2008 8th IEEE-RAS International Conference on Humanoid Robots
December 1 ~ 3, 2008 / Daejeon, Korea

Obstacle Avoidance Control of Humanoid Robot
Arm through Tactile Interaction
Dzmitry Tsetserukou, Naoki Kawakami, Susumu Tachi
University of Tokyo, Japan, dima_teterukov@ipc.i.u-tokyo.ac.jp, {kawakami, tachi}@star.t.u-tokyo.ac.jp

system with application in mobile robotics, taking advantage
of high performance/cost ratio of the components and low
computational demands of the detection method.
Due to the specular nature of ultrasonic waves reflection,
the only objects normally located to the sensor acoustic axis
can be accurately detected. When it comes to infrared sensor,
one of the most important problems is limited measuringperformance. The amplitude from the infrared sensor largely
depends on reflectivity of the object, and it changes with thetarget distance in non-linear manner. There is high possibility
that proximity sensors fail to detect obstacle along the robot
trajectory. In this case an immediate vicinity of the target canmislead robot control system invoking the abrupt change inthe speed resulting in harm of the environment.
I. INTRODUCTION
We argue that robot should be mainly controlled not to
Obstacle avoidance and motion planning are both necessary avoid the collision but rather to ensure tactile interaction withcomponents for any robotic task. Obstacle avoidance refers to environment. The benefits of such interaction are obvious inplanning collision-free trajectories for robotic systems while nature. From the early childhood, humans touch objects tomotion planning refers to planning smooth motions.
investigate the world and acquire a plenty of fundamental
Many efforts have been devoted to path planning in information about objects (shape, stiffness, texture, location,
cluttered environment, but in most of approaches the exact fixation, etc.). Conventional approaches to handle theworld model is assumed and no sensors are utilized [1], [2]. interaction between a manipulator and environment are based
When we consider the real indoor environments, known on impedance control of a robot arm according to applied
obstacles (e.g. chairs, tables, etc.) and unknown obstacles force vector measured at the manipulator wrist [6]. However,(persons approaching the robot, unmapped environment, etc.) the rest parts of the robot body (forearm, elbow, upper arm,change their location dynamically. Moreover, the object shape, shoulder, and torso) are presenting significant danger not only
speed and position can also alter in unpredictable way. Robot to human being, but also to the robot structure itself. A fairly
control system operating in unstructured dynamic small work has been done on tactile interaction of the wholeenvironment must execute skilful manoeuvre that avoids a robot arm with environment.
collision and directs the robot to its goal position. In order toBauer [7] conducted very practical and useful research on
provide the robot with detailed real-time environment view it exploration of the environment and accomplishment of
is imperative to use sensor data.
pushing task by autonomous mobile robot. The idea
The most effective solution of preventing collision is to underlying the algorithm is to identify free space, the object
endow the whole robot arm with the ability to safely interact location, and object shape by several attempts made by theand contact with environment in real time. Lumelsky [3] robot arm in order to pass obstacle through. It should be noted,
pioneered in the idea to cover manipulator with a sensitive however, that the proposed system cannot detect the contact
skin capable of detecting nearby objects. An array of infrared point coordinates, requires time-consuming obstacle
proximity sensors delivers the information about obstacles identification process, and, as authors reported, theobstructing arm motion to the control system. The algorithm exploration algorithm fails when several collisions occurof motion planner manoeuvres the robot arm avoiding impact simultaneously.
[4]. Recently proposed sophisticated imaging systems, such as
To cope with spatial uncertainty of unknown, unstructured
stereovision and laser scanning, presume usage of expensive environment we elaborated novel technique of obstacle
detectors and complex signal processing techniques. They avoidance through interaction. When the robot arm issense only narrow space around the robot body. The concept obstructed by obstacle the controller directs the manipulator toof sensor array composed of ultrasonic rangefinders and the target point in such a way that robot arm surface follows
infrared detectors is described in [5]. Researchers are pursuing the contour of the object.
the goal of the development of a robust proximity sensor

Abstract— In this paper we introduce a novel concept of obstacle
avoidance through tactile interaction. The implementation of theapproach was realized on humanoid robot arm with opticaltorque sensors distributed to each robot joint. Whenmanipulator collides with an object, the control system enables tofollow the object outline smoothly till robot reaches the target
point. Such approach ensures not only safe obstacle avoidance
but also acquisition of indispensable information about
environment. The methods of object stiffness calculation, contact
point estimation, and shape interpolation are detailed in thepaper. The possible tasks of the robot with intelligent whole-arm
obstacle avoidance control are summarized and illustrated in thiswork as well. The controllable compliance of robot arm joint canbe extremely useful in a wide range of applications.

