a hidden markov model-based assembly contact recognition system

Mechatronics 13 (2003) 1001–1023

A hidden Markov model-based assemblycontact recognition system

H.Y.K. Lau *

Department of Industrial and Manufacturing Systems Engineering, The University of Hong Kong,

Pokfulam Road, Hong Kong

Received 15 August 2002; accepted 23 August 2002

Abstract

A hidden Markov model (HMM)-based assembly contact state recognition system is de-

signed and implemented. The system utilizes the force/torque data captured from a wrist force

sensor to extract the intrinsic spatial relationships of contact formations arise from robotic

assembly. The paper introduces a theoretical framework for contact recognition based on

discrete HMM with special emphasis on the practical realization of the system using an in-

dustrial robot. With the detailed exposition of the major algorithms for solving the three key

problems in HMM, namely, the evaluation of observation sequence probability, optimization

of state sequence probability, and optimization of model parameters, a working prototype of

HMM-based system is developed. The performance of the contact recognition system is in-

vestigated by using experimental studies. The results obtained clearly demonstrate that HMM

is an effective means for assembly contact modelling and identification, and that the frame-

work reported in this paper provides an essential ground work for the development of a

practical intelligent robotic system.

� 2003 Elsevier Science Ltd. All rights reserved.

Keywords: Intelligent assembly; Hidden Markov model; Contact recognition; Industrial robotics

1. Introduction

Robotic assembly is a classical problem in industrial robotic where a rigid robot

with accurate actuators under a position-based controller executes sequences of pre-

determined operations in a structured workspace. In reality, jigs and fixtures ware,

and tolerance exists in work pieces, thus limiting the deployment of robots in most

* Fax: +852-2858-6535.

E-mail address: [email protected] (H.Y.K. Lau).

0957-4158/03/$ - see front matter � 2003 Elsevier Science Ltd. All rights reserved.

doi:10.1016/S0957-4158(03)00012-6

mail to: [email protected]

1002 H.Y.K. Lau / Mechatronics 13 (2003) 1001–1023

assembly tasks especially where tight tolerance contacts and mating of parts are

involved.

With a view to overcome this limitation, force-based control strategies have been

widely investigated. In the past decades, force-control strategies including the gen-eralized spring and damper [22], hybrid force/position control [10,16], impedance

control [8] and others more recent developments [24] have been suggested. These

strategies provide means to construct force feedback control systems where force

information acquired from joint torque and wrist force sensors is used to modify the

robot motion.

For most practical assembly systems, definitive models are often difficult to obtain

for a force controlled system to perform satisfactorily. In order to relax the con-

straints that required precise modeling of the environment and assembly systems;and uncertainties such as actuator frictions, artificial intelligence (AI) techniques

have been deployed in recent years. AI techniques such as neural networks, fuzzy

logic and genetic algorithms have been used to learn and optimize parameters that

are very difficult to model (see Section 3).

1.1. Fundamental issues of robotic assembly

However, the incorporation of AI techniques into control algorithms to �self-tune�control parameters for robotic assembly does not address the fundamental problem

of knowing what the robot is doing at a particular moment in time. In practice,

a typical assembly operation often consists of a sequence of multi-step motions [22].

Due to the discontinuous nature of an assembly process that is dictated by the ge-

ometry of the robot, the work piece and the fixtures, such a motion sequence

computation is often so complex for a single control strategy to efficiently accom-

plish. Furthermore, effective control strategies are highly nonlinear and dependenton the �states� of the assembly process. Direct feedback control strategies are limited

unless the control rules are modified in accordance with the change of assembly

states in an assembly operation [1,7]. Thus, the fundamental problem in robotic

assembly is the ability to recognize assembly states, and this very problem must be

addressed prior to the deployment of appropriate control strategies.

The primary objective of this paper is to develop a framework to recognize the

nature and classify the assembly contact states based on the force/torque information

resulted from contact formation between a work piece and its environment. Al-though it may seems more direct to obtain information of contact formations with

computer vision, under cost consideration, complexity of vision algorithms, and

most importantly, the practicality in assembly operations where the relative motion

is very small, it is more favourable to using force/torque measurement in contact

recognition.

