arXiv:1609.04946v1  [cs.RO]  16 Sep 2016
Robot Contact Task State Estimation via Position-based Action
Grammars.
Juan Rojas, Zhengjie Huang, and Kensuke Harada.
Abstract— Uncertainty is a major difficulty in endowing
robots with autonomy. Robots often fail due to unexpected
events. In robot contact tasks are often design to empirically
look for force thresholds to define state transitions in a
Markov chain or finite state machines. Such design is prone
to failure in unstructured environments, when due to external
disturbances or erroneous models, such thresholds are met,
and lead to state transitions that are false-positives. The
focus of this paper is to perform high-level state estimation
of robot behaviors and task output for robot contact tasks.
Our approach encodes raw low-level 3D cartesian trajectories
and converts them into a high level (HL) action grammars.
Cartesian trajectories can be segmented and encoded in a way
that their dynamic properties, or “texture” are preserved.
Once an action grammar is generated, a classifier is trained
to detect current behaviors and ultimately the task output.
The system executed HL state estimation for task output
verification with an accuracy of 86%, and behavior monitoring
with an average accuracy of: 72%. The significance of the work
is the transformation of difficult-to-use raw low-level data to
HL data that enables robust behavior and task monitoring.
Monitoring is useful for failure correction or other deliberation
in high-level planning, programming by demonstration, and
human-robot interaction to name a few. The data, code,
and supporting resources for this work can be found at:
https://www.juanrojas.net/research/position_based_action_grammar.
I. INTRODUCTION
Uncertainty is a major difficulty in endowing robots with
autonomy. Robots often fail due to unexpected events or
behaviors. Low-level state estimation using robot pose has
been extensively studied to help robots improve their belief
about their state [1]. However, for contact tasks the interpre-
tation of signals is not as straightforward. One key question
is how can we use information from an FT sensor to know
the system state? Especially at a high level (i.e. a behavior
description) where the knowledge can be exploited to correct
failures or deliberate. In practice, contact tasks are often
designed to empirically look for force thresholds to define
state transitions in a Markov chain or finite state machine.
Such design is prone to failure in unstructured environments,
when due to external disturbances or erroneous models, the
force thresholds are met but lead to state transitions that are
false-positives. Consider an assembly task that consists of
an alignment and insertion. If the two parts do not mate
Juan Rojas is with the School of Electromechanical Engineering in the
Guangdong University of Technology in Guangzhou, China.
Zhengjie Huang is with the School of Software at Sun Yat Sen University
in Guangzhou, China.
Kensuke Harada is with the Graduate School of Engineering Science at
Osaka University in Osaka, Japan.
properly during the alignment, the force threshold might
nonetheless still be met, giving rise to the insertion behavior,
but in which case the insertion will fail. The focus of
this paper is to perform continuous state estimation (also
referred to as process monitoring). In particular, we are
interested in yielding high level state estimates that are useful
representations for error correction and action deliberation.
As stated earlier, process monitoring has undertaken dis-
crete event detection approaches. In such cases, contact
points are detected and then evaluated as a contact sequence
[2], [3], [4], [5]. With respect to continuous detection,
our previous work [6], [7], [8], used a hierarchical tax-
onomy that encoded relative change from FT signatures
and increasingly abstracted basic primitives to perform state
estimation of a snap assembly task and identified behavior
and anomaly information using statistical methods. In [9], a
sticky-Hierarchical Dirichlet Process Hidden Markov Model
was used for continuous estimation of alignment tasks for
a block and identified class anomalies caused by a various
extraneous objects.
Additionally, we have begun to consider the inclusion of
multi-sensor modalities for contact task’s continuous state
estimation. The neuroscience literature has been showing
evidence on how humans perform haptic tasks best when
using multi-sensory inputs [10], [11]. While in this paper,
