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Learning Probabilistic Discriminative Models of Grasp Affordances
under Limited Supervision
Ays¸e Naz Erkan†∗, Oliver Kroemer†, Renaud Detry‡, Yasemin Altun†, Justus Piater‡, Jan Peters†
Abstract— This paper addresses the problem of learning
and efficiently representing discriminative probabilistic models
of object-specific grasp affordances particularly in situations
where the number of labeled grasps is extremely limited.
The proposed method does not require an explicit 3D model
but rather learns an implicit manifold on which it defines
a probability distribution over grasp affordances. We obtain
hypothetical grasp configurations from visual descriptors that
are associated with the contours of an object. While these hypo-
thetical configurations are abundant, labeled configurations are
very scarce as these are acquired via time-costly experiments
carried out by the robot. Kernel logistic regression (KLR) via
joint kernel maps is trained to map these hypothesis space
of grasps into continuous class conditional probability values
indicating their achievability. We propose a soft-supervised
extension of KLR and a framework to combine the merits
of semi-supervised and active learning approaches to tackle
the scarcity of labeled grasps. Experimental evaluation shows
that combining active and semi-supervised learning is favorable
in the existence of to an oracle. Furthermore, semi-supervised
learning outperforms supervised learning, particularly when
the labeled data is very limited.
I. INTRODUCTION
Grasping is a fundamental skill for robots that need to
interact with their environment in a flexible manner. A wide
spectrum of tasks (e.g., emptying a dishwasher, opening
a bottle, or using a hammer) depend on the capability to
reliably grasp an object or tool as part of a larger planning
framework. It is therefore imperative that the robot learns
a task-independent model of an object’s grasp affordances
in an efficient manner. Given such a flexible model, a
planner can be used to grasp and manipulate the object for
a wide range of tasks. In this paper, we investigate learning
probabilistic models of grasp affordances for an autonomous
robot equipped with a 3D vision system (see Figure I). An
object’s affordances refers to the likelihood of a location on
the object being graspable, from a specific orientation, by
the robot.
Until this decade, the most predominant approach to
grasping has been obtaining a full 3D model of the object and
then employing various techniques such as friction cones [1]
and form- and force- closures [2]. Given the difficulties of
obtaining a 3D model with sufficient accuracy to reliably
apply these techniques, designing statistical learning methods
†Max Plank Institute for Biological Cybernetics, Spemannstraße 38,
Tuebingen Germany
{naz,oliverkro,altun,jan.peters}@tuebingen.mpg.de
‡Department of Electrical Engineering and Computer Science Montefiore
Institute, Universit´
e de Li`
ege 4000 Li`
ege Sart Tilman Belgium
{renaud.detry,justus.piater}@ulg.ac.be
∗New York Unversity, Computer Science Department New York, NY
for grasping has become an active research field [3], [4],
[5], [6]. These new learning methods often employ efficient
representations and vision based models, without requiring
full 3D reconstruction, in order to provide a more robust
alternative to traditional approaches. Much of the previous
work focuses only on learning successful grasps [3], [4].
While such generative approaches can be advantageous in
cases of a well-defined data distribution, it is well-known
that discriminative learning methods have three main advan-
tages over generative models [7]: Firstly, they model class-
conditional probabilities of both successful and unsuccessful
grasp configurations, leading to a more descriptive model and
higher confidences for unsuccessful grasp regions. Secondly,
they can incorporate arbitrary feature representations more
flexibly. Thirdly, due to the conditional training, they are not
affected from any modeling error of the data distribution.
The investigation of discriminative learning methods for
grasp affordances presented in this paper continues on from
previous approaches of conditional grasp affordance models,
namely [5] and [6]. In [5], the authors propose extracting a
set of 2D image features and apply a discriminative super-
vised learning method to model grasp affordance probabili-
ties given the 2D image. In [6], this approach is extended by
combining the classifier of [5] with a probabilistic classifier
using a set of arm/finger kinematics features in order to
identify physically impossible 2D points for the robot to
reach. The strength of their approach is the combination of
two important kinds of information, i.e., image and kinematic
features, in a probabilistic manner.