1.2. Assembly state recognition

As the focus of the research is to address the problem of recognizing assembly

contact states, an HMM-based contact state recognizer (HMM-CSR) is designed

H.Y.K. Lau / Mechatronics 13 (2003) 1001–1023 1003

and developed using a modified industrial robot to demonstrate the feasibility and

operation of contact state recognition. The system can be viewed is a high-level

feedback control system that aims at perceiving the environment in terms of sym-bolic expressions, in this case, the force/torque patterns that are captured. In the

classification of contact states, the concept of fundamental contact (FC) is intro-

duced that provides a basis for describing generic contact formations that may

consist of zero, one or more contact pairs between the work piece and the interacting

environment. In simpler terms, the concept of FC can be regarded as a primitive

form of contact formation, where a FC only involves a single pair of contact fea-

tures. An HMM-modeled FC is interpreted and analyzed with the attachment of

symbolic meaning such as spatial relationship and geometrical information of con-tacting objects. It is seen that this approach to geometrical analysis can provide high-

level knowledge for robot motion planning systems to execute appropriate motion to

achieve fully intelligent and unsupervised robotic assembly.

The paper starts by introducing the concept and definition of assembly contact

states, which is followed by their HMM-based modeling. The design of the contact

state recognizer is discussed and an implementation of such system is described. The

paper concludes with the presentation of the results from experimental studies with

the implemented system for the classification and identification of representativecontact formations that are found in robotic assembly.

2. Assembly contact states

2.1. The notion of assembly contacts

Contacts are common scenarios in the robotic assembly. A contact is discrete in

nature and can be defined and interpreted as a physical contact formation that is

resulted from the geometric arrangement of the work piece and its interacting en-

vironment, which may consists of zero, one or more contact pairs [12]. The philo-

sophy of contact-based control strategy for robotic assembly is based on the fact each

contact formation between a work piece that is held by a robot end-effector and itsenvironment produces a pattern of force/torque. Such force/torque information can

be captured accurately and clustered to represent a corresponding contact state that

characterizes a unique spatial configuration of the interaction made between the

work piece and the environment. Furthermore, as long as contact occurs, the degree

of freedom posed to the manipulated object is reduced by at least one. Thus, it is

resourceful to use the interpreted or resolved geometric information to guide the

process of assembly. Therefore, the successful representation of contact space and

the analysis of contact state is a directed approach to achieve successful roboticassembly.

In an automated assembly framework as shown in Fig. 1, recognition of contact

states is essential in planning and executing contact-based assembly motions [23].

The objective of providing an intelligent assembly robot with a contact recognizer

is to equip it with the capability of perception of the environment. The contact

Symbolic-Level

Control-Level

Low-levelControl Actuators

Sensors andSignal

Processing

ControlStrategy Library

Contact MotionPlanning

ContactState

Recognition

Task Planner

Assembly and TaskModel

Encode

World Model

Trigger

IndustrialManipulator

Fig. 1. The context of contact state recognition in an automated assembly system.


recognizer provides the robot with the necessary symbolic information where the

robot is operating. It follows that the achievement of contact recognition also fa-

cilitates automated robot programming. The programming approach is a form of

task-level programming paradigm that required accurately identified contact for-mations in conjunction with contact motion planning to guide the motion of an

assembly robot.

2.2. Definitions of contact states

This section introduces the definitions and notations adopted in this paper for

specifying contact states. Two types of objects are considered, namely, the convex

three-dimensional polyhedra and concave three-dimensional polyhedra. In the typ-

ical case of the peg-in-hole assembly, the convex polyhedron is the peg and the

concave polyhedron is the fixture. In general, the peg is referred as the movableobject whereas the fixture is referred as the stationary object.

Definition 1 (Configuration of an object). Configuration of an object, denoted as c, isdefined as a set of kinematics parameters that commands the robot to locate an


object for a given set of joint angles, fhig. The corresponding representation in

Cartesian space is given by c ¼ ðx; y; z; yaw; pitch; rollÞT . As a result, configuration

can be regarded as the lowest level of the assembly, which is formed in accordancewith the specific kinematics constraints. Therefore, c can be expressed as

fhig; or

ðx; y; z; yaw; pitch; rollÞT�

Definition 2 (Configuration space). Configuration space, denoted by C, is defined as

an Rn space that collects all the configuration of an object, C.

Definition 3 (Contact feature). A contact feature is defined as a surface element of a

polyhedron. A contact feature contacting with the environment or another poly-

hedron is denoted by F,ff ; e; vg where f is the face of the object, e is the edge of theobject and v is the vertex of the object.