we do not yet attempt a multi-model system, we wish to
test the efficacy of performing high level continuous state
estimation of contact tasks with position information while
using the same principle used earlier in the wrench domain–
that is, encoding of relative changes to yield high-level
representations. Our hypothesis is that information from the
position domain will corroborate and complement the results
derived from state estimation in the wrench domain.
In the area of process monitoring using position data,
we find two approaches: Iterative 3D chain code construc-
tion, and Neighborhood feature extraction with a multi-level
representation. The former uses two adjacent vectors with
which, an alphabet of motion directions is generated. For
neighborhood feature extraction there are two main lines
of work: (i) the use of Frenet frames (FF) instead of 3D
chain code constructs [12], [13], and (ii) the Scaled Indexing
of General Shapes (S-IGS) [14], [15], [16], which analyzes
curvature and torsion at each trajectory point to do point-
level or segment-level descriptions and construct primitives
from point sequences with similar features. S-IGS methods
have only been applied to human hand motions, while FF
Fig. 1.
A series of 3D plots representing snap assembly tasks under
controlled failure experiments.
methods have been applied to suturing task for minimally
invasive surgery.
In our work, we wish to analyze whether FF-based ap-
proaches can effectively perform high level state estimation
for contact tasks. In particular, we tested snap assemblies,
which are characterized by high frequency contact during
alignment and insertion phases, see Fig. 1 as an example.
Such application would be novel, since the aforementioned
approaches have not been tested in highly non-smooth, noisy
signals. We want to study how accurately these approaches
can perform both behavior (or sub-task) recognition and
task (output) verification. If a force-dominant task can be
accurately estimated with position data, then we can comple-
ment state estimation methods that use wrench information
as the sensor modality. The contribution of our work is an
efficacy analysis in use of FF related techniques for state
monitoring and task verification for robot contact tasks. Our
analysis looks at both sub-and-whole-task identification, in
success and failures cases, both in simulation and with a real
humanoid robot.
Our approach can be organized into three stages: segmen-
tation, encoding, and classification. Signal segmentation is
effected through the use of FF-based methods. The encoding
of the segmentation uses Direct Curve Coding (DCC), which
gives rise to a grammar of motions, and, the action grammar
classification is done using linear SVM. The system executed
HL state estimation for task output with an average value of
86%, and behavior monitoring with an average performance
value of: 72%. The significance of the work is the transfor-
mation of difficult-to-use raw low-level data to HL data that
enables robust behavior and task monitoring. Monitoring is
useful for failure correction or other deliberation in high-level
planning, programming by demonstration, and human-robot
interaction to name a few.
II. METHODOLOGY
High-level state estimation using position data is boot-
strapped by segmenting a 3D position curve according to
FF or AFF (see Sec. II-A), the segmented curve is then
encoded using DCC. Encoded signals of different lengths,
are post-processed to have equal number of segments. Post-
processed data is then trained using classification algorithms
(both for behavior estimation and task output verification).
An overview of the process is presented in Fig. 2.
A. Segmentation and Encoding
The use of FFs is motivated by the fact that this dis-
cretization is able to capture the “texture” of the motion in
a way other techniques have not [12]. Texture is captured
since FFs capture the motion’s local curvature from the point
of view of an observer traveling on the curve. This also
makes the technique coordinate-independent and robot setup-
independent. This principle is similar to the approach taken
in our state estimation work using wrench information where
we capture relative change by fitting the signal with straight
line segments using regression over a growing window [6].
Both focus on relative change. FFs consists of a base frame
consisting of three orthonormal vectors: tangent ⃗t, normal ⃗n,
and binormal ⃗b. On continuous curves s(t) =
R t
0