978-1-4244-2822-9/08/$25.00 ©2008 IEEE

II. ROBOT ARM AND SENSORY SYSTEM
The developed robot arm (Fig. 1(a)) has 4-DOF: Roll, Pitch,
Yaw joints of a shoulder, and Pitch joint of an elbow. Suchorthogonal disposition of the axes simplifies the installation of
the torque sensors and motor drives into the joints, allowing
thus avoidance of application of additional belt driven
actuators. Coordinate systems based on Denavit-Hartenberg
convention are represented in Fig. 2. The 8-DOF robot handallows performing dexterous manipulations.
Yaw

Z1

Torquesensors

J2

Y1

Y2

Z0

Y0
+
X0 +
Pitch
Roll
J1

X1

X2

Z2

+

L1
J3

Z4

Y4

Y3

X4

J4

X3
Z3

Z5

a)

b)

L2

A. Contact State Recognition
During the first stage of control the robot links rotate until
one of them contacts the object. Below, the elaborated
algorithm of contact detection is demonstrated.
In addition to contact force, torque sensors continuously
measure the gravity and inertial load. As robot arm moves
with low angular speed, the inertial load component can bedisregarded. Let us consider gravity torque calculation in thecase when robot arm performs only planar motion, and only
the first and fourth joints operate (Fig. 3).
τg1

LM 2

X5

Each robot joint is equipped with optical torque sensor
directly connected to the output shaft of harmonic drive. We
kept the arm proportions the same as in average height
Japanese male, aged 25: upper arm length L1 of 0.308 m;
upper arm circumference of 0.251 m; forearm length L2 of
0.241 m; forearm circumference of 0.189 m.
In order to facilitate the realization of torque measurementin each arm joint, we developed new optical torque sensors
based on results presented in [8]. The novelty of our method isapplication of the ultra-small size photointerrupter (PI) RPI121 as sensitive element to measure relative motion of sensor
components. The dimensions of the PI (3.6 mm × 2.6 mm ×
3.3 mm) and its weight of 0.05 g allow realization of compact
design. The optical torque sensor is set between the driving
shaft of the harmonic transmission and driven shaft of thejoint (Fig. 2). When the load is applied to the robot joint, themagnitude of the output signal from the PI corresponds to theexerted load.
PI

θ2
τ θ1

III. CONTACTING OBJECT PARAMETER IDENTIFICATION WITH
TACTILE SENSING

Y5

Fig. 1 Humanoid robot arm and coordinate system

ShieldNm, ± 10.5 Nm, and ± 4.5 Nm respectively. Each sensor wascalibrated by means of attachment of reference weights to thelever arm. Non-linearity of 2.5 % of Full Scale was calculatedusing maximum deviated value from the best-fit line.
The developed optical torque sensors have highdependability, good accuracy (even in electrically noisy
environment), low price, compact sizes, and light weigh.

SpringHarmonic
drive

Fig. 2 Torque sensor of the elbow joint

The spring members attached to the first, second, andthird/fourth joints were designed to measure torque of ± 12.5

θ1

LM 4
τg4
m1 g

θ4

m2 g

Fig. 3 Robot arm subjected to gravity loading

The Newton-Euler dynamics formulation was adopted to
calculate reference value of the gravity torques. The gravity
torques acting in the first τg1 and fourth joints τg4 are derivedfrom:τ g1 = m2 g ( LM 4 sin(θ1 + θ 4 ) + L2 sin(θ1 ) ) + m1 gLM 2 sin(θ1 )(1)
τ g 4 = m2 gLM 4 sin(θ1 + θ 4 ) ,where m1 and m2 are the point masses of the first and second
link, respectively; LM2 and LM4 are the distances from the firstand second link origins to the centers of mass, respectively.
The experiment with the fourth joint of the robot arm wasconducted in order to measure the gravity torque (Fig. 4(a))
and to estimate the error by comparison with reference model(Fig. 4(b)).
As can be seen from Fig. 4, the pick values of the gravity
torque estimation error arise at the start and stop stages of thejoint rotation. The reason of this is high inertial loading thatprovokes the vibrations during acceleration and decelerationtransient. This disturbance can be evaluated by using
accelerometers and excluded from further consideration.
Observing the measurement error plot, we can assign therelevant threshold that triggers control of constraint motion.