Definition 4 (Fundamental contact). A FC is specified by an ordered pair of contact

feature, F . Accordingly, a FC is described and formulated as a contact pair } ¼ðF i

A; FjBÞ 2 FAFB where F i

A and F jB are the contacting features i and j selected from

object A and object B, respectively.

Definition 5 (Contact state). A contact state (CS) between two polyhedra is a set ofFCs. The contact state may consists of several FCs depending on the geometry of the

two polyhedra. A multiple contact state, CSn is denoted by

CSn ¼ f. . . ; ðF iA; F

jBÞ; . . .g 2 }� }� � � � � }|fflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflffl}

n

where n is the number of contact pairs.

3. Contact recognition with symbolic feedback

3.1. Contact recognition in robotic assembly

In general terms, contact recognition in robotic assembly is defined as a process of

using contact sensing technique to obtain geometrical information of contact with

corresponding symbolic interpretations during an assembly process. As abovemen-

tioned, the primary objective introducing a contact state recognizer to an assembly

robot is to give it the capability of perception of the environment such that appro-

priate control actions can be exerted to successfully an assembly task.Results from forgoing studies suggested that the benefits of deploying a contact-

based assembly system are numerous. Firstly, symbolic interpretations of assembly

states provide invaluable high-level knowledge of assembly operations to robot

programmers. Secondly, the approach reduces the precision requirement of sensors

as captured signals are mapped to symbolic information, rather than directly using


the acquired sensory information. The uncertain and error-prone sensory data are

empirically validated through the incorporation of a template training process, by

which a smaller number of training data is used to train the recognition system.

Performing contact recognition by means of active sensing has widely beenstudied. Numerous researches such as analytical analysis by polyhedral convex

theory [7], static modelling by Petri net [11], rule-based contact analysis [18], fuzzy

logic- and neural network-based approaches [13,19] have been adopted in designing

high-performance recognition systems with different degrees of success. However,

due to intensive computation, extensive training regimes, and difficulties in con-

structing analytical models, some limitations are encountered.

An alternative approach of using HMM to model contact formations in assembly

operations is considered in this paper. Researches in pattern recognition [6], speechrecognition [14], character recognition [17] and data verification, DNA and protein

modeling [2] has established the power of HMM in modeling physical phenomena.

In particular, HMM was used as a speech recognizer to model and recognize input

voice arising from human speech [15]. With the view that assembly states within a

typical assembly sequence are inter-related and that the occurrence of contact for-

mation between a work piece and the mating parts are normally distributed, this

paper adopts the hidden Markov model (HMM) [9] to model contact formations

that characterized assembly states in robotic assembly. As such, the adaptation of aHMM-based contact recognition system in the reported research provides cognitive

knowledge for assembly operations by way of symbolic interpretations and geo-

metrical relationships.

3.2. Hidden Markov modeling

HMM is a probabilistic model, which consists of a doubly stochastic process [4].

From a topological viewpoint, HMM can be treated as a class of graphical models

[2] where an HMM is structured as a network consisting of nodes and links (Fig. 2).Each node in the network is connected by a link and each link is weighted by a

qt 2

qt

qt 1

qt 1

qt 2

ot 2 ot 2ot 1otot 1− − − −

−−−−

Fig. 2. A graphical interpretation of a HMM.


probabilistic value. A HMM consists of two stochastic processes, with an under-

lying process being a Markov chain and an observable process being another sto-

chastic process characterized by a probabilistic distribution, either discrete orcontinuous.

As depicted by Fig. 2, qi and oi are the underlying states and observable symbols

in an HMM, respectively. As the basic infrastructure of an HMM is a Markov chain,

a state of the underlying process is also a Markov chain that has a strong Markov

property. In general, an HMM is defined as a triplet k ¼ ðA;B; pÞ, where A is a

transition matrix consists of transition probabilities aij ¼ Prðqtþ1 ¼ sjjqt ¼ siÞ, Bcontains the probabilities of the observable symbols bij ¼ Prðot ¼ vkjqt ¼ siÞ, and p is

the initial state distribution. Other important parameters of an HMM include thenumber of Markov states, N , the number of observable symbols,M , and the states of

the model si 2 S.From the nature of an HMM, it can be used as a generative model to generate an

observation sequence O ¼ foig where 16 i6 T and T is the number of observations

in the sequence given appropriate values of N , M , A, B and p. In the context of

assembly state modeling, given a sequence of force/torque data as the observable

symbols, the underlying assembly state can be evaluated accordingly provided that

suitable HMM parameters are defined. Specifically, in adopting the hidden Markovmodeling technique to real-world applications such as assembly state modeling, the

problems of (1) evaluating the probability of observation sequence O ¼ o1; o2; . . . ; oTfor a given model k, (2) evaluating the most probable state sequence Q ¼ q1; q2; . . . ;qT given the observation sequence, O ¼ o1; o2; . . . ; oT , and the model k, and (3)

adjusting the model parameters N , M , A, B and p in order to maximize the prob-

ability PrðQjO; kÞ such that the performance of the HMM in contact recognition is

optimized must be considered.