r′(σ)


 dσ,
the vectors are defined according to Eqtn. 1.
⃗t
=
dr
ds,
⃗n
=
dt/ds


dT/ds


,
(1)
⃗b
=
⃗t × ⃗n.
For a discrete curve connected by a sequence of points
xk(k = 1, 2, 3, ...), discrete Frenet frames (DFF) assign the
orthonormal vectors according to Eqtn. 2.
⃗tk
=
⃗xk+1 −⃗xk
∥⃗xk+1 −⃗xk∥,
⃗nk
=
⃗tk−1 × ⃗tk



⃗tk−1 × ⃗tk



,
(2)
⃗bk
=
⃗bk × ⃗tk.
The first frame placement on the curve is arbitrary and
selected by the user. Each succeeding frame is placed every
unit step and follows Eqtn’s 1 or 2. Direction can be encoded
iteratively as long as a current xs and a previous xs−1 frames
exist. The sequence of FFs, generated from the position
time-series, are encoded into a string representation, (hereto
referred as an action grammar) by mapping direction changes
through a small set of canonical directions.
The number of canonical directions is related to the
number of vectors used in the frame assignment. The base
case, with three orthonormal vectors, can represent a minimal
set of directions. Namely: forward, backward, up, down, left,
right, and no motion. These directions can be encoded with
strings: “0,1,...,6” respectively. Mathematically, the direction
d for time-step s is selected as the tendency of motion
towards one of the 7 possible directions. d is assigned by
projecting the current tangent vector ts, onto the previous
Segmentation
Encoding
Classification
Post
Processing
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
4
5
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
4
5
Fig. 2.
Methodology overview: 3D curves can be segmented, encoded, and trained for behavior and task classification.
orthonormal basis xs−1 and choosing the direction that ts is
closest to one of the existing directions.
ds = arg max
i {ts.[xs−1]},
xs = [ts−1, ns−1, bs−1, −ts−1, −ns−1, −bs−1].
(3)
This encoding technique is known as Direct Curve Coding
(DCC).
1) Accumulated Frenet Frames (AFF): One weakness in
the FF method is that it is unable to adequately represent
smooth trajectories, where the curve is characterized by small
direction changes. The FF’s action grammar only updates
when turns greater than pi/4 take place. AFF’s, on the other
hand, is a method that accumulates change over small spatial
or temporal windows and is more sensitive to gradual change.
It does so first by expanding DCC to be systematic and allow
different granularity levels to partition space. DCC partitions
space depending on a base parameter p according to Eqtn.
4:
[⃗x]p = [⃗x]p−1
[