We propose using Kernel Logistic Regression (KLR) [8]
for training grasp affordance models. The main motivation
behind this approach is to have the system learn a mapping
from local visual features to probabilities directly, as this
yields more general models than a comparison of explicit
geometric models to those in an object database. While this
approach enjoys the advantages of a probabilistic model, it
can also capture the non-linear relations between potential
grasps efficiently via kernels. This is an essential merit, since
our visual grasp features are extracted from the contours of
the objects and the orientation of the robot’s hand, which
results in the grasps lying on a non-linear manifold.
The KLR method provides a principled way of combining
information from the object as well as from the robot hand
via joint kernels [9]. By training a single classifier using
joint kernels, as opposed to training two separate classifiers
as was previously done [6], our approach can capture non-
linear interactions of the morphology of the robot hand and
the surface characteristics of the object implicitly. The system
therefore does not have to rely on explicit representations
such as closed form geometric descriptions or libraries of
feasible grasps.
Executing and labeling grasps of novel objects is a time-
consuming process that requires human monitoring and may
damage the objects. However, a vast number of hypothetical
grasp configurations can be generated by a vision model,
such as the Early Cognitive Vision reconstructor. These
hypothetical grasps can not be given any confident labels,
as they have not been empirically tested, and are therefore
effectively unlabeled. We investigate using such unlabeled
data in our KLR approach to reduce the number of grasps
that need to be annotated for the affordance model. In
particular, we propose combining a novel semi-supervised
KLR method with active learning in the context of robot
grasping.
Semi-supervised learning and active learning are sub-fields
of machine learning that aim to handle the scarcity of labeled
data. Semi-supervised learning methods, e.g., [10] and the
references therein, use a large set of unlabeled data in
order to improve the classification performance by revealing
the underlying geometry of the data. Active learning does
not rely on a source of unlabeled data, but rather assumes
the existence of an annotator, commonly referred to as the
oracle, that can provide labels to queries. In a robotics
context, the annotator corresponds to the robot attempting
to perform new grasps. The goal of active learning is to
guide the robot to evaluate the most informative grasps so
that the classification error is reduced with the fewest queries
possible.
Fig. 1. Three-finger Bar-
rett hand equipped with a 3D
vision system. A table tennis
paddle is used in the experi-
ments.
This framework enables the
robot to learn incrementally
by autonomously evaluating
grasps. We provide comparisons
between supervised, semi-
supervised as well as a
hybrid of semi-supervised
and active learning setups, as
minimizing the need for large
amounts of labeled data is an
essential concern. Experimental
evaluations show not only that
the proposed active learning and semi-supervised learning
methods individually improve the system’s performance,
but that the amount of necessary annotated data is also
significantly reduced when supervised learning is combined
with active learning.
This paper is organized as follows, in Section II, we de-
scribe the details of the acquisition of the features. Section III
gives a detailed explanation of the machine learning tech-
niques evaluated in the context of robot grasping. Section IV
overviews relevant work in the literature. In Section V, we
introduce the experimental setup, give empirical results and
provide a comparison of supervised, semi-supervised and
active learning approaches. Finally, Section VI provides a
discussion and directions for future work.
(a) Feasible configurations (b) Infeasible configurations
(c) Hypothesis space
Fig. 2. Kernel logistic regression algorithm is used to discriminate the
successful 2(a) and unsuccessful grasps 2(b) lying on separable nonlinear
manifolds. The entire hypothesis space 2(c) of potential grasp configurations
extracted from pairs of ECV descriptors contains feasible grasps as well as
infeasible configurations.
II. VISUAL FE ATURE EXTRACTION FOR GRASPING
The inputs of our learning algorithm are represented as
grasp configurations generated from Early Cognitive Vision
(ECV) descriptors [11], [12], which represent short edge
segments in 3D space, as described in [3]. Accordingly,
an ECV reconstruction is performed. Next, pose hypotheses
for potential grasps are generated from pairs of co-planar
ECV descriptors. The grasp position is set to the location
of one of the ECV descriptor pairs whereas the grasp
orientation is computed from the normal of the plane on
which these descriptors lie. The assumption is that two co-
planar segments constitute a potential edge of the object that
the robot hand can hold. However, this is quite optimistic
as many infeasible edges and orientations will be included
in the hypothesis space, see Figure II. Hence, we need a
learning algorithm to discriminate between the feasible and
infeasible grasps contained in this set.