The robot was commanded to follow the trajectory in freespace with constant angular velocity. An object was placed on
this path so that the second link would contact it. The joint
torque was recorded for the fourth joint while contacting with
object. The Fig. 5(a-e) shows experimental results when link
comes into contact with objects having different stiffness
varying from very low rate to very high, namely, piece ofsponge, rubber sponge, rubber, chemical wood, and aluminum,
respectively. The time derivative of torque during impact withaluminum plate is given in Fig. 5(f). It is apparent from theplots presented above that the stiffer object comes into contact
with robot arm the smaller angle the joint rotates.
Heterogeneous nature of sponge material explains highly nonlinear behavior of stiffness curve (Fig. 5(a)).
The elastic deformation of the object and inherent
compliance of the robot joints lead to rotation of robot arm by
angle ∆θi during contact transience (Fig. 6).

Joint torque τ4, Nm

0.300
0.225
0.150
0.075
Measured torque τm4
Reference torque τr4

0.000-0.005

Error of measurement ε, Nm

a)

0

30

60

90

120

Joint angle θ4 , deg

150

180

Maximum error

0.04

Upper margin of average error

0.02
0.00
Lower margin of average error-0.02

Maximum error

-0.04

b)

0

30

60

90

120

Joint angle θ4 , deg

150

180

Fig. 4 Experimental results of gravity measurement

B. Estimation of Contacting Object Stiffness
During contact transition we can acquire information about
collision danger of contacting object through its stiffness
estimation. This can be done by establishing stiff contact
through PD control of robot arm with high P-gain and setting
the high threshold value. For the following experimental
results the threshold was chosen as high as 0.05 Nm.
Joint torque τ4, Nm

0.05

θ4 = 0.4184 deg
τ4 = 0.05 Nm

0.04

θ4 = 0.1336 deg
τ4 = 0.05 Nm

Force arm length PC4 = 0.17 m

Force arm length PC4 = 0.17 m

0.03
0.02

θ4 = 0.1919 deg
τ4 = 0.0202 Nm

0.01
0.00
0.0

a)

0.1

0.2

Joint torque τ4, Nm

0.070

0.01
0.00
0.000

c)

0.014

0.028

0.105

Force arm length PC4 = 0.1755 m

0.042

d)

0.01

0.02

0.03

Joint angle θ4 , deg

0.20
θ4 = 0.0334 deg
τ4 = 0.049 Nm

0.04

0.15

Force arm length PC4 = 0.175 m

hi

A

ϕi

bo Rni
ko

C'

B

1

The distance, on which contact point C on the robot link
surface 1 moves perpendicularly to the radius ri under torque∆τi, is equal to ri∆θi (since the angle ∆θi is small). The
unknown angle ϕi can be found taking into account that
∠C’CB=∠OCA=ϕi:⎛ hi ⎞⎛ OA ⎞
φi = arctan ⎜⎟,⎟ = arctan ⎜⎜⎟P⎝ CA ⎠⎝ Ci ⎠

θ4 = 0.0237 deg
τ4 = 0.0208 Nm

0.056 .00

Joint angle θ4 , deg

0.05

0.14

Joint angle θ4 , deg

θ4 = 0.0344 deg
τ4 = 0.0211 Nm

∆θi

PCi
ri

kri

Fig. 6 The scheme for elastic deformation calculation

θ4 = 0.0457 deg
τ4 = 0.05 Nm

Force arm length PC4 = 0.17 m

0.02

Joint torque τ4, Nm

0.035

θ4 = 0.058 deg
τ4 = 0.049 Nm

0.04

0.03

b)

Joint angle θ4 , deg

0.05

0.03

0.4 .000

τi
O

ϕi

ri

bri

δi

C

1'

θ4 = 0.0716 deg
τ4 = 0.02 Nm

0.3

Fni
Fni

0.04

Pick value(2)

where hi equals half of the robot link thickness.
From the right triangle ∆CBC’ the total elastic deformation
is calculated as:

Time derivative of torque, Nm/s

δi = ∆θi ri cos ( φi ) .