⃗xa + ⃗xb



⃗
xa + xb




,
(4)
|⃗xa ⊗⃗xb| ̸= 0,
g.t.
⃗xa, ⃗xb ∈

[⃗x]p−1

.
This base case, where p = 1, yields 7 vectors: 6 orthogonal
(up, down, forward, back, left, right) + one null vector for
null motion. It divides the space into octants. Granularity can
be increased (and thus the set size of canonical directions)
by inserting more vectors in the projection function (Eqtn.
3). Additional vectors can be inserted by taking the union of
the previous base xp−1 with the normalized sum of its parts.
The partitioning level ascribed to a base p = 2 yields 19
vectors. The third base has 91 vectors, and the fourth 2891.
Note that the space is not evenly partitioned in these two
latter cases. Fig. 4 illustrates such space partitions.
Secondly, in AFF, new frames no longer set their ⃗ts vector
along the current tangent of the curve (represented as ⃗ws
in Fig. 3), instead, new frames keep the same orientation
until a directional threshold is met. At the time, we align
the new ⃗ts with the current tangent ⃗ws. In Fig. 3, we
compare FF and AFF. Notice that both techniques keep the
same code for the first four steps, but for the fifth step, the
directional change of the curve has accumulated enough that
the directional threshold is met and AFF updates its direction.
In doing so, the action grammar is also modified. Directional
thresholds are set by the equation: αp = π/2p+1. The
equation is dependent on the DCC base number. For DCC7,
the threshold is α1 = π/4. For DCC19 it is α = π/8. Once
the directional threshold is met, we use the same projection
function from Eqtn. II-A, although with the appropriate
number of vectors for a DCC specification. Possible direction
changes and DCC specifications can be appreciated in Fig. 4.
In the end, the action grammar–a sequence of labels that span
the entire trajectory, describes the local curvature changes
experienced by the 3D position curve. This grammar encodes
behavior and task properties that help us characterize how the
motion was executed. In effect we have taken a continuous
position signal and mapped into discrete changes that will
aid in the high-level estimation of the robot contact task.
B. Classification
In this work, we classify behaviors and task output. A
task is composed of a sequence of behaviors. A behavior’s
action grammar is obtained by performing DCC on the time
segment of a given behavior. At this time, the time transitions
are provided by the robot controller: when a threshold is met,
a transition time is recorded. A task’s action grammar is the
set of string labels for the entire task. The action grammar
is used as a feature vector for the supervised classification
algorithm. Fig. 6 shows an encoded color map for the action
grammar of a full snap assembly task for multiple trials. The
map provides an intuitive way to see the texture and patterns
across a task.
w1
w2
w3
w4
w5
b1
n1
t1
b2
n2
t2
b3
n3
t3
b4
n4
t4
b5 n5
t5
b1
n1
t1
b2
n2
t2
b3
n3
t3
b4
n4
t4
b5 n5
t5
Fig. 3.
Comparison between action grammar updates between FF and
AFFs.
Fig. 4.
Illustration of possible direction changes in a curve and possible
space partitioning configurations. (a) Shows the change in direction between
succeeding frames, (b) DCC7 with 7 vectors and a directional threshold of
π/4, (c) DCC19 with 19 vectors and a directional threshold of π/8. [13].
As part of the classification, feature vectors used across
trials need to have the same length for proper evaluation.
In this work we take two approaches to align the features:
one is a blind approach where there is information loss and
the second approach is a simple interpolation procedure. In
the blind approach, we search for the feature vector with the
smallest length in an experiment and then proceed to cut the
additional elements contained in the longer vectors for other
trials through a logical AND operation. In the resampling
case, we consider all trajectories in a training or testing set;
count the number of frame assignments for each trajectory,
and compute the average number of points. We then roughly
approximate the length of each curve by summing the linear
distance between points and divide by the average number
of points. This gives a unit length for resampling. All curves
are then re-segmented with this length and later encoded with
sDCC.
C. Support Vector Machines
Linear Support Vector Machines (SVMs) approximate a
boundary to separate binary classes through a hyperplane
for large feature spaces. The feature vector is used to learn
a hyperplane: ωT xb = 0, where ω are the weights and b is
the bias from the zero point. In effect, the separation of each
training point from the hyperplane is the functional margin
ˆγ(i) and can be modeled as:
ˆγ(i) = y(i)(ω(i)x + b)
(5)
Here the pair y(i), x(i) represents the class as y(i) ∈1, 1 and
x(i) is the input vector for training and testing. The SVM
optimizes the functional margin by maximizing the distance
to both true and failure cases by solving the quadratic
programming problem:
max(γ)
s.t.
γ =
min
i=1,..,m ˆγ,
(6)
where, γ is the geometrical margin of the input points from
the hyperplane. The larger the geometrical margin the more