Each grasp is represented with seven values in the object
relative reference frame, three for the position and four for
the orientation in unit length quaternions. The object relative
reference frame is a coordinate system that is attached to the
object such that any rigid body transformation applied to
the object will also be applied to the coordinate system and
objects therein.
III. LEARNING GRASP AFFORDANCES
In this section we outline the key concepts of our learning
algorithm. First, we describe a kernel used as a distance
metric between pairs of grasp configurations. This kernel
decomposes into separate distance measures on the position
and rotation parameters. We use this kernel in the KLR al-
gorithm. Later, we propose a soft-supervised variation of the
KLR algorithm so that it can accommodate unlabeled data
via this distance metric. Finally, we describe the uncertainty
criterion to select grasps for the queries in the active learning
setting.
A. Joint Kernel
Each grasp configuration x= (s, r)consists of seven
parameters, i.e., three from the 3D position sof the robot
hand in the object’s reference frame, and four from the
unit quaternions rdefining the rotation. These values have
different coordinate systems and have to be treated separately
in order to obtain a proper distance metric. This distance
metric, which indicates the similarity of two configurations,
is employed for both the kernel computation and the sim-
ilarity measure required by semi-supervised learning, see
Equation (2). We define the joint kernel as
K(xa, xb) = exp −ksa−sbk2
2σ2
s
−f(θab)2
2σ2
f(θ)!,
where fis the rotational distance, σsand σf(θ)are the
standard deviation of the pose and rotation distances of all
pairs of samples respectively. In order to cope with the
double cover property [13] of quaternions, we compute the
rotational distance f(θab), as the smaller angle between the
two unit length quaternions raand rb. This definition allows
us to use a Gaussian distribution on this rotational distance
metric. Here, θab is the angle of the 3D rotation that moves
rato rb, i.e., θab =θ(ra, rb) = arccos(rT
arb), and
f(θab) = min{θ(ra, rb), θ(ra,−rb,)}.
For further details on distance computations between unit
quaternions see [13]. This joint kernel is similar to that
in [14] in the way it decomposes into kernels on position
and rotation features. However, there the authors employ a
Dimroth-Watson distribution to get the rotational kernel as
opposed to the Gaussian distribution, which is preferable due
to the computational complexity of the former.
B. Kernel Logistic Regression
Our goal is to model the conditional probability distribu-
tion of grasp success y∈ {−1,1}given a grasp configuration
xas defined in Section III-A. Given labeled data S=
{(xi, yi)}l
i=1, KLR achieves this goal by maximizing the
regularized log-likelihood of the data R(w;S)defined by
R(w;S) =
l
X
i=1
log p(yi|xi;w)−kwk2,(1)
p(y= 1|x;w) =1/(1 + exp(− hw, f (x)i)),
where f(x)refers to an implicit feature representation in-
duced by a kernel kand wis the corresponding weight
vector. It has been shown that this optimization problem can
be derived from the Maximum Entropy (MaxEnt) framework,
where the goal is to find a conditional probability distribution
p(y|x)that matches the data (in the sense that the expected
values of features with respect to p(y|x)should match
their empirical counterparts) while remaining as simple as
possible, or equivalently maximizing the class conditional
entropy H=−Pyp(y|x) log p(y|x),
max
pEx∼˜pm[H(p(y|x))] st.
Ex∼˜pmEy∼p(y|x)[yf(x)]−E(x,y )∼˜pj[yf(x)]
≤.
Here ˜pjdenotes the empirical joint distribution and ˜pm
denotes the empirical marginal distribution over x. Defining
˜pm(xi)=1/l and ˜pj(xi, yi) = 1/l for all (xi, yi)∈Sand
using duality techniques yield (1).