The solutions to the three problems that are deployed in the implementation ofthe contact state recognition system in this research is given in Appendix A.

4. An HMM-based contact recognition system

4.1. System design

The design of the HMM-based contact state recognition system is built upon a set

of HMMs that are suitably trained with force/torque information of assembly

contact states. Each well-trained HMM represents a corresponding contact type,

that constitutes the knowledge of geometrical information of assembly operations, in

terms of a set of FC states. The contact state recognition system consists of a signalpreprocessing module, a symbol mapping process, and the set of HMMs repre-

senting the FCs. The architecture of the contact state recognition system is given by

Fig. 3.

The following procedures are undertaken to develop a suitable system for robotic

assembly state recognition.

Fig. 3. The architecture of the HMM-based contact state recognition system.


• Defining the task unit: Firstly, it is necessary to define what are to be represented

by the HMMs in the system concern. From the experience obtained from speech

recognition, it is known that an HMM can be used to represent an acoustic unit.

Hannaford and Lee [5] used an HMM to represent an assembly operation. Each

state in a Markov chain represents a subassembly task. Hovland and McCarra-

gher [21] used an HMM to represent a change of contact states in robotic assem-

bly. The contact state recognition system reported in this paper uses HMMs to

represent unique FC states.• Defining the observation symbols: An HMM is an information-rich statistical

model. One-dimensional HMMs are generally deployed for scalar observation

symbols whereas multi-dimensional HMMs are used for multi-dimensional input

vectors. The system uses multi-dimensional HMMs as the force/torque data ob-

tained are vector quantities.

• Training the models: An HMM-based recognition system requires a training pro-

cess. In the context of assembly, special jigs and fixtures are required to generate

the appropriate force/torque information for the training of the HMMs. Repre-sentative templates for each contact event are trained and Baum-Welch re-estima-

tion algorithm is applied to estimate the HMM parameters iteratively.

• Tuning for the best performance: This is to find the best HMMs that matches the

input signal pattern. The Forward/Backward algorithm is adopted to compute the

values of PrðOjkÞ The maximum value of argmaxi PrðOjkiÞ provides the best

description of the assembly task.


4.2. Practical implementation

The implementation of the practical contact state recognition system incorporatesa preprocessing process that enhances and filters the noise prone force/torque sen-

sory data. It also reduces the computation required in traditional HMMmodeling by

vector quantizing the analogue force/torque information. Fig. 4 shows the principal

components of the preprocessing module of the contact state recognition system.

In Fig. 4, each block represents a distinct signal processing function where by the

input signal is transformed to appropriate forms for HMM modeling. The force/

torque capture module acquires the force signal resulted from contact formation

during an assembly operation. The continuous signal are sampled and then fed intothe discrete Fourier Transform module where the time domain signal is transformed

into a frequency domain data. The transformed data is then input to the vector

quantization module. As discrete HMMs are used, the vector quantization (VQ)

process that deploys the LGB-VQ algorithm (Appendix B) is aimed at reducing the

sampled data to produce a sequence of observable symbols. This symbol sequence

is then modeled with HMM for parameter estimation.

After obtaining a sequence of quantized observable symbols, the HMM-based

contact state recognizer then computes the probability of the sequence for the

Capture Force/Torque data

Discrete FourierTransform

(DFT)

LBG-basedVector

Quantization

Signal Labeling

SymbolSequenceGeneration

Training Pathfor Codebook

Design

Nominal Pathfor HMMModeling

Codebook

To Contact StateRecognizer

Fig. 4. Preprocessing of the force/torque sensory data.

Parameter Optimization

SensoryInformation

Pattern

SignalPreprocessor

Define TaskUnit

DefineDistribution ofObservation

Train Models

Evaluation

Training?

A Collection ofHMMs

Yes

No

Contact State

End

Training?