accurate the classifier. Our linear classifier was tested with
a linear, polynomial, and a radial basis function as kernels
using Scikit’s machine learning library [17].
III. EXPERIMENTS
NX-HIRO, a 6 DoF dual-arm anthropomorph robot was
run both in the OpenHRP 3.0 simulation environment [18]
and in the real robot. Male and female 4-snap cantilever
camera parts were used. The male part was rigidly mounted
on the robot’s wrist, while the female snap was rigidly fixed
to the ground as in Fig. 5. For this work we consider the
Pivot Approach strategy presented in [6] where, a successful
assembly task consists of four behaviors: an approach, an
alignment, an insertion, and a mating. The Approach behav-
ior drives the male part along a smooth trajectory until it
contacts the female part at an angle at a docking pivot as in
Fig. 5. The rest of the behaviors are achieved using modular
force-moment controllers as stated in [6].
With respect to the test configuration, two kinds of experi-
ments were conducted. One experiment only considered con-
trolled failure experiments, while the other only considered
successful assemblies. The failure experiments introduced
small but large enough deviations from a nominal trajectory
in the Approach state to generate failure early in the assembly
task. The small deviations are characteristic of what a human
adult would make when trying to enact a parts alignment
but narrowly misses the mark. The failure experiment was
only conducted in simulation, classification was conducted
for both behaviors and task output. The other successful
assembly task experiments, simulation and real-robot tests
were conducted, and behaviors and task output were both
classified. The data sets stand as follows:
• A: Successful Assembly Simulation
• B: Controlled Failed Assembly Simulation
• C: Successful Assembly with the Real-Robot
As for our testing, we sought to thoroughly analyze the
performance of the system. We performed classification eval-
uations for data sets A,B,C, as well as their combinations:
AB, AC, and ABC. We ran linear SVM with three kernel
types: linear (SVC based on libsvm & LinearSVC based
on liblinear), polynomial, and RBF. A 2-to-20 cross fold
validation was used–we start with 2 folds and move up to
20. For each k-value we run classification 10 times. Average,
maximum, and minimum classification accuracy results are
collected. We also compared the results from FF and AFFs
both running DCC19.
Fig. 5.
The HIRO-NX robot performing the snap assembly of a male and
female camera part with 4 cantilever snaps. Top-left is a zoomed-in version
of the assembly.
a
b
c
Fig. 6.
Encoded color map for action grammars. The x-axis represents color coded string labels from the action grammar for a contact snap assembly task
under controlled failures. The y-axis represents different trials. The visible patterns in the map indicate similarities across different parts of the trajectory.
(a) and (b) show different controlled failure experiments in simulation, (c) illustrates the successful assembly task by the real robot.
TABLE I
SVM PERFORMANCE WITH DIFFERENT KERNELS.
SVC_Linear Linear_SVC RBF Polynomial
FF
behavior
72
60
48
66
task
86
85
63
81
AFF behavior
70
59
44
66
task
86
85
63
80
A. Results
We first present color-coded maps for the action grammars
of some of the data sets in Fig. 6. The color-coded maps,
provide an intuitive representation of motion texture as well
as the patterns therein. Each row corresponds to an encoded
string for a given trajectory in the data subset and the 19-
element alphabet (given by the DCC19-encoded strings) is
mapped to 19 levels of color brightness. From the color
coded maps in Fig. 6, notice the similarities within class for
successful and failure trials. There is more variability in the
failure class because in these controlled experiments there
are up to 6 different subclasses (that we did not classify in
this work). Not explicitly considering the failure sub-classes
hurts our classification result and this is something that will
be addressed in future work.
The first set of results to report is the SVM performance
for different kernels. SVM performance is reported both for
behavior classification and task output classification. The
numbers reported are the average of all data set results
(A,B,C,AB,AC,ABC) for both FF and AFF: Table I reveals
that SVC_Linear performs best across the board: both under
FF and AFF for both behavior and task classification.
The next set of results presents the overall performance of
SVC_Linear under 2-to-20 fold cross validation, for all data
sets under different alignment methods for both behavior and
task output, for both FF and AFF. The results can be seen
in Table II.
With respect to “Alignment” methods, Table II shows that
generally, the cut-off alignment method performs better than
the resampling alignment. The results can be misleading as
TABLE II
OVERALL PERFORMANCE FOR THE FF METHOD.
Method
Level
Alignment
A
B
C
AB
AC
ABC
avg
81
76
64
64
62
64
Interp
min
73
73
51
54
57
58
Behavior
max 93
80
73
76
69
70
avg
83
77
82
76
68
67
Cut
min
69
76
77
71