C. Semi-Supervised Kernel Logistic Regression
The duality relation mentioned in Section III-B suggests
that the accuracy of KLR depends on accurate estimates of
the empirical marginal and joint distributions. Our goal in the
semi-supervised KLR (SSKLR) method is to use unlabeled
data to reduce the sampling bias of these distributions.
This can be achieved by imposing the smoothness of the
conditional distribution in the sense that two similar grasp
configurations have similar success and failure probabilities.
To this end, we propose assigning soft-labels to unlabeled
grasp configurations {xi}n
i=l+1 that are in the vicinity of
labeled grasp configurations with respect to the manifold
on which the grasp configurations lie. If the similarity
metric conveys the true geometry of the grasp configurations
and KLR is trained with respect to the soft success/failure
assignments for unlabeled grasp configurations as well as
the true labels of labeled grasp configurations, the resulting
conditional probability distribution is expected to be smooth.
Similarity based soft-label assignment is equivalent to
manipulating the joint distribution ˜pjto include soft labeled
data. We define ˜pm(xi)=1/n and ˜pjas
˜pj(xi, y) =
1/Zjif 1≤i≤l, y =yi,
sik/Zjif l < i ≤n, 1≤k≤l, xi∈Nk, y =yk,
0otherwise,
(2)
where Nxis the neighborhood of xand Zjis the normal-
ization factor for ˜pjto be a proper probability distribution.
Equation (2) allows an unlabeled data to be soft-labeled by
multiple labeled data with possibly different labels, which
is desirable if an unlabeled data point lies close to multiple
label regions. Given these definitions and using duality, we
derive the SSKLR problem as maximizing
R(w;S) =
n
X
i=1 X
y
˜pj(xi, y)hw, y f(xi)i(3)
−
n
X
i=1
˜pm(xi) log X
y
(exp hw, yf (xi)i)−kwk2.
The Representer Theorem [15] states that optimal
weight vector of Equation (3) admits the form w∗=
Pn
i=1 yαif(xi)[15]. When we substitute the solution into
Equation (3), we get a convex optimization over αwhich can
be solved using any convex optimization technique. Inference
of a new grasp configuration xis given by the sign of
Pn
i=1 Pyyαik(xi, x).
D. Uncertainty based active learning
We can employ active learning in scenarios where the
robot has the means to choose what to learn. For the active
selection of grasps, we use uncertainty sampling [16] which
is straightforward for probabilistic models. In this method,
the algorithm queries for the grasps on which it is the least
confident. Therefore, at each iteration, the algorithm requests
the true label for the grasp, x∗that has the highest class
conditional entropy among the set of unlabeled grasps, U
x∗= argmax
x∈U
H(p(y|x)).
In turn, the robot carries out the configuration that corre-
sponds to x∗and labels it accordingly.
IV. RELATED WORK
Efficient representation and vision based modeling of
grasp configurations is an active research field [3], [5]. We
follow the methodology in [3] to obtain grasp pose candi-
dates and orientations as described in Section II. However,
the authors learn grasp densities using successful grasps
only, whereas in this paper, we model the class condi-
tional probabilities of both successful and unsuccessful grasp
configurations in a discriminative manner. Furthermore, we
focus on the scarcity of the labeled data points and we
evaluate active and semi-supervised learning algorithms with
the smallest number of annotated experiences possible.
Granville et al. [4] present a method where the robot
learns a mapping from object representations to grasps from
human demonstration. They cluster the orientations of grasps
and each cluster is associated with a canonical approach
orientation. The authors indicate that limiting the encoding
to orientations or excluding position knowledge, is due to
their underlying assumption that orientation and position are
independent.
As labeled data collection is expensive for most robotics
tasks, active learning techniques have already been consid-
ered. Salganicoff et al. [17] proposed some of the earliest
work on uncertainty based active learning for vision-based
grasp learning by modifying the ID3, a decision tree algo-
rithm. Montesano and Lopes [18] also propose a method to
learn local visual descriptors of good grasping points via self-
experimentation. Their method associates the outputs with
confidence values.