Yes (Training completed)

No (Recognition)

Selection of Discrete andContinuous

Selection of Markov StateRepresention

Evaluation?

Yes

No

DefineDistribution ofObservation

Train Models

Subtask-basedHMM

Estimation ofState Sequence

The EndRecgonzied

Hidden StatesSequenceRecovered

Fig. 5. The operation of the HMM-based contact recognition system.



well-trained HMMs. That is, the computation of PrðOjkiÞ, where O is an observ-

able sequence, ki is the ith HMM. Then the contact state is mapped (Appendix B)

by selecting the corresponding index i according to the condition argmaxi PrðOjkiÞ.The recognized assembly contact state is then obtained and can be used by the

robot controller to derive appropriate control actions to complete the assembly

task. The operation of the entire contact state recognition system is summarized in

Fig. 5.

4.3. Prototyped contact state recognition system

An experimental platform is configured for the implementation of the contact

state recognition system and to perform experimental study. The system consists of

an industrial manipulator (Staubli RX130) that is being enhanced to incorporate a

Pentium II processor. The architecture provides a distributed platform whereby the

computation of the HMM-based contact recognition algorithms (Appendixes A and

B) are undertaken by the Pentium computer running a real-time operating system

QNX, and the low-level joint control is undertaken by the Adept robot controllerrunning the V+ operating system. Figs. 6 and 7 illustrate the hardware and software

configuration of the system.

Xycom PentiumComputer

VGA

DPR

CPU

ForceSensor

Adept MVController

Staubli RX130Industrial Robot

Fig. 6. Hardware platform of the experimental system.

Motor Control

Motion Control

Trajectory Control

Dua

l Por

ted

Ram

Inte

rfac

e (A

PI)

QNX O/S Kernel

Adept Robot Controller Xycom Pentium Computer

V+ O/S

Motion Library Control Strategy Generator

HMM-basedContact State

Recognition System

QNX O/S

Fig. 7. Software configuration of the experimental system.


5. Experimental studies

The experimental studies of the prototyped contact state recognition system aim

at investigating the following aspects:

1. The sensitivity of parameter selection for an HMM-based contact recognition sys-

tem.2. The performance of recognizing 2-D and 3-D contact formations.

3. The ability of classify a sequence of contact formation in a typical assembly ope-

ration.

Through these experimental studies, the feasibility of the HMM-based approach

is demonstrated and the performance of the prototyped system is evaluated. In the

experimental studies, the following conventions for labeling and naming contacts are

adopted. Fig. 8 shows the labeling conventions and Figs. 9 and 10 shows two majortypes of fundamental contact. In particular, a FC refers to a pair of contact features

from different objects making contact with each other. The contact pair describes

the contact condition for a fundamental contact. Fig. 10 shows an example of a

vertexab � facea FC in which the contact features are vertex and face. Therefore, the

vertexab � facea FC is defined as a pair of vertex and face, and is expressed in the

form of FC ¼ fvertexab; faceag.In the experimental studies, specific training data sets are collected to study

the performance of the contact state recognition system and the sensitivity of theparameters of the HMMs. For example, the �Batch 10� training data consists of 10

sequences of data captured for training each type of FC. Table 1 summarizes the

different sets of training data introduced. In order to be representative, in the case of

training edge-face and vertex-face FCs, a range of contacting angles between 5� and40� are used.

surface_front

surface_rightsurface_left

surface_rear

surface_bottom

edge_a

edge_b

edge_c

edge_d

SURFACE_LEFTSURFACE_RIGHT

SURFACE_BOTTOM

SURFACE_VLEFT SURFACE_VRIGHT

EDGE_LEFT

EDGE_RIGHT

TX

TY

TZ

WX

WYWZ

vertex_ab

vertex_bcvertex_cd

vertex_da

Fig. 8. Labeling convention for contact formations.

Fig. 9. A face–face contact.


A means to measure the performance of contact recognition is introduced, and is

known as the recognition accuracy. Its definition is given by the following expres-

sion:

Fig. 10. A vertex-face contact.