65
63
FF
max 95
82
90
82
72
72
avg
78
92
89
80
83
Interp
min
71
86
84
70
77
Task
max
83 100
96
85
90
avg
77 100
100
81
80
Cut
min
74 100
100
78
75
max
85 100
100
85
86
avg
76
64
64
63
64
Interp
min
73
56
51
56
56
Behavior
max
80
72
76
71
70
avg
77
82
76
70
68
Cut
min
74
77
72
65
65
AFF
max
81
87
81
74
71
avg
78
91
88
81
82
Interp
min
72
85
83
76
77
Task
max
88
97
96
85
87
avg
76
99
100
80
81
Cut
min
71
99
100
75
77
max
82 100
100
85
88
there is information loss in the blind approach. Even so, the
resampling approach performed well for task classification
when using AFF-DCC19. For the successful assembly with
the real-robot, it correctly classified 91% of the time, while
for data set combinations AB, AC, and ABC, it correctly
classified between 81% −88% of the time.
With respect to the performance between output task
classification and behavior classification, the former has a
much higher accuracy on most data set combinations except
for B, the failure data set. We mentioned in Sec. III that
the failure data can be subdivided in multiple dissimilar
classes, hence the poorer classification in sets with failure
data: B, BC and ABC. The task-level classification has an
outstanding 100% classification accuracy on the success data
set combinations C and AB with cut-off alignment. We see
that the longer the action grammar, the higher classification
accuracy. Behavior classification rated as follows: 64%−81%
for FF-Interpolated for classes A, B, C. FF-Cut does better
from 77% −83%. AFF-Interpolated for classes A, B, C,
performed less accurately: 64% −76%, while FF-Cut did
better: 76% −82%.
With respect to the performance between the FF and AFF
techniques (both using DCC19), we generally did not see
improvements anywhere. In fact, FF seems to do marginally
better all around. The reason for this might be that in fact
our contact task problem consists of trajectories full of
discontinuities. Therefore, the advantages offered by AFF
for smooth curves cannot be appreciated in this domain.
IV. DISCUSSION
In this work, we performed high level state estimation
of robot contact tasks by taking 3D Cartesian trajectories
and encoding them in action grammar and then classifying
them to monitor behavior and task output. Our trajectories,
unlike previous works, have segments with significant non-
smoothness and discontinuities. Nonetheless, the results are
comparable to previous works that analyzed suturing tasks
in minimally invasive surgery. In our domain, the system
had average classification accuracy of 86% for output task
verification. Though the system also reached values of 92%−
100% for real-robot success assemblies. For behavior HL
state estimation the average classification rate was: 72% but
reached 82% for real-robot successful assemblies (the aver-
age value was lowered by not considering the classification
of failure subclasses). In [13], for their DCC19 experiments
on data set DS-I, with known state boundaries and for spatial
quantization, their average behavior classification rate was:
82.16%. For their second data set DS-II, for spatial DCC19,
their average classification results across k-fold validation
and one-user out validation (for all their skill sets) was
75.22%.
Our classification results may be also hurt due to the
fact that the feature vector fed to the SVM classifier lacks
notions of similarity between different trials. A similarity
measure should be designed and used to formulate a new
feature vector for the classifier. The second limitation is that
our classifier is only running offline. We are considering
implementing a dynamic time warping solution that is a pow-
erful similarity measure that is optimal for online monitoring
[19] and combine this with online supervised methods or
probabilistic models.
Additionally, we are not yet performing automatic detec-
tion of state transitions. We currently rely on transition times
provided by the controller, which we earlier stated to be an
important source of error.
Finally, we are interested in integrating this work into a
multi-modal architecture for HL state estimation. By com-
bining both low-level and high-level information from multi-
sensor modalities promises to increase robustness in state
estimation, especially for contact tasks, that consist of harder
to predict signals.
V. CONCLUSION
This work presented a system to perform HL state es-
timation for behavior monitoring and task verification for
robot contact tasks. The system generates an action grammar
from a 3D position trajectory generated from the robot end-
effector that encodes the dynamic properties of the motion.
This grammar is used as a feature vector for a classifier that
in turns helps to identify executing behaviors or the final
result of a task. The work is significant in that it transforms
raw low-level data into useful high-level that can be used for
failure correction or deliberation about future actions.
VI. ACKNOWLEDGEMENTS
This work is supported by “Major Project of the Guang-
dong Province Department for Science and Technology
(2014B090919002), (2016B0911006).”
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