In machine learning, various methods to combine semi-
supervised and active learning have been proposed to exploit
the merits of both approaches [19], [20]. We attempt to
be the first in the context of robotics. The active learning
methodology in [20] is similar to ours, as the authors
employ confidence sampling for active learning based on the
probabilistic outputs of a logistic regression classifier. Their
method differs from ours since they perform semi-supervised
learning via self-training, whereas we propose a soft-labeling
approach motivated from the maximum entropy framework.
V. EMPIRICAL EVALUATION
We have empirically evaluated the methods described in
Section III on a 3-finger Barrett robot with simple objects
such as a table tennis paddle. For supervised learning, we
have used a Kernel Logistic Regression classifier and the
joint kernel defined on position and orientation features. The
labels were collected by a human demonstrator. For the semi-
supervised experiments we have used SSKLR loss given in
Section III-C. Details on the experimental setup such as data
collection, preprocessing, model selection and the results are
given below.
A. Experimental Setup
We collected 200 samples, 100 successful (positive labels)
and 100 unsuccessful (negative labels) grasps. We preprocess
the data by normalizing the position parameters to zero
mean and unit variance. The unit quaternions do not require
preprocessing.
All experiments are carried out using the following varia-
tion of a fourfold cross validation. We have separated the
200 samples into four non-overlapping validation sets of
size 50. The model variance in semi-supervised and active
learning can be high as the training set is typically very
small. In order to compensate for the resulting high variance,
we have generated five random training sets from each of
the remaining 150 samples with equal numbers of positive
and negative samples. For the data set simulations of the
active learning scenario, we used the rest of the samples
as the active learning pool for each of the 20 training sets,
trn1. . . trn20. Model selection is performed over the averages
of the models trained on these 20 training sets and their
classification performance is assessed on the correspond-
ing validation sets. To summarize, models trained on sets
trn1. . . trn5are assessed on validation set val1, trn6. . . trn10
on validation set val2and so on.
Our framework has two hyper-parameters which are to be
set during the model selection. The first parameter, Kis the
size of the neighborhood in the soft-label assignment step in
Equation 2. The second parameter, is the regularization
constant of the kernel logistic regression algorithm. We
sweep over a grid of values K={10,20,30,50}, and
={10−2,10−3,10−4}and report the error for the hyper-
parameters with the cross validation error described above.
Note that, for active learning model selection is performed
only once, at the initial step.
B. Evaluation on collected data sets
We evaluate the supervised and semi-supervised models
with increasing sizes of labeled data. When additional data
is selected with uncertainty sampling, we assess the ac-
tive supervised and active semi-supervised performances. In
all experiments, we train initial models with 10 randomly
selected labeled samples. We perform model selection in
this setup and fix the value of the hyper-parameters for the
following experiments. The semi-supervised algorithm uses
an additional unlabeled set of size 4000. All results are the
averages over the models trained over 20 realizations of the
training set and the fourfold cross validation.
First, we empirically evaluate the performance of semi-
supervised learning versus supervised learning. Figure 3
shows the improvement of classification error as randomly
selected samples are added to the training sets one at a
time (hence, classification error of KLR and SSKLR with
0 5 10 15 20 25 30 35 40 45 50
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
Number of randomly selected grasps
Classification Error
Random Sampling − Supervised
Random Sampling − Semi−supervised
Fig. 3. Supervised and semi-supervised logistic regression error on the
validation sets versus the number of randomly selected labeled samples
added to the initial training of size 10. Model selection is carried out at the
initial step with 10 samples. 50 samples are added in an incremental manner
and all models are retrained at each iteration. SSKLR uses an unlabeled
training set of size 4000. K, the neighborhood size for the similarity based
augmentation (Equation 2) is set to 30.
respect to increasing labeled data). As expected, when the
size of the labeled data is small, semi-supervised learning
is advantageous over supervised learning. The difference
diminishes as the dataset gets larger.
An alternative evaluation measure is the perplexity of
the data, 2H(p)= 2(Px−p(x) log2p(x))which measures
the uncertainty of the predictions of the trained models.