Table 1

The training data sets

Name No contact Face–face Edge-face Vertex-face

Batch 10 10 10 10 10

Batch 20 20 20 20 20

Batch 30 20 20 30 30

Batch 100 20 20 30 100


Recognition accuracy ¼ Total number of correctly identified contacts

Total number of classified contact formations

� 100%

5.1. Sensitivity analysis

Prior to the full evaluation of the performance of the HMM-based contact rec-

ognition system, it is vital to access the significance of the parameters of which the

HMMs are constructed. The following parameters are considered and studied via

experimentation:

I. Number of Markov states: To study the effect of using the different number of

Markov states in the HMMs so as to obtain the best performing system, the rec-ognition system with a VQ size of 64 using the Batch 10 training data, and

HMMs with different number of states are constructed to perform contact state

recognition on different FCs. The recognition accuracy obtained (Fig. 11) indi-

cates that the system is insensitive to the number of states used. The findings

agree with those obtained from speech recognition [14].

Fig. 12. Recognition accuracy versus VQ sizes.

Fig. 11. Recognition accuracy versus number of HMM states.


II. Quantization size: As VQ is one of the essential processes deployed in the rec-

ognition system based on discrete HMM, different quantization sizes for differ-

ent HMMs are studied using the Batch 10 training data to identify edge-type

FCs. The results (Fig. 12) shows that the recognition accuracy for different

Table 2

Recognition accuracy for different training data sets

VQ size ¼ 64 VQ size ¼ 128 VQ size ¼ 256 VQ size ¼ 512

Batch 10 75.00% 83.33% 75.00% 73.33%

Batch 20 81.67% 80.00% 73.33% 71.67%

Batch 30 76.67% 75.00% 80.00% 83.33%


quantization size is quite close (between 72% and 83%), with a local maximum

attained for VQ size of 128.

III. Training data size: In theory, a larger training data set will enhance the perfor-

mance of the recognition system. The study varies the size of the training data

set (using Batch 10, 20 and 30) with HMMs using different VQ sizes to recognize

edge-type FCs. The results shown in Table 2 indicate that by increasing training

data alone does not guarantee an improvement in recognition accuracy. It is

concluded that the size of training data set should be proportional to the VQsize as the VQ size is one of the key parameters that determines the modeling

condition of a HMM-based system. In general, a large training data together

with a large VQ size should attain a better performing system (Table 2).

IV. Distribution probabilities: The initial setting of the transition matrix of an HMM

affects the performance of the recognition system. In this experiment, five-state

HMMs are used with a VQ size of 64 with evenly-distributed (ED) and left-to-

right (LR) HMMs. The results show that the difference in recognition accuracy

between the ED and LR-HMMs are very small.

According to the findings, an optimal HMM configuration is defined for the

recognition system. A five-state HMM with a quantization (VQ) size of 64 will be

used in the subsequent experimental studies.

5.2. Contact recognition

Using the HMM-based system with the optimal settings, the system is put to

identify different classes of FCs that are made up from pairs of contact features. Inthis study, different combinations of contact features that are typical in robotic as-

sembly operations in both 2-D and 3-D are investigated. Primarily, three types of

contact pairings, namely, (1) a face of a peg making contact with a surface (face–face

contact), (2) an edge of a peg making contact with a surface (edge-face contact), and

(3) a vertex of a peg making contact with a surface (vertex-face contact) are con-

sidered. Five-state HMMs with different VQ sizes and both initialization structures

for the HMM-based system, i.e., ED and LR-HMM are used.

Table 3 summarizes the normalized recognition accuracy for the contact paringsspecified above. It is evident that both ED and LR-HMM initialized systems per-

form very similarly and the recognition accuracy for identifying different contact

pairs are relatively high (above 80%). The results demonstrate the capability of an

HMM-based system in separating FCs that are originally combined with different

Table 3

Contact pair recognition and classification

VQ size ¼ 64 VQ size ¼ 128 VQ size ¼ 256 VQ size ¼ 512

ED-HMM initialized system

Batch 10 92.5% 90% 82.5% 90%

Batch 30 95% 92.5% 82.5% 90%

Batch 100 95% 90% 85% 90%

LR-HMM initialized system

Batch 10 95% 90% 82.5% 90%

Batch 30 95% 92.5% 82.5% 90%

Batch 100 95% 90% 85% 90%


contact features. It is also observed that an increase in training data (from Batch 10

to Batch 100) only improves the performance of the overall system marginally (from

92% to 95%). This indicates the efficiency of an HMM-based system that requires

relatively small amount of training data to operate.

