are distributed over hands and objects. To explore the synergies all postures of a single robot hand are considered at once,
separately of each hand.

PC1

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Armar IIIDLR 1
Schunk SDH
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Explained Variance [%]Handdata-set on objects with holes and with complex geometry.
We found that the first two synergies account for a large
percentage of the variance in our data-set. The first two
postural synergies were found to describe the general shapeof the hands indicating that they might be well-suited to be
used in the planning of caging grasps on complex objects.

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90

ACKNOWLEDGMENT

80

This work was supported by the EU project FLEXBOT(FP7-ERC-279933) and the Swedish Foundation for Strategic
Research.

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R EFERENCES
Armar IIIDLR 1

Schunk SDH

iCub

Fig. 4: Synergies can be found by consider the share of total
variance that the first n principal components (PC) of the joint
space data explain. For each robot we show the first six PC.
The first two PC explain 78, 74, 67, 72 percent and the first
three explain 85, 86, 80, 80 percent of the total variance.

to the object’s geometry. On the lawn mower the DLR 1 andthe Schunk hand have elongated gripper-like postures aroundthe power switch box because that part is too wide to beproperly enveloped. Such a posture can be seen for the Schunk
hand at the 9 o’clock position in Fig. 8.
The interpretation of the fist two principal components canbe investigated in Fig. 8. For the Armar III hand the firstcomponent mainly describes flexing of the short finger joints
while the 2nd component governs the longer fingers. The
thumb of the DLR 1 hand is controlled by the first component
and the 2nd component describes bending of the long fingers.
For the Schunk SDH the first component decides the distal
joint bending. The 2nd component controls whether the fingers
towards the left are more bent than the fingers towards theright. The opening of the longer fingers of the iCub handrelates to the first component while the 2nd component isconcerned with the shorter fingers.
V. CONCLUSIONS
Research on caging has so far mainly focused on industrial
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Fig. 5: From left to right: First two first principal components of the joint space data (red) and principal components (blue) of
Armar III (right hand), DLR 1, Schunk SDH, iCub (right hand).

b) Lawn Mowera) ChairFig. 6: First principal components of the joint space data-set, color and size are defined by the volume of the grasping target.
Top row: first two PC. Bottom row: First three PC.
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4) iCub (right hand)Fig. 7: Coloring of intended grasp center points by the first two principal components of the joint space data. The RGB color
scheme maps the 1st PC from blue (min) to red (max) and decides the amount of green by the 2nd PC.

1Component 2

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Fig. 8: Example postures from the secure caging data-set together with their first two principal component coordinates.

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