0.10

(3)

0.05

0.02

θ4 = 0.0176 deg
τ4 = 0.0197 Nm

0.01

Radius of contact point trajectory ri is found as

0.00

ri = PC2i + hi2 through consideration of right triangle ∆CAO.

-0.05

0.00
0.000

e)

0.008

0.016

0.024

Joint angle θ4 , deg

0.032 0.0f)

-5

5.0x10-4

1.0x10-4

1.5x10Time t , sec-4

2.0x10Fig. 5 Experimental results of stiffness estimation

Now, we can easily solve for total stiffness:

ki =

=

Fni
∆τi
=
=
δi
PCi ∆θi ri cos ( φi )∆τi(PCi ∆θi P + h cos arctan(hi PCi )
2
Ci

2
i

TABLE IITOTAL STIFFNESS AND OBJECT STIFFNESS

)

.

(4)

By linear approximation, we take into account only twovalues of θi for τi nearest to 0.02 Nm and 0.05 Nm. Then,from the experimental diagrams (Fig. 5(a-e)) we obtain ∆θiand ∆τi and list them in Table 1.
TABLE I
FINDINGS FROM EXPERIMENTAL DIAGRAMS

Parameter

SpongeRubberspongeRubberWood∆θi 10-4 [rad]

39.53

10.82

4.12

3.84

∆τi 10-2[Nm]

2.98

3.0

2.79

2.92

The total elastic deformation δi is made up of elastic
deformation caused by object compliance δo and one
generated by joint flexibility δri. That is, we can write:FRF
δi = ni =δo +δ ri = ni + ni ,kiko kri(5)where Rni is the reaction, absolute value of which equals Fni;
ko and kri are stiffness of the object and stiffness of robot link,respectively.
The coefficient kri is mainly defined by torque sensor
stiffness, harmonic drive stiffness, structural flexibility, and Pgain magnitude. Detailed examination has showed thatcomplex theoretical model of robot link stiffness can hardly
provide accurate estimation of kri. Therefore, we can set thevalue of robot link stiffness close to total stiffness in the mosthard contact case. This assumption is valid because during
impact with hard environment, such as aluminum plate, thecontact deformation of the object is too small to be accountedfor (ko ≈ ∞). Thus, using Eq. (2)-(4) and the data presented inFig. 5(a-e) we derive unknown value of kri:
kri =0.0293 Nm
N=3468.6
0.175 ⋅ 2.758 ⋅10−4 ⋅ 0.1776 ⋅ 0.986 m 2
m

The stiffness of the objects are calculated from thefollowing equation:ko =kri ⋅ ki ,kri − ki(6)

where ki is defined by Eq. (4). Derived values of ki and ko are
given in Table 2.

Parameter

SpongeRubberspongeRubberWoodki [N/m]

260.84959.3

2343.782469.04

ko [N/m]

282.041325.927223.948562.90

The obtained results demonstrate strong correspondence ofcorrelation among calculated object stiffness with that of real
objects. Naturally, the actual stiffness of colliding
environment differs from calculated one with finite error. To
achieve high accuracy, specific equipment is needed.
However, our aim was only assessment of the danger level ofrobot arm collision with object. Specifically, we can definethat sponge and rubber sponge material are safe for interaction,
but rubber, wood, and metal pose threat while striking therobot arm. Consequently, we have succeeded in solving maintask, that is, object classification by getting information about
stiffness during impact.
In case when collision must be detected robustly without
consideration of object properties, the value of time derivativeof torque can be used to judge the impact value (Fig. 5(f)).