5.3. Sequence classification

In this section, the contact state recognition system is put to identify a sequence of

contact formations that resemble a real assembly operation. Three sequences are

used, namely, face–face transition (Fig. 13), edge-face transition (Fig. 14) and vertex-face transition (Fig. 15). The results (Table 4) show that the recognition system

manages to identify changes in contact formation and classify the type of contact

formation. In general, a drop in recognition accuracy when compared with previous

Fig. 13. Sequence A: the face–face transition contact sequence.

Fig. 14. Sequence B: the edge-face transition contact sequence.

Fig. 15. Sequence C: the vertex-face transition contact sequence.

Table 4

Contact state recognition for motion sequences A, B and C

No contact Face–face Edge-face Vertex-face

Sequence A 80% 100%

Sequence B 100% 50%

Sequence C 100% 40%


studies may be due to the decrease in the quality of force/torque signals captured

when the robot is in motion and the occurrence of sliding motions between the peg

and the surface in contact. However, when compared with results obtained fromspeech recognition where the recognition accuracy for discrete HMM is in the region

of 35%, the results obtained for assembly state recognition is comparable and con-

sistent. Despite the simple nature of the sequences used in this experimental study,

the results demonstrate the ability of the HMM-based system in extracting contact

state information in a dynamic situation.

6. Conclusions

This paper focuses on the developments of an assembly contact state recognition

system based on the stochastic framework of HMM. A force-based approach has

been adopted to infer assembly contact states, which is in contrast to more tradi-tional kinematics-based or CAD-based approaches. It has been shown by experi-

ments that such an approach allows for dynamic force and moment measurements,

and there are no restrictions to system accelerations, which is in contrast to the

limitations of quasi-static motions.

In this paper, discrete hidden Markov modeling techniques have been deployed

where FCs are represented by mapping force and torque signals. Each FC has been

modeled by a discrete HMM that consists of a set of parameters that characterize the

physical properties and contact conditions of interacting objects. Based on thetheoretical framework of HMM, the design and implementation of a practical

HMM-based contact state recognition system has been presented. In addition, an

experimental system that consists of a modified industrial robot has been developed

to study the performance of the proposed contact recognition system. The results


have clearly indicated the superiority of the HMM-based system in recognizing

typical contact formations, and in identifying the potential of deploying the state

information for the future construction of an intelligent assembly robotic system.

Acknowledgement

The research is partially funded by the Hong Kong Research Grant Council

under the Grant HKU 7075/98E.

Appendix A

A.1. Solutions to evaluation

The practical computation of the probability of an observation sequence O ¼o1; o2; . . . ; oT given an HMM model k is to evaluate the following:

PrðQjkÞ ¼X

q1q2...qT

pq1bq1ðo1Þaq1q2bq2ðo2Þ . . . aqT�1qT bqT ðoT Þ

using the forward or backward algorithms [3].

Algorithm A.1: forward algorithm

1. Initialization:

atðiÞ ¼ pibiðo1Þ; 16 i6N

2. Induction:

atþ1ðjÞ ¼XNi¼1

atðjÞaij

" #bjðotþ1Þ; 6 t6 T � 1; 16 j6N

3. Termination:

The sum of all N final forward variables, i.e. aT ðiÞ, 16 i6N

PrðOjkÞ ¼XNi¼1

aT ðiÞ

Algorithm A.2: backward algorithm

1. Initialization:

btðiÞ ¼ 1; 16 i6N

2. Induction:

btðiÞ ¼XNj¼1

aijbjðotþ1Þbtþ1ðjÞ; t ¼ T � 1; T � 2; . . . ; 1; 16 i6N

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H.Y.K. Lau / Mechatronics 13 (2003) 1001–1023
A.2. Solutions to sequence optimization

The find the best sate sequence Q ¼ fq1; q2; . . . ; qTg, for the given observation

sequence O ¼ fo1; o2; . . . ; oTg, the following expression is evaluated:

dtðiÞ ¼ maxq1q2...qT�1

Prðq1q2 . . . qT ¼ i; o1o2 . . . otjkÞ

where dtðiÞ is the highest probability of a state sequence along a fixed observation

sequence at time t that accounts for the first t observations and ends in state si.Viterbi algorithm [20] is implemented to find the best state sequence.