This information theoretic measure is commonly used for
probabilistic models in fields such as speech recognition and
natural language processing [21]. In Figure 5, we plot the
perplexity of KLR and SSKLR. This figure shows that the
semi-supervised model is more confident (smaller perplexity)
of its predictions than the supervised model, and thus yields
preferable results. We also note that the variance of perplex-
ity across different validation sets are smaller in the case
of SSKLR, when the dataset is small. This renders semi-
supervised learning more robust compared to supervised
learning in real-life scenarios.
Secondly, we comparatively demonstrate the impact of
active learning. Figure 4 illustrates the performance of both
KLR and SSKLR when incrementally trained with uncer-
tainty based sampling. The corresponding perplexity plots
are shown in Figure 6. The comparison of KLR and SSKLR
in the active learning setting shows a similar behaviour to that
of random selection, Figure 3 and 5. Figure 7 illustrates the
classification error rate for all four scenarios together. For the
supervised classifier, the improvement rate is clearly faster
with active learning than random selection. A 10% error rate
is achieved with 17 samples whereas to get the same error
rate 40 samples are required for the random selection case.
C. On-Policy Evaluation
In order to test our approach in a real life setting we
have used a second object, the watering can shown in
Figure 8(a). For the experiments we have collected a total
0 5 10 15 20 25 30 35 40 45 50
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
Number of actively selected grasps
Classification Error
Uncertainty Sampling − Supervised
Uncertainty Sampling − Semi−supervised
Fig. 4. Supervised and semi-supervised classification error on the validation
sets as actively selected samples are queried via uncertainty sampling. The
error bars indicate one standard deviation of uncertainty over 20 models.
The initial 10 labeled samples are randomly selected.
0 5 10 15 20 25 30 35 40 45 50
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5 x 1014
Number of randomly selected grasps
Perplexity
Random Sampling − Supervised
Random Sampling − Semi−supervised
Fig. 5. Perplexity in random sampling.
0 5 10 15 20 25 30 35 40 45 50
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5 x 1014
Number of actively selected grasps
Perplexity
Uncertainty Sampling − Supervised
Uncertainty Sampling − Semi−supervised
Fig. 6. Perplexity in active sampling.
0 5 10 15 20 25 30 35 40 45 50
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
Number of incrementally added grasps
Classification Error
Active Sampling − Supervised
Active Sampling − Semi−supervised
Random Sampling − Supervised
Random Sampling − Semi−supervised
Fig. 7. Classification error rate for KLR, SSKLR, active-KLR and active
SSKLR.
(a) Watering can
(b) Initial set of training samples
Fig. 8. The watering can used for the on-policy evaluation is shown in (a).
We initiate the incremental algorithm with 20 labeled configurations shown
in (b).
of 20 labeled instances of 10 successful and 10 unsuccessful
configurations. Figure 8(b) illustrates these initial training
set of data samples where green refers to feasible grasps and
red refers to infeasible ones. Later, we trained the system
incrementally with 15 more samples separately, both with
random (RS) and actively sampled (AS) data. After we
stopped training we have identified 10 test configurations on
which the AS and RS algorithms disagree the most. When
we carried out these configurations on the robot, in 10 out
of 10 configurations the decision of the AS was correct and
RS failed indicating that the AS is stronger in the decision
boundaries.
VI. CONCLUSION AND FUTURE WORK
We have presented a probabilistic approach to model the
success likelihoods of grasp configurations from a pool of
hypothetical configurations extracted from ECV descriptors.
The main bottleneck in the learning process is the scarcity of
labeled data due to time-consumption of annotating grasps.
Therefore, we have used semi-supervised and active learn-
ing approaches in the context of robot grasping. We have
experimentally evaluated these approaches in two settings,
in the former the data is provided only once as a batch
whereas in the latter the agent has the means to query new
labeled samples incrementally. We provided the results for
three-finger Barrett hand and simple objects. Experimental
evaluation indicates that combining semi-supervised and ac-
tive learning approaches is effective in improving the robot’s
performance with limited supervision. However, it may not
always be possible to incrementally train a system. When that
is not possible, semi-supervised learning is advantageous.
The future direction is to learn visual cues that are shared
among various objects so that the grasp affordance models
are not object-specific but can be generalized to many object
categories. We plan to investigate this direction by using
the features proposed in [6] within the joint kernel KLR
framework.
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