C. Shape Recognition and Contact Point Determination
The information about contact point coordinates isnecessary in calculation of the object stiffness, applied force
vector, and for shape reconstruction. The tactile sensor can be
useful in this case. However, our goal is to perform tactileinteraction with environment without complicated sensory
system of the robot. The method, we are presenting here,
results from the assumption that the coordinates ofintersection of the subsequent profiles of the robot arm while
tactile obstacle avoidance equals the coordinates of contact
points. Since the increment of joint angles is small enough, we
can detect contact point with admissible accuracy.
Let us consider the case when forearm is contacting with
object. The line representing the robot forearm is located by
the following position vectors:⎡ Ptx ⎤ ⎡ L2 ( s1s2 s3 s4 + c1c3 s4 + s1c2 c4 ) + L1s1c2 ⎤⎢⎥Pt = ⎢⎢ Pty ⎥⎥ = ⎢− L2 ( c2 s3 s4 − s2 c4 ) + L1s2⎥⎣⎢ Ptz ⎦⎥ ⎢⎣ − L2 ( c1s2 s3 s4 − s1c3 s4 + c1c2c4 ) − L1c1c2 ⎥⎦⎡ Pex ⎤ ⎡ L1s1c2 ⎤
Pe = ⎢⎢ Pey ⎥⎥ = ⎢⎢ L1s2 ⎥⎥⎢⎣ Pez ⎥⎦ ⎢⎣ − L1c1c2 ⎥⎦

(7)

(8)

where s1, s2, s3, s4, c1, c2, c3, and c4 are abbreviations forsin(θ1), sin(θ2), sin(θ3), sin(θ4), cos(θ1), cos(θ2), cos(θ3), andcos(θ4), respectively; L1, L2 are the lengths of the upper arm
and forearm, respectively, Pt, Pe are vectors locating tip of therobot and elbow joint, respectively.
On the next step of iteration θi+∆θi we calculate the newcoordinates of the end points of forearm. The intersection

point of two consequent lines will define the coordinates ofcontact point.
Object shape recognition is usually performed by global
scanning. This method requires the sensor to scan large
segments of an object surface that makes recognition process
slow. We propose tactile object-recognition method based on
the acquisition and formulation of information in the form ofimage primitives. Tactile images are generated when robot
arm registers a series of contact points with an object.
Graphical modelling of the movement of the robot arm
following along round countor is shown in Fig. 7.

manipulator can be expressed as:
J di ∆θi + Ddi ∆θ i + K di ∆θi = τ EXTi ; ∆θi = θ ci − θ di ,(10)

where Jdi, Ddi, Kdi are the desired inertia, damping, andstiffness of i-th joint, respectively; τEXTi is torque applied to ith joint; ∆θi is the difference between the current compliant
angle θci and desired one θdi.
The state-space presentation of Eq. (10) is:⎡ ∆θ i ⎤ ⎡ 0⎢ ⎥=⎢⎣ υ i ⎦ ⎣ − K d J d

1 ⎤ ⎡ θi ⎤ ⎡ 0 ⎤τ (t ) , (11)+− Dd J d ⎥⎦ ⎢⎣ υi ⎥⎦ ⎢⎣1 J d ⎥⎦ EXTi

where υi is the state variable (υi = ∆θ i ) .
The discrete presentation of Eq. (11) with sampling time of
T is needed for program code implementation:⎡ ∆θ k +1 ⎤⎡ ∆θ k ⎤⎢ ∆θ ⎥ =Ad ⎢ ∆θ ⎥ + Bd TEXT ( k ) .
⎣ k +1 ⎦
⎣ k⎦

(12)

For the fastest non-oscillatory response we have:
a)
b)
c)
d)
Fig. 7 Round shape recognition through tactile interaction

The node points obtained by employing the abovementioned algorithm can be interpolated by B-splines [9]:Si ( t ) = ⎡⎣t 2⎡ 1 −2 1 ⎤ ⎡ pi −1 ⎤1⎢⎤
t 1⎦ ⎢ −2 2 0 ⎥⎥ ⎢⎢ pi ⎥⎥ ,2⎢⎣ 1 1 0 ⎥⎦ ⎢⎣ pi +1 ⎥⎦(9)where Si(t) is a quadratic parametric polynomial, pi are thecontrol points, t ∈ [0,1] is the global parameter.
Fig. 7(a) shows arc of the object contour, while Fig. 7(b-d)
represents polylines obtained by linear, arc, and B-splineinterpolation (have precise convergence), respectively. The
algorithm of following the contour of the rectangular-shaped
object is as follows. In presence of vertex the lines intersect in
one point. When coordinates of intersection point change
drastically the edge of the object is recognized.
IV. CONTROL OF TACTILE INTERACTION OF ROBOT ARM WHILEOBSTACLE AVOIDANCE
To achieve skillful human-like behavior, the robot has to beable to change its dynamic characteristics depending on timevarying interaction forces. The most efficient method ofcontrolling the interaction of a manipulator and environmentis impedance control. This approach enables to regulate
response properties of robot to external forces throughmodifying the mechanical impedance parameters [10].
The desired impedance properties of i-th joint ofT⎡ 1 − λ1T⎤,
Ad = eλ1T ⎢
⎥
K
T
/
J
1
λ
T
D
T
/
J
−
−
−
d
d
d⎦
1
⎣ d
λ1T
1 ⎡ 1 − e (1 − λ1T ) ⎤ ,Bd = ( Ad − I ) A−1 B =⎢⎥K d ⎢⎣( Dd /(2 J d ) )2 Teλ1T ⎥⎦

(13)
(14)

where I is the identity matrix.
The control algorithm includes several stages. When the
joint torque value exceeds the threshold, the contact state isrecognized. Then, the stiffness of the robot arm is assigned
according to the calculated object stiffness. Finally, robot arm
follows the trajectory of the object outline by means of local
impedance controller. On each step of iteration the control
system verifies the magnitude of the applied force vector to beequal constant value (Fig. 8).

Fni
L2

L4

Fig. 8 Robot arm following the trajectory along the table surface

As example of control implementation, robot arm moving
along the object surface is shown in Fig. 9.

Initial statet= 0.0 sec
Contact statet= 2.7 sec

t= 5.4 sec

t= 8.1 sec

t= 10.9 sec

t= 13.6 sec

t= 19.0 sec

Fig. 9 Implementation of the obstacle avoidance through tactile interaction

The remarkable opportunity of ensuring safe robotenvironment interaction is that we can establish different
dynamic parameters of robot arm contacting with environment
according to calculated object stiffness. This is inherent
capability of humans, since when we collide with stiff objects
we tend to soften our muscles as much as we can.
We summarize possible cases of application of the robot
enabling intelligent tactile obstacle avoidance as follows:
1) In extremely cramped environment robot arm finds thepath through interaction with obstacles.
2) A robot reaches for visible object located inside narrow
space. The robot arm must contact and follow thesurface of the obstacle represented by sides of the box
to fulfill the task.
3) A robot reaches for object located beyond of the robot
camera visibility range. In such cases robot arm needs
to be equipped with additional cameras in order toprocess collision softly on its own.
4) A robot investigates the indoor area to achieve
situational awareness without necessity of its bulky
body to enter the room. When the situation is assessed,
the robot body can elude the jamb and enter into theroom carefully.
5) A robot structures the environment. A vision system ofrobots cannot determine the distance to the object in
3D space. By tactile interaction, robot can precisely
define the object location and reachable working area.
V. CONCLUSIONS AND FUTURE WORKIn this paper we proposed a novel approach to obstacle
avoidance through whole-arm tactile interaction. The
developed robot arm and control system enable manipulator
encountered with object to adapt the planned motion to the
obstacle shape. Such algorithm is especially valuable for thereal indoor environments, when obstacles change theirlocation dynamically.
We proposed the methods of object stiffness evaluation,
contact point calculation, and object shape reconstruction. To
verify their feasibility and robustness, the experiments andsimulations were performed. Obtained results show that many

essential parameters of the obstacle can be accurately
identified through physical contact. The knowledge of object
stiffness endows robot control with human-like ability tosafely interact with environment. The robot can modify thejoint compliance to avoid high impact forces.
Our future research will be devoted to control of the robot
arm interacting with movable objects. The method of thefriction estimation while pushing the object will also be thesubject of our research.
ACKNOWLEDGMENT
The research is supported in part by a Japan Society for the
Promotion of Science (JSPS) Postdoctoral Fellowship for
Foreign Scholars.
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