Algorithm A.3: Viterbi algorithm

1. Initialization:

dtðiÞ ¼ pibiðo1Þ; 16 i6N

w1ð1Þ ¼ 0

2. Recursion:

dtðjÞ ¼ max16 i6N

dt�1ðiÞaij �

bjðo1Þ; 26 t6 T ; 16 j6N

wtðjÞ ¼ argmax16 i6N

dt�1ðiÞaij �

; 26 t6 T ; 16 j6N

3. Termination:

P � ¼ max16 i6N

dT ðiÞ½ �q�T ¼ argmax16 i6N

dT ðiÞ½ �

4. Path (state sequence) backtracking

q�T ¼ wtþ1ðq�tþ1Þ; t ¼ T � 1; T � 2; . . . ; 1

A.3. Solutions to parameter optimization

For finding an optimal set of parameters for an HMM, the Baum-Welch re-

estimation algorithm is used. The following re-estimation formulae are given forfinding the values of p, A and B.

pi ¼ expected frequency in state si at time t ¼ 1 ðor c1ðiÞÞ

¼XNj¼1

a1ðiÞaijbjðo2Þb2ðjÞPNi¼1

PNj¼1 a2ðiÞaijbjðo2Þb2ðjÞ

aij ¼expected number of transitions from state si to sjexpected total number of transitions from state si

¼PT�1

t¼1 atðiÞaijbjðotþ1Þbtþ1ðjÞPT�1

t¼1 atðiÞbtðjÞ

wh

bo


bjðkÞ ¼expected number of times in state j and observing symbol vk

expected number of times in state j

¼PT�1

t¼1 atðiÞbtðjÞdðot; vkÞPT�1

t¼1 atðiÞbtðjÞwhere dðot; vkÞ ¼

1 if ot ¼ vk0 otherwise

�
According to the following stochastic constraints: XN
i¼1

pi ¼ 1 andXNi¼1

pi ¼ 1 andXNi¼1

pi ¼ 1 for 16 i6N

Appendix B

Algorithm B.1: ALBG-VQ algorithm [25]

1. Initialization:

Assume all N k-dimensional training vectors to be one cluster C0, with a codebook

size of M ¼ 1 and codeword o0 ¼ 0. Evaluate its k-dimensional cluster centroidc0ð1Þ where iteration 1 is first to be initialized:

c0ð1Þ ¼ 1

N

XNn¼1

x0n

where x ¼ fxng is one sample of all N k-dimensional feature vectors at cluster C0.

2. Splitting:

To double the size of the codebook,M , by splitting each cluster into two. Thus, thecurrent codebook size M is split into 2M . Set M ¼ 2M by

ciþð1Þ ¼ cið1Þ þ eci�ð1Þ ¼ cið1Þ � e

�where 06 i6M � 1

i i
ere c is the centroid of the ith cluster of C , M is the size of the current code-
ok, e is a k-dimensional splitting parameter vector.

3. Classification:

At the lth iteration, according to the nearest neighborhood rule, each k-dimensional sample x of training feature vectors is classified into one of he cluster

Ci.

x 2 CiðlÞifkx� ciðlÞk < kx� cjðlÞk where i 6¼ j; i; j ¼ 0; 1; . . . ;M � 1

4. Codebook updating:

The codeword (symbol) oi of each cluster Ci is updated by computing new cluster

centers ciðlþ 1Þ where j ¼ 0; 1; . . . ;M � 1 at the ðlþ 1Þth iteration.

ciðlþ 1Þ ¼ 1

N

XNn¼1

xin where xi 2 Ciðlþ 1Þ


and N is the number of feature vectors in cluster ciðlþ 1Þ at the ðlþ 1Þth itera-

tion, and, where 06 oi 6M � 1 and qð�Þ is the quantization operator.

5. Termination 1:

If the difference between the current overall distortion Dðlþ 1Þ and that of theprevious iteration DðlÞ is below a selected threshold, proceed to step 6, otherwise

returns to step 3, i.e.:

if jDðlþ 1Þ � DðlÞj < threshold; then goto Step 6

if jDðlþ 1Þ � DðlÞjP threshold; then goto Step 3

�6. Termination 2:

Is the codebook size M , is equal to the required VQ codebook size?

if yes; then STOP

if no; then goto Step 2

�

Algorithm B.2: symbol mapping algorithm

1. Choose the input signal x and calculate the centroid of the codeword accordingly:

kx� cik ¼Xk

h¼1

ðxh � cihÞ2

for i ¼ 0; 1; . . . ;M

2. Compute input signal x against each centroid.

3. Select the minimum values of the distance function.

4. Set codeword representing the signal x according to Step 3.

5. Obtain qðxÞ ¼ oi for 06 oi 6M � 